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Logistic Substitution Model

Logistic Substitution Model and Technological Forecasting

| On 02, Feb 2009

By Dmitry Kucharavy and Roland De Guio


Extensive historical and logistic analysis of competition dynamics was presented in the authors’ work at INSA (National Institute of Applied Science) in France titled: Logistic Substitution Model and Technological Forecasting. This work treated the economic system as a technical model, where the models modified forecasts. The application of several models (more than 300) based on the logistic growth function including simple logistic, component logistic models (CLM) and logistic substitution models (LSM) in the context of technology changed the future of forecasting.

The main idea of this paper is to revise existing models and arrange a working hypothesis for future research. First, the authors review the features of a simple logistic model as they are presented with different types of competition including a component logistic model that is presented in brief. Second, logistic substitution models in the context of long-term technological forecasting are reviewed. And lastly, a hypothesis about how to improve the reliability of logistic substitution models for studying the technological future is proposed.


Bi-logistic, multi-logistic, logistic substitution model, resource limitations, technology future study, logistic S-curve, socio-economic cycles


“The whole purpose of science is to find meaningful simplicity in the midst of disorderly complexity.”
— Herbert A. Simon, Models of My Life (1991)

The main objective of scientific study is to reveal and describe regularities, which can be used to predict the future. Among inventor and researcher, Galileo Galilei’s (1564-1642), many achievements was his excellent forecast about the periodic return and nature of a comet. As the “father of modern science,” he made this forecast based on observations and a mathematical model. In fact, forecasting plays a significant role in the development of science as soon as it is employed as a method to verify proposed theories and hypothesis.

Research on long-term technological forecasting is inspired by the description of “the lifeline” of technological systems from the father of the Theory of Inventive Problem Solving (TRIZ), Genrich Altshuller.1Where contradiction models, S-curves and the limitation of resources play important roles. A 2005 paper by the authors focuses on problems with the stages of the generic forecasting process – where the distinction among short-, medium- and long-term forecasts, based on three phases of S-curves, is also proposed.2 One S-curve is typically divided into three phases (Figure 1): before point a, between points a andb and after point b. A short-term technological forecast is one phase of an S-curve, while a medium-term forecast considers two phases. The scope of study for a long-term forecast is usually beyond one technology, since it studies at least three phases on an S-curve and may consider several growth processes and more than one system.

Figure 1: Growth of a Bacteria Colony Consuming Sugar and Minerals in a Closed Petri Dish Fitted to a Logistic Curve

where limit of growth k = 50 species, characteristic duration Dt = 2.2 days, midpoint tm = 2.5 days

An article presented at the 2007 International Conference on Engineering Dynamics depicts theoretical and practical results from two forecasting projects.4A critical-to-X feature merges qualitative and quantitative natures of long-term forecasting. This paper will illustrate through energy technology case studies how the prediction of technological barriers can be facilitated by mapping the contradictions in combination with the assessment of limiting resources.

At the TRIZ-Future Conference 2007 the definition of the growing parameters for many logistic growth models was emphasized.3In order to address the issue when there is no data for emerging technologies, causal methods for long-term forecasting are discussed. The causal method is applied to adopt quantitative models for predicting the diffusion of new technologies. In particular, a growing parameter for consecutive logistic growths is proposed to apply the amount of knowledge in percent of readiness for the transition from exploration to experimentation toward exploitation phases.

This paper will also develop the applications for reliable and reproducible long-term technological forecasting using the casual method and logistic growth function. After revising the component logistic model and logistic substitution models some hypotheses for improving their reliability are proposed. According to the findings these models can help cope with the problems of qualitative-quantitative forecasting described in previous publications.2,3,19

The following section is a short history of particular logistic models and concepts of competition. A later section focuses on the questions:

  • “How do LSMs work?”
  • “What are the known difficulties?”
  • “What can be done in order to improve reliability of forecasting with LSM?”

The conclusion will propose possibilities for further work.

Logistic Models and Forecasting

Most of the studies of technological changes are based on the application of logistic models and S-curves. Not all S-shaped curves, however, are logistic ones. There are symmetric and non-symmetric logistic curves, which are classified as simple logistic functions or complex ones.

