Diffusion of innovations

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The diffusion of innovations according to Rogers. With successive groups of consumers adopting the new technology (shown in blue), its market share (yellow) will eventually reach the saturation level. In mathematics the S curve is known as the logistic function.

Diffusion of innovations is a theory that seeks to explain how, why, and at what rate new ideas and technology spread through cultures. Everett Rogers, a professor of communication studies, popularized the theory in his book Diffusion of Innovations; the book was first published in 1962, and is now in its fifth edition (2003).[1] The book says that diffusion is the process by which an innovation is communicated through certain channels over time among the members of a social system. The origins of the diffusion of innovations theory are varied and span multiple disciplines. The book espouses the theory that there are four main elements that influence the spread of a new idea: the innovation, communication channels, time, and a social system. This process relies heavily on human capital. The innovation must be widely adopted in order to self-sustain. Within the rate of adoption, there is a point at which an innovation reaches critical mass. The categories of adopters are: innovators, early adopters, early majority, late majority, and laggards (Rogers 1962, p. 150). Diffusion of Innovations manifests itself in different ways in various cultures and fields and is highly subject to the type of adopters and innovation-decision process.


The concept of diffusion was first studied by the French sociologist Gabriel Tarde in late 19th century[2] and by German and Austrian anthropologists such as Friedrich Ratzel and Leo Frobenius.[3] Its basic epidemiological or internal-influence form was formulated by H. Earl Pemberton,[4] who provided examples of institutional diffusion such as postage stamps and standardized school ethic codes.

In 1962 Everett Rogers, a professor of rural sociology published his work: "Diffusion of Innovations". In this seminal piece, Rogers synthesized research from over 508 diffusion studies and produced a theory applied to the adoption of innovations among individuals and organizations.

Roger's work asserts that 4 main elements influence the spread of a new idea: the innovation, communication channels, time, and a social system. These elements work in conjunction with one another: diffusion is the process by which an innovation is communicated through certain channels over time among the members of a social system. Rogers adds that central to this theory is process. Individuals experience 5 stages of accepting a new innovation: knowledge, persuasion, decision, implementation, and confirmation. If the innovation is adopted, it spreads via various communication channels. During communication, the idea is rarely evaluated from a scientific standpoint; rather, subjective perceptions of the innovation influence diffusion. The process occurs over time. Finally, social systems determine diffusion, norms on diffusion, roles of opinion leaders and change agents, types of innovation decisions, and innovation consequences. To use Rogers’ model in health requires us to assume that the innovation in classical diffusion theory is equivalent to scientific research findings in the context of practice, an assumption that has not been rigorously tested. How can we spread and sustain innovations in health service delivery and organization? Greenhalgh et al., evaluate an evidence-based model for considering the diffusion of innovations in health service organizations.[5]

The origins of the diffusion of innovations theory are varied and span across multiple disciplines. Rogers identifies six main traditions that impacted diffusion research: anthropology, early sociology, rural sociology, education, industrial sociology, and medical sociology. The diffusion of innovation theory has been largely influenced by the work of rural sociologists.[6] In 1971, Rogers published a follow-up work: Communication of Innovations; A Cross-Cultural Approach. building on his original theory on the diffusion process by evaluating social systems. This extension aimed to add value to Roger’s 1962 touchstone work (Rogers & Shoemaker, 1971).


The key elements in diffusion research are:

InnovationRogers defines an innovation as "an idea, practice, or object that is perceived as new by an individual or other unit of adoption".[7]
Communication channelsA communication channel is "the means by which messages get from one individual to another".[8]
Time"The innovation-decision period is the length of time required to pass through the innovation-decision process".[9] "Rate of adoption is the relative speed with which an innovation is adopted by members of a social system".[10]
Social system"A social system is defined as a set of interrelated units that are engaged in joint problem solving to accomplish a common goal".[11]


Two factors determine what type a particular decision is:

Based on these considerations, three types of innovation-decisions have been identified within diffusion of innovations.

Optional Innovation-DecisionThis decision is made by an individual who is in some way distinguished from others in a social system.
Collective Innovation-DecisionThis decision is made collectively by all individuals of a social system.
Authority Innovation-DecisionThis decision is made for the entire social system by few individuals in positions of influence or power.