In the scope of research, the authors apply the simple logistic S-curves due to the ease in interpreting the meaning of their parameters and the simplicity in estimating the parameters from their observed phenomenon. In numerous publications it was concluded that the other models of non-symmetric growth have limited application due to their complexity and low efficiency for technology forecasts.6,7,8,9,10

The widespread practical application of the logistic function as a means to depict growth processes started with Thomas Malthus (1766-1834), English economist and author of An Essay on the Principle of Population. It was in 1825 when Benjamin Gompertz, the founder of the law of mortality, published work developing the Malthusian growth model for demographic study. Pierre-Francois Verhulst, mathematician and doctor of number theory, offered the first reference to the logistic curve as a model of population growth. In 1923 T. Brailsford Robertson, professor of physiology and biochemistry, suggested using the function to describe the growth process in a single organism or individual. Biologist Raymond Pearl rediscovered the function and used it extensively to describe population growth including human ones. In 1925 and 1926, while working independently, Alfred J. Lotka and Vito Volterra, developers of the Volterra-Lotka equations, generalized the growth equation to quantify competition among different species and coined the predator-prey equations.

One of the earliest studies about technological substitution described by S-curves was done in 1957 by economist Hirsh Zvi Griliches. Using Griliches’ concepts in 1961, Edwin Mansfield, one of the minds behind the diffusion of innovations, developed a model to depict the rate at which firms follow an innovator. In the early 1960s, S-curves were regularly employed for technological forecasting.8The diffusion of innovation theory was formalized by Everett M. Rodgers, author of Diffusion of Innovations, in 1962, which postulated innovations that were spread in society in an S-curve.18

A significant achievement was accomplished by J. C. Fisher and R. H. Pry (1970), authors of A Simple Substitution Model of Technological Change, in formulating the model for binary technological substitution as an extension of Mansfield’s findings.12 A logistic substitution model proposed by Cesare Marchetti described technology substitution in the dynamics of long-run competition (1976-1979) by extensively using the Fisher-Pry transform model.7Perrin S.Meyer, author of Bi-logisitic Growth, proposed in 1994 the component bi-logistic growth model.5Later on, a component logistic model with multi-logistics generalizes this bi-logistic growth model.6The application of bi-and multi-logistics makes possible the description of complex growth processes through a family of simple logistic curves.

Logistic substitution and component logistic models in combination with the Fisher-Pry transform technique provide clear and suggestive outputs for supporting medium- and long-term forecasting of technology changes.5,6,7,8,11,13,14,15,16

Simple Logistic Models (SLM)

The natural growth of autonomous systems in competition might be described by logistic equation and logistic curve, respectively. In the context of our proposed research, natural growth is defined as the ability of a species (system) to multiply inside finite niche capacity (or carrying capacity of a physical limit of resources) through a certain time period.5,1

As soon as the function parameters can be calculated using a partial set of data such as the efficiency of changes in the internal combustion engine over the last 20 years, it is possible to use the equation in a predictive mode, as in how much that efficiency will grow and when. The availability of a reliable set of data is a principal limiting factor for S-curve model application in the forecast of emerging technologies.

For socio-technical systems the three-parameter S-shaped logistic growth model is applied to describe continuous trajectories of growth or decline through time.1

Example 1:

Where N(t) is the number of species or growing variables in question; k is the asymptotic limit of growth;a specifieswidth or steepness of the S-curve (for example,a = 0.19 means approximately 19 percent growth per time fraction); it is frequently replaced with a variable that qualifies the time required for the trajectory to grow from 10 percent to 90 percent of limit k; (Dt)2 is characteristic duration;b specifies the time (tm) when the curve reaches 0.5k at midpoint of the growth trajectory (tm implies symmetry of a simple logistic S-curve).
These three parameters k, a and b are usually calculated by fitting the data. The method used to fit S-curves on data aims at minimizing the next sum:

Example 2:

Where Ni, Di and Wi are at times ti, which is the value of the function, and the value and the weight assigned to the data.

The function is originally evaluated by assigning arbitrary starting values to the parameters of N. After that, an iterative search is performed to determine those values for which the sum becomes as small as possible.

There are also diverse fitting techniques. For instance, the asymptotic limit of growth k can be estimated such as expert judgment, when a and b are optimized to minimize residuals.

For case N(t) << k, the logistic model closely resembles exponential growth:3

Example 3:

An equivalent form of logistic equationfor practical application can be defined as:1

Example 4:

Empirical studies have shown that the characteristic S-shaped curve is present in thousands of growth and diffusion processes.7,11This model, therefore, can be applied to both systems where the mechanisms of growth are understood and growing principles are hidden.

Technology Diffusion and Competition

Technology diffusion is the process of obtaining (new) technology adapted through practical use. In the context of long-term technological forecasts, technology diffusion can be presented as a process of transition from invention to innovation.17,18Such a transitional process from the first feasible prototype to the first regular product and new market creation takes time, for example:

  • The photography medium took 112 years
  • The steam locomotive took 55 years
  • Rolled wires took 47 years
  • The lead battery took 79 years
  • Arc welding took 49 years17

In the framework of present research invention is defined as: the result of engineering activities in a technological context, which resolves contradictions between specific needs (how it was perceived) and known laws of nature. The output of the invention process is a feasible solution and working prototype, but not necessarily a patent. Innovation is the result of socio-economic and technological activities. It produces added value because of an uncommon way of doing business. It seems meaningless to compare invention and innovation. They result from different activities and their values are measured by different parameters.

From invention to innovation, technology diffusion is a long and bumpy road full of uncompromising competition. Hundreds of thousands of inventions have never become innovations. When innovation occurs, the long delay from invention to innovation makes it difficult to study the causality of the innovation process.Unfortunately, these facts are frequently ignored in studies about invention/innovation relationships.

Competition among emerging technologies plays a crucial role in technology diffusion. One of the basic assumptions for long-term forecasts is: all systems (super-systems, sub-systems) that evolve under competition according to the law of logistic growth. Mechanisms of competition should be divulged and purposefully applied for technology forecasting in a reproducible way.

Physicist and futurist Theodore Modis, described the scientific approach of managing competitionwhere two competitors can influence each other’s growth rate in six ways:

  1. Pure competition: Pure competition is when both species suffer from each other’s existence because they use the same resources to survive. The traditional example of this occurs between rabbits and sheep. Each one decreases the growth of the other, but at a different rate (sheep multiply more slowly than rabbits, but eat more grass).
  2. Predator-prey: Predator-prey competition is a relationship where two species interact as predator and prey. The predators flourish when there is abundant prey. Ultimately, predators surpass their food supply and decline. When the predator population is low the prey population will increase once again. These dynamics go on in cycles of growth and decline. A classic example of this is in the case of rabbit (prey) and fox (predator) populations. The Lotka-Volterra equations are usually applied to simulate the dynamics of this kind of competition.
  3. Symbiosis: Symbiosis is a situation where both species benefit thanks to their association. For instance, mobile phone sales trigger the increase of operators and new services and this escalation provokes sales of the latest mobile phone models.
  4. Parasitic (win-impervious): Parasitic (win-impervious) is a relationship between two species where one obtains some benefit while the other is unaffected. A classic example of this comes from biology: the remora fish attaches to sharks and feeds on their leavings without hindering its hosts. A market example of this is the increase in digital camera and computer sales, which prompted growth in the external hard disc market. The sale of external hard disks, however, does not influence the sale of digital cameras.
  5. Symbiotic (loss-indifferent): Symbiotic (loss-indifferent) is a situation when one species suffers from the existence of another, which remains insensible to what is happening. A textbook case from biology is the shading out of one plant by a taller and wider one.
  6. No-competition: No-competition is a relationship between two species when there is no overlap in using resources to evolve. For instance, sales of coffee do not affect sales of tea in the same supermarket. Sales depend on seasonal variations rather than on competition between two products.13

In addition to two-competitor cases, the competition of one species for resources (Malthusian case), such as multiple competitors as well as a model of indirect competition (as in spatial competition when A interacts with B, and B with C, then C affects A through B) are revealed. Given the number of various competition models it is not easy to subsequently build a practical instrument. Such a study becomes inadequately complex and time-consuming with multiple opportunities for hidden errors and biases.

Problems can be formulated when it is necessary to take into account competition mechanisms. In order to be considered intrinsic processes they must occur within a technology diffusion with multiple competitors. But it is necessary to avoid the analysis of competition mechanisms because it complicates applied models and increases study costs. In addition, the complex models leave room for hidden errors, biases and as a result they cause inadequate output.

Component Logistic Model (CLM)

“If it walks like a duck and quacks like a duck, it must be a duck.”
— Theodore Modis

The necessity of a feasible model to describe systems that experience two or more phases of growth became vital (for medium- and long-term forecasting) as soon as the logistic S-curve had been extensively applied to and studied in a wide range of socio-technical systems.