Diffusion of an innovation occurs through a five–step decision-making process. It occurs through a series of communication channels over a period of time among the members of a similar social system. Ryan and Gross first indicated the identification of adoption as a process in 1943 (Rogers 1962, p. 79). Rogers' five stages (steps): awareness, interest, evaluation, trial, and adoption are integral to this theory. An individual might reject an innovation at any time during or after the adoption process. Scholars such as Abrahamson (1991) examine this process critically by posing questions such as: How do technically inefficient innovations diffuse and what impedes technically efficient innovations from catching on? Abrahamson makes suggestions for how organizational scientists can more comprehensively evaluate the spread of innovations.[12] In later editions of the Diffusion of Innovations, Rogers changes the terminology of the five stages to: knowledge, persuasion, decision, implementation, and confirmation. However, the descriptions of the categories have remained similar throughout the editions.

DoI Stages.jpg
Five stages of the adoption process
KnowledgeIn this stage the individual is first exposed to an innovation, but lacks information about the innovation. During this stage the individual has not yet been inspired to find out more information about the innovation.
PersuasionIn this stage the individual is interested in the innovation and actively seeks related information/detail.
DecisionIn this stage the individual takes the concept of the change and weighs the advantages/disadvantages of using the innovation and decides whether to adopt or reject the innovation. Due to the individualistic nature of this stage, Rogers notes that it is the most difficult stage on which to acquire empirical evidence (Rogers 1964, p. 83).
ImplementationIn this stage the individual employs the innovation to a varying degree depending on the situation. During this stage the individual also determines the usefulness of the innovation and may search for further information about it.
ConfirmationIn this stage the individual finalizes his/her decision to continue using the innovation. This stage is both intrapersonal (may cause cognitive dissonance) and interpersonal, confirmation the group has made the right decision.

Rate of adoption[edit]

The rate of adoption is defined as the relative speed in which members of a social system adopt an innovation. Rate is usually measured by the length of time required for a certain percentage of the members of a social system to adopt an innovation (Rogers 1962, p. 134). The rates of adoption for innovations are determined by an individual’s adopter category. In general, individuals who first adopt an innovation require a shorter adoption period (adoption process) when compared to late adopters.

Within the rate of adoption, there is a point at which an innovation reaches critical mass. This is a point in time within the adoption curve that the number of individual adopters ensures that continued adoption of the innovation is self-sustaining. Illustrating how an innovation reaches critical mass, Rogers outlines several strategies in order to help an innovation reach this stage. Strategies to propel diffusion include: when an innovation adopted by a highly respected individual within a social network, creating an instinctive desire for a specific innovation. Also, injecting an innovation into a group of individuals who would readily use said technology, and provide positive reactions and benefits for early adopters of an innovation.

Difference between diffusion and adoption[edit]

Adoption is an individual process detailing the series of stages one undergoes from first hearing about a product to finally adopting it.
The diffusion process, however, signifies a group of phenomena, which suggests how an innovation spreads among consumers.
Overall, the diffusion process essentially encompasses the adoption process of several individuals over time.

Adopter categories[edit]

Rogers defines an adopter category as a classification of individuals within a social system on the basis of innovativeness. In the book Diffusion of Innovations, Rogers suggests a total of five categories of adopters in order to standardize the usage of adopter categories in diffusion research. The adoption of an innovation follows an S curve when plotted over a length of time.[13] The categories of adopters are: innovators, early adopters, early majority, late majority, and laggards (Rogers 1962, p. 150) In addition to the gatekeepers and opinion leaders who exist within a given community, there are change agents from outside the community. Change agents essentially bring innovations to new communities– first through the gatekeepers, then through the opinion leaders, and so on through the community.

Adopter categoryDefinition
InnovatorsInnovators are the first individuals to adopt an innovation. Innovators are willing to take risks, have the highest social class, have great financial liquidity, are very social and have closest contact to scientific sources and interaction with other innovators. Risk tolerance has them adopting technologies which may ultimately fail. Financial resources help absorb these failures. (Rogers 1962 5th ed, p. 282)
Early adoptersThis is the second fastest category of individuals who adopt an innovation. These individuals have the highest degree of opinion leadership among the other adopter categories. Early adopters have a higher social status, have more financial liquidity, advanced education, and are more socially forward than late adopters. More discrete in adoption choices than innovators. Realize judicious choice of adoption will help them maintain central communication position (Rogers 1962 5th ed, p. 283).
Early MajorityIndividuals in this category adopt an innovation after a varying degree of time. This time of adoption is significantly longer than the innovators and early adopters. Early Majority tend to be slower in the adoption process, have above average social status, contact with early adopters, and seldom hold positions of opinion leadership in a system (Rogers 1962 5th ed, p. 283)
Late MajorityIndividuals in this category will adopt an innovation after the average member of the society. These individuals approach an innovation with a high degree of skepticism and after the majority of society has adopted the innovation. Late Majority are typically skeptical about an innovation, have below average social status, very little financial liquidity, in contact with others in late majority and early majority, very little opinion leadership.
LaggardsIndividuals in this category are the last to adopt an innovation. Unlike some of the previous categories, individuals in this category show little to no opinion leadership. These individuals typically have an aversion to change-agents. Laggards typically tend to be focused on "traditions", likely to have lowest social status, lowest financial liquidity, be oldest of all other adopters, in contact with only family and close friends.
LeapfroggersThe phenomenon when resistors upgrade they will often need to skip several generations in order to reach the most recent technologies.