Starting with the assumption that the standard logistic S-curve describes one period (or pulse) of growth for a particular system then multiple growth pulses depict many systems.5 Defining a system is a difficult task in itself. One of the fundamental facts of the system approach is that all systems interact with their environment. In order to portray this phenomenon the system operator (multi-screen schema) must link super-systems, systems and sub-systems as well as past, present and future dimensions.

A system is a demarcated part of the universe, which is separated from the rest by an imaginary border. These artificial borders are unavoidable. In order to perceive or know anything one must make this distinction. How can one be sure about the delineation of a system? What are the criteria that justify the location of an artificial boundary?To develop a system definition it is necessary to situate the boundaries and describe the characteristics of the system. The features of the universe affect the system outside of the system (super-system) along with the interactions between universe and system.

Due to difficulties with the definition of the system, the time-series data cannot be cleaned and split properly. This leads to problems with fitting logistic S-curves to data. Before Perrin S. Meyer proposed bi-logistic and multi-logistic(for multi-logistic model growth is the sum of n simple logistics) models, complex multi-parameter functions were applied for the extrapolation of this sort of data.5,6

The Problem

The evolution of systems should be described by multi-parameter complex functions and curves since the systems rarely follow a single S-curve trajectory due to indigenous complexity (systems such as sub-systems and sub-processes; the irregularity of system parts evolution, etc.) as well as exogenous complexity (systems such as quasi-random behavior due to multiple interactions with other systems, etc.). The evolution of systems, however, should be described by (symmetrical) simple three-parameter logistic functions to provide clear physical interpretations. These interpretations are comparable with other system evolutions in order to decrease errors during forecasting and to be applicable in practice.

The Solution

The component logistic model describes the complex growth processes using a combination of simple three-parameter functions by applying bi-logistics or multi-logistics.5,6 The mechanism of combination resembles the nested doll principle and once again confirms the fractal feature concept of natural growth.1,20

For instance, a single simple logistic curve does not provide adequate level of residuals to study the dynamics of U.S. nuclear tests.5,21While a bi-logistic growth curve fits data with acceptable residuals (Figure 2).

Such a result was interpreted the following way: “…the fastest rate of growth (midpoint) of the first pulse occurred in 1963 following the Cuban missile crisis. While the first logistic pulse was largely the race to develop bombs with higher yields, the second pulse, cantered in 1983 and nearing saturation now (1994), is probably due to research on reliability and specific weapons designed for tactical use. The bi-logistic model predicts that we are at 90 percent saturation of the latest pulse. Processes often expire around 90 percent, though sometimes processes overshoot. The residuals show the extraordinary, deviant increase in U.S. tests after the scare of the 1957 Sputnik launch…”5

When reasonable interpretation is done the application of component models provides suggestive and attention-grabbing results. The practical experience shows, however, that experts might need several weeks to propose a realistic interpretation for obtained fits.

One of the remarkable characteristics of the component logistic model is its self-adjustment to a proposed definition of a system. Through the reduction of residuals and decomposition of an initial set of data by multi-logistic ones the initial definition of a system can be corrected and refined. In the example (Figure 2) the initial system for nuclear tests was decomposed to nuclear tests for aircraft and for missile delivery and they demonstrate different features and interactions.

Figure 2: U.S. Nuclear Weapon Tests With a Decomposed Bi-logistic Growth Curve

Inset:The component growth curves after using the Fisher-Pry model transform model.

Logistic Substitution Model (LSM)

“…No two people, working independently, will ever get exactly the same answer for an S-curve fit…”
—Theodore Modis, Ph.D.

Fisher and Pry’s classic paper titled A Simple Substitution Model of Technological Change was built on a simple set of assumptions. It was suggested that the model could be applied to “…forecasting technological opportunities, recognizing the onset of technologically based catastrophes, investigating the similarities and differences in innovative change in various economic sectors, investigating the rate of technical change in different countries and different cultures and investigating the limiting features to technological change.”12

First, the proposed mathematical transform decreases the number of parameters defining logistic growth and then, it allows the comparison of growth processes with very different absolute values. For example, the growth of total length (for U.S.) for canals is 7×103km and for roads is 6×106km.