Rogers’ five factors[edit]

Rogers defines several intrinsic characteristics of innovations that influence an individual’s decision to adopt or reject an innovation.

Relative advantageHow improved an innovation is over the previous generation.
CompatibilityThe level of compatibility that an innovation has to be assimilated into an individual’s life.
Complexity or simplicityIf the innovation is perceived as complicated or difficult to use, an individual is unlikely to adopt it.
TrialabilityHow easily an innovation may be experimented. If a user is able to test an innovation, the individual will be more likely to adopt it.
ObservabilityThe extent that an innovation is visible to others. An innovation that is more visible will drive communication among the individual’s peers and personal networks and will, in turn, create more positive or negative reactions.

Failed diffusion[edit]

Rogers, in his "Diffusion of Innovation" writings, discussed a situation in Peru involving the implementation of water boiling to obtain higher health and wellness levels of the individuals living within the village of Los Molinas. The residents of the village have no knowledge of the link between particular sanitation and reduced levels of illness. The campaign was working with the villagers to try to teach them how to boil their water to make it healthier for consumption, as well as to burn their garbage, install working latrines, and report cases of illness to local health agencies. In Los Molinas, a stigma is linked to boiled water as being something that only the "unwell" consume, and thus, the idea of healthy residents boiling their water prior to consumption was frowned upon, and those who did so wouldn't be accepted by their society. Thus, the two-year campaign to help bring more sanitary ways of living to this village was considered to be largely unsuccessful. Much of the reason for the lack of success is because the social norms and standards of acceptance into society greatly outweighed the idea of taking on this innovation, even at the sake of the health, well-being, and greater levels of education to the villagers. This failure better exemplified the importance of the roles of the interpersonal communication channels that are involved in such a health-related campaign for social change. Burt, R.S. (1973) also looked at the process of diffusion in El Salvador and asks: Is there a differential influence exercised by social integration on participation in the diffusion process and is such influence, significant above that exerted by other important diffusion relevant variables? [14]

Heterophily and communication channels[edit]

Lazarsfeld and Merton first called attention to the principles of homophily and its opposite, heterophily.[15] Using their definition, Rogers defines homophily as "the degree to which pairs of individuals who interact are similar in certain attributes, such as beliefs, education, social status, and the like".[15] When given the choice, individuals usually choose to interact with someone similar to him or herself.[16] Furthermore, homophilous individuals engage in more effective communication because their similarities lead to greater knowledge gain as well as attitude or behavior change.[16] However, most participants in the diffusion of innovations are heterophilous, meaning they speak different languages, so to speak.[16] The problem is that diffusion requires a certain degree of heterophily; if two individuals are identical, no diffusion occurs because no new information can be exchanged.[16] Therefore, an ideal situation would involve two individuals who are homophilous in every way, except in knowledge of the innovation.[16]

The role of social systems[edit]

Opinion leaders[edit]

Throughout the diffusion process there is evidence that not all individuals exert an equal amount of influence over all individuals. In this sense there are Opinion Leaders, leaders who are influential in spreading either positive or negative information about an innovation. Rogers relies on the ideas of Katz & Lazarsfeld and the two-step flow theory in developing his ideas on the influence of Opinion Leaders in the diffusion process.[17] Opinion Leaders have the most influence during the evaluation stage of the innovation-decision process and late adopters (Rogers 1964, p. 219). In addition opinion leaders have a set of characteristics that set them apart from their followers and other individuals. Opinion Leaders typically have greater exposure to the mass media, more cosmopolitan, greater contact with change agents, more social experience and exposure, higher socioeconomic status, and are more innovative.

Research was done in the early 1950s at the University of Chicago attempting to assess the cost-effectiveness of broadcast advertising on the diffusion of new products and services.[18] The findings were that opinion leadership tended to be organized into a hierarchy within a society, with each level in the hierarchy having most influence over other members in the same level, and on those in the next level below it. The lowest levels were generally larger in numbers, and tended to coincide with various demographic attributes that might be targeted by mass advertising. However, it found that direct word of mouth and example were far more influential than broadcast messages, which were only effective if they reinforced the direct influences. This led to the conclusion that advertising was best targeted, if possible, on those next in line to adopt, and not on those not yet reached by the chain of influence. It can be a waste of money to market to those not yet ready to buy.

Other research relating the concept to public choice theory finds that the hierarchy of influence for innovations need not, and likely does not, coincide with hierarchies of official, political, or economic status.[19] Elites are often not innovators, and innovations may have to be introduced by outsiders and propagated up a hierarchy to the top decision makers.

Electronic communication social networks[edit]

Prior to the introduction of the Internet, it was argued that social networks had a crucial role in the diffusion of innovation particularly tacit knowledge in the book The IRG Solution – hierarchical incompetence and how to overcome it. The book argued that the widespread adoption of computer networks of individuals would lead to the much better diffusion of innovations, and with greater understanding of their possible shortcomings, and the identification of needed innovations that would not have otherwise occurred – the relevance paradox. The social model proposed by Ryan and Gross (1943) (Rogers 1962, p. 79) is expanded by Valente (1996)[20] who uses social networks as a basis for adopter categorization instead of solely relying on the system-level analysis used by Ryan and Gross. Valente also looks at an individual's personal network, which is a different application than the organizational perspective espoused by many other scholars.[20]


Innovations are often adopted by organizations through two types of innovation-decisions: collective innovation decisions and authority innovation decisions. The collective innovation decision occurs when the adoption of an innovation has been made by a consensus among the members of an organization. The authority-innovation decision occurs when the adoption of an innovation has been made by very few individuals with high positions of power within an organization (Rogers 2003, p. 403). Unlike the optional innovation decision process, these innovation-decision processes only occur within an organization or hierarchical group. Within the innovation decision process in an organization there are certain individuals termed "champions" who stand behind an innovation and break through any opposition that the innovation may have caused. The champion within the diffusion of innovation theory plays a very similar role as to the champion used within the efficiency business model Six Sigma. The innovation process within an organization contains five stages that are slightly similar to the innovation-decision process that individuals undertake. These stages are: agenda-setting, matching, redefining/restructuring, clarifying, routinizing.

Policy diffusion[edit]

The theories of diffusion have spread beyond the original applied fields. In the case of political science and administration, policy diffusion focuses on how institutional innovations are adopted by other institutions, at the local, state or country level. An alternative term is 'policy transfer' where the focus is more on the agents of diffusion such as in the work of Diane Stone.

The first interests with regards to policy diffusion were focused in the variation over time (Berry & Berry 1990[21] or [1], state lottery adoption) but more recently the interest has shifted towards mechanisms (emulation, learning, coercion, as in Simmons & Elkins (2004)[22] or Gilardi (2010)[23] or in channels of diffusion (as in Jordana, Levi-Faur and Fernández-i-Marín (2011)[24]), where the authors find that the creation of regulatory agencies is transmitted by country and sector channels).

Diffusion of new technology[edit]

Peres, Muller and Mahajan (2010) suggest that Innovation diffusion of a new technology is "the process of the market penetration of new products and services that is driven by social influences, which include all interdependencies among consumers that affect various market players with or without their explicit knowledge".[25]

Eveland (1986) evaluated diffusion of innovations from a strictly phenomenological view, which is very different from the other perspectives he found. He asserts that, “Technology is information, and exists only to the degree that people can put it into practice and use it to achieve values”[26]

Diffusion of existing technologies has been measured in S curves. These technologies include radio, television, VCR, cable, flush toilet, clothes washer, refrigerator, home ownership, air conditioning, dishwasher, electrified households, telephone, cordless phone, cellular phone, per capita airline miles, personal computer and the Internet. This data[27] can be assessed as a valuable predictor for future innovations.

Diffusion curves for Infrastructures[28] This data reveals stunning contrast in the diffusion process of personal technologies versus infrastructure.

Consequences of adoption[edit]

There are both positive and negative outcomes when an individual or organization chooses to adopt a particular innovation. Rogers states that this is an area that needs further research because of the biased positive attitude that is associated with the adoption of an innovation (Rogers 2005, p. 470). In the Diffusion of Innovation, Rogers lists three categories for consequences: desirable vs. undesirable, direct vs. indirect, and anticipated vs. unanticipated.