Most of the sources for the LSM refer to the publications of Cesare Marchetti and Nebojsa Nakicenovic issued in 1979.7,22A study of technological substitution under long-term competition, however, is in a 1976 publication showing early traces of the Fisher-Pry transform model.23

The logistic substitution model describes the competitors’ niche market (e.g., fraction of market share). The life cycle of competitive technologies is subdivided into three periods:

  1. Growth
  2. Saturation
  3. Decline

In these periods, the growth and decline stages are logistic growth processes.


In order to provide long-range forecasting (more than 50 years)in areas of the energy market and energy use, the researchers were faced with the problem of applying models, which capture and simulate numerous relationships and feedback characteristics (complex ones) to represent the activity of an economic system and to report competition phenomena.

It was also necessary, however, to apply models with minimum characteristics (simple ones) in order to provide a clear unambiguous interpretation and satisfy a 50-year forecast horizon.

Proposed Solutions and Results

For the purpose of dealing with long-term technological forecasting for energy systems, a basic hypothesis was formulated: “primary energies, secondary energies and energy distribution systems are just different technologies competing for a market and should behave accordingly.”7

The authors emphasized three basic assumptions they applied to the LSM:

  1. New technologies enter the market and grow at logistic rates.
  2. Only one technology is in the saturation period at any given time.
  3. Declining technologies fade away steadily at logistic rates uninfluenced by competition from new technologies.7,22

Two additional suppositions can be recognized as well:

  1. There are n competing technologies ordered chronologically in the sequence of their appearance in the market.
  2. A technology in saturation follows a non-logistic path that connects the period of growth to its subsequent period of decline.

About 300 cases were examined by the International Institute for Applied Systems Analysis (IIASA). Their energy system program used the LSM for historical periods ranging from 20 to 130 years ago. (The descriptions in the reportdetail the resulting model with comments spanning nine pages. Additional examples, graphs and captions occupy 60 pages.7)
Descriptions of numerical methods for the LSM can be found in numerous publications.22,6,7 There are also at least two non-commercial software packages for experimentation for the LSM without the complications of equations and programming.24,25

How Does it Work?

To illustrate how a forecast can be supported with the LSM, the data of recording media sales in the U.S. was fitted with the help of Loglet Lab software.24 (The latest data sets can be found at: In order to recognize the strong and weak points of the LSM the authors started with a set of data from 1998.

At first, initial data shows millions of U.S. dollars in vinyl record, cassette and CD sales. They represent market shares using the Fisher-Pry transform model.

Next, the years in between where a logistic should be fitted are entered. These years are the assumptions about a period for Dt (shown in Figure 1). They are based on the visual observation of transformed data. Linear behavior corresponds to logistic growth or decline for the Fisher-Pry transform model. In this case, assumptions about Dt and midpoint tm can be done instead of a period evaluation.

As in any judgment, these assumptions contribute to the accuracy of a fit and future forecast. It was assumed that for vinyl a decline logistic should be fitted from 1977 to 1985. For cassettes a growth logistic is between 1977 to 1985. For CDs a growth logistic is between 1987 to 1995 (shown in Figure 3). (Note: the data sets for the early years of the CD and for the later years of vinyl do not follow the model. Based on the results of thousands of fits such growth is usually irregular when a market share is less than 5 percent.26,11,20)

The results strengthen the forecast about the growth of the CD and the decline of cassette market shares. To convert this information into an absolute value in millions of U.S. dollars return to the initial data and fit them with the parameters learned from the LSM.

Figure 3: Recording Media Sales Data with the Logistic Substitution Model

Now make an assumption about the next (new) technology. Find one where there is not yet any data. Then create logistics for hypothetical technology demands with assumptions using a fourth saturation curve. At least two parameters should be defined:

  1. Characteristic duration Dt
  2. Midpoint tm

This curve will approximately show when and how fast the technology will grow (shown in Figure 4).

A question to consider: how can these two parameters be predicted? When the technology has already entered the market (meaning it has passed 10 percent of the market share threshold) then the assumption about growth rate is based on the logistics from past technologies. For vinyl, cassettes and CDs the calculated Dt was 12, 13 and 14 years, respectively. In Figure 4 the projected result of the fourth emerging technology shows Dt=14 and tm=2005.

Figure 4: Anticipating the Impact of New Technology:
Recording Media Sales Data with a Hypothetical Fourth New Technology

But, in 1998, the DVD was chosen as the new technology and this turned out to be an incorrect prediction.

Known Difficulties

To illustrate some known difficulties and ambiguities, the diagrams reported in 1999 are compared to diagrams reported in 2007covering the same topic (shown in Figure 5).6,24,25,26

Figure 5: Recording Media Sales with MP3 Data Set (through 2003)25

The first issue to note is the definition of parameters for the hypothetic technology. There were two papers published by the same author in the same year with different assumptions made about characteristic time Dt and midpoint tm to describe logistic growth of new music technology.

Inthe table belowthe second, third and fourth columns represent the years of logistic decline/growth that were chosen as parameters for the LSM.

Variation of Assigned Parameters for the Logistic Growth Description




















The analysis of datain the tableonce again confirms the absence of a formal procedure to define the parameters for the given time periods.

The second issue is linked to the definition of the new technology. How is a prospective competitor defined in advance? In publications from 1999 the digital versatile disc (DVD) was a candidate. Today, however, MP3 technology is following the predicted growth curve, whereas the DVD is mostly used for video records instead of for music.

Another example to underline the second issue is a famous 1979 diagram called the world primary energy substitution.7 In his 2002 book, Modis wrote “that turned out to be a most inaccurate forecast…”11

Why? According to the world energy statistics 28 the nuclear primary energy supply in 2005 was about 6.3 percentwith combustible renewable and waste supply representing about 10 percent. (Fuel share of total primary energy supply (TPES) is made up of indigenous production plus imports minus exports minus international marine bunkers ± stock changes.28) Thus, the trajectory for nuclear energy evolution fell below what had been predicted.

Even if the LSM can predict logistic growth and decline it is a challenging task to name a new technology within the long-term.

The third issue includes time-series data sets (selection, cleaning, transformation) and the assumptions made to fit logistics into data. In the second and third rows in the table above, the same data were fitted with different assumptions. The primary question is: how can one have confidence in obtained fits? Unfortunately, the analysis of residuals is not allowed for the LSM in referenced software.24,25

The fourth issue (but not the last) is about the interpretation of obtained results. The LSM represents changes in competitor niches (specifically changes in market share). On the other hand, the trustworthiness of a model depends on the initial estimations of niche capacities (k) for each technology.

The difficulty for the LSM is not building or running a model several times to get the best fit, but the interpretation of those obtained results. The interpretation of plausible results does not always correspond to the actual future. A formal mechanism, therefore, is required to predict implausible events.

How to be More Reliable

“…The system had a schedule, a will, and a clock…”
— Cesare Marchetti and Nebojsa Nakicenovic

The working hypothesis to answer the first issue (in regards to the definition of parameters for logistic growth curves) is based on studies of cycles in economic, technological and social environments.11 (Detailed reviews of long economic wave cycles can be found in additional articles.39And in documents from the NATO Advanced Research Workshop conference on Kondratieff Waves, Warfare and World Security (February 2005, Covilhã, Portugal at:

Modis proposes the diagram shown in Figure 6.11 In the upper part of the diagram, a harmonic wave with a 56-year time period represents deviations of the logistic growth of energy consumption in the U.S. (The periodicity in energy consumption was first observed by Hugh.B. Stewart.38) At the bottom, more than 50 growth processes are shown with their ceiling normalized to 100 percent. (Most of the data for curves have been taken from Arnulf Grubler’s The Rise and Fall of Infrastructures.37)

The growing parts of curves coincide with the upswing of the cycle indicating growth and prosperity, while saturation periods correspond to economic recession.

Data sets showing basic innovationsrepresent regularity as well: the peaks in innovation correspond to valleys in energy consumption.11,17 Energy consumption, therefore, resonates with making basic innovations. (Cesare Marchetti first correlated Stewart’s energy cycle with Gerard Mensch’s basic innovations one.40)

The results shown in Figures 6 and 7 coincide with the conclusions proposed in 1924 about activities in social systems and were confirmed by Russian professor Alexander Tchijevsky using extended data sets in 1936.29,36 These results are also in accordance with Nikolai Kondratieff’s concept of long waves in economicsand data about basic innovations collected by Gerhard Mensch from Stalemate in Technology: Innovations Overcome the Depression.17,30

The hypothesis, which the authors plan to check in the future, defines logistic growth characteristics for the LSM (characteristic time Dt and midpoint tm) in accordance with the schedule from the nearest environmental, social and economic super-systems. The surprisingly accurate predictions made using software such as TechSignal (based on the study of cycles) gives confidence in expectations.44

Figure 6: S-curves Describing Technological Growth and Substitution Processes
(All normalized to reach 100 percent when they are completed)11

Figure 7: .S. Transport Infrastructure
(The growth in length of each infrastructure is expressed as a percentage of its final ceiling
where the absolute levels of these ceilings in miles are different)11,37

Addressing the Second, Third and Fourth Issues

In the second issue the definition of prospective competitive technology can be addressed with the help of a genetic algorithmand using problem flow technology.41,42 In order to identify the next generation of technology, techniques and models should be applied (similar to the ones applied in inventive problem solving); the description of an X-element, Algorithm of Inventive Problem Solving (ARIZ), the ideal final result (IFR)and the element – name of feature – value of feature (ENV) model.1,42,43

Progress regarding the third issue demands research on logistic growth models and the development of software. This will facilitate the LSM construction using a rigorous analysis of data and residuals.

Advancement on the fourth issue in regards to the interpretation and initial estimation of a ceiling for S-curves will come from analysis of limiting resources and further development of the network of the contradictions approach.19


In this paper the authors introduced the direction through super-systems for problems of long-term forecasting from emerging technologies using the CLM and LSM in the dimension of the casual method. In further research, the plan is to explore the direction through sub-systems using this casual method based on logistic growth of knowledge within the invention-to-innovation process.3

The authors conclude that the basic patterns of technological changes are invariant based on the application of laws of technical system evolution, logistic growth and cyclesas main components.1,11,39 This application of knowledge about cycles and laws of logistic growth models (SLM, CLM, LSM) makes long-term technological forecasting possible as it soon helps resolve an incompatibility between cause-effect description (scientific) and the inadequate complexity of a model (practical).

The multi-screen scheme of thinking,in combination with the concept that “competition is possible only in a common infrastructure,”makes the management of model complexities possible through the synergy of the CLM and the LSM.1,37 The CLM allows the description of the logistic growth of a system from a viewpoint of sub-system evolution and endogenous competition mechanism. The LSM provides a means for depicting technological change and performing long-term forecasting of socio-technical systems from super-systems and exogenous competition factor viewpoints.

For logistic growth models, the critical point for forecasting is the interpretation of results. For instance, in the case of the CLM, it is a nontrivial task to recognize the essential underlying mechanisms of obtained bi- or multi-logistic growths. In one practical case it takes more than three weeks to understand the underlying mechanism of the constructed triple-logistic model. In the case of the LSM, it is a challenging task to name the next technology. Even the time parameters of growth can not be accurately identified in such a short period of time.

Another remaining question is what are the regularities of evolution for systems which never show innovation? It is a well-known fact that before point a, systems do not display logistic growth behavior (see Figures 3, 4 and 5).

In conclusion, it is necessary to emphasis the crucial role of forecasters, especially since they play a decisive one. The reliable forecasting method alone is not enough for accurate long-term prediction. It will never be a push-button solution. Like any powerful tool, a method can produce a great outcome in the hands of the intelligent, but it may demonstrate misleading results in the hands of the inexperienced.


This research was partially supported by the European Institute for Energy Research (EIFER) in Karlsruhe, Germany. The authors would like to thank their colleagues from the LICIA team from LGECO, INSA Strasbourg for constructive discussions. They are also grateful to all participants from the June 2008 seminar in Vinci, Italy for their goodwill, curiosity, questions and helpful criticism.


  1. G.S. Altshuller, Creativity as an Exact Science, Sovietskoe Radio Publishing House, Moscow, 1979, p.184 (in Russian).
  2. D. Kucharavy, and R. De Guio, Problems of Forecast, ETRIA TRIZ Future 2005, Graz, Austria, 2005. 219-235.
  3. D. Kucharavy, and R. De Guio, Application of S-Shaped Curves, 7th ETRIA TRIZ Future Conference, Kassel University Press GmbH, Kassel, Frankfurt, Germany, 2007.
  4. D. Kucharavy, R. De Guio, L. Gautier, and M. Marrony, Problem Mapping for the Assessment of Technological Barriers in the Framework of Innovative Design, 16th International Conference on Engineering Design, ICED’07, Ecole Centrale Paris, Paris, France, 2007.
  5. P. S. Meyer, “Bi-logistic Growth,Technological Forecasting and Social Change, 47(1), (1994) 89-102.
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This paper was originallypresented at the European TRIZ Association’s TRIZ Future 2008 meeting in Enschede, NL.