In her article, "Integrating Models of Diffusion of Innovations," Barbara Wejnert details two categories for consequences: public vs. private and benefits vs. costs.[29]

Public versus private[edit]

Public consequences comprise the impact of an innovation on those other than the actor, while private consequences refer to the impact on the actor itself.[29] Public consequences usually involve collective actors, such as countries, states, organizations, or social movements.[29] The results are usually concerned with issues of societal well-being.[29] Private consequences usually involve individuals or small collective entities, such as a community.[29] The innovations are usually concerned with the improvement of quality of life or the reform of organizational or social structures.[29]

Benefits versus costs[edit]

The benefits of an innovation obviously are the positive consequences, while the costs are the negative.[30] Costs may be monetary or nonmonetary, direct or indirect.[30] Direct costs are usually related to financial uncertainty and the economic state of the actor.[30] Indirect costs are more difficult to identify.[30] An example would be the need to buy a new kind of fertilizer to use innovative seeds.[30] Indirect costs may also be social, such as social conflict caused by innovation [30] Marketers are particularly interested in the diffusion process as it determines the success or failure of a new product. It is quite important for a marketer to understand the diffusion process so as to ensure proper management of the spread of a new product or service.

Mathematical treatment[edit]

Main article: Logistic function

The diffusion of an innovation typically follows an S shaped curve which often resembles a logistic function. Mathematical programming models such as the S-D model apply the diffusion of innovations theory to real data problems.[31]

Complex Systems models[edit]

Complex network models can also be used to investigate the spread of innovations among individuals connected to each other by a network of peer-to-peer influences, such as in a physical community or neighborhood.[32]

Such models represent a system of individuals as nodes in a network (or Graph (mathematics)). The interactions that link these individuals are represented by the edges of the network and can be based on the probability or strength of social connections. In the dynamics of such models, each node is assigned a current state, indicating whether or not the individual has adopted the innovation, and model equations are used to describe the evolution of these states over time.[33]

In threshold models[34] the uptake of technologies is determined by the balance of two factors: the (perceived) usefulness (sometimes called utility) of the innovation to the individual as well as barriers to adoption, such as cost. The multiple parameters that influence decisions to adopt, both individual and socially motivated, can be represented by such mathematical models.

Computer models have been developed to investigate the balance between the social aspects of diffusion and perceived intrinsic benefit to the individuals.[35] When the effect of each individual node was analyzed along with its influence over the entire network, the expected level of adoption was seen to depend on the number of initial adopters and the structure and properties of the network. Two factors in particular emerged as important to successful spread of the innovation: The number of connections of nodes with their neighbors, and the presence of a high degree of common connections in the network (quantified by the clustering coefficient).

International Institute for Applied Systems Analysis (IIASA)[edit]

Several papers on the relationship between technology and the economy have been written by researchers at the International Institute for Applied Systems Analysis (IIASA). The pertinent papers deal with energy substitution and the role of work in the economy as well as with the long economic cycle. Using the logistic function, these researchers were able to provide new insight into market penetration, saturation and forecasting the diffusion of various innovations, infrastructures and energy source substitutions.[36] Cesare Marchetti published on Kondretiev waves and on diffusion of innovations.[37] Grübler (1990) presents a mathematical discussion of diffusion and substition models.[38]


Much of the evidence for the diffusion of innovations gathered by Rogers comes from agricultural methods and medical practice.

Various computer models have been developed in order to simulate the diffusion of innovations. Veneris developed a systems dynamics computer model which takes into account various diffusion patterns modeled via differential equations.[39][40]

There are a number of criticisms of the model which make it less than useful for managers. First, technologies are not static. There is continual innovation in order to attract new adopters all along the S-curve. The S-curve does not just 'happen'. Instead, the s-curve can be seen as being made up of a series of 'bell curves' of different sections of a population adopting different versions of a generic innovation.

Rogers has placed the contributions and criticisms of diffusion research into four categories: pro-innovation bias, individual-blame bias, recall problem, and issues of equality.[1]

One of the cons of the Diffusion of Innovation approach is that the communication process involved is a one-way flow of information. The sender of the message has a goal to persuade the receiver, and there is little to no dialogue. The person implementing the change controls the direction and outcome of the campaign. In some cases, this is the best approach, but other cases require a more participatory approach.

See also[edit]




  1. ^ a b Rogers, E. M. (2003). Diffusion of innovations (5th edition). New York, NY: Free Press.
  2. ^ see the article Founding Father of Innovation Diffusion.
  3. ^ see the article on Trans-cultural diffusion or Roland Burrage Dixon (1928): The Building of Cultures.
  4. ^ Pemberton, H. E. (1936) 'The Curve of Culture Diffusion Rate', American Sociological Review, 1 (4): 547–556.
  5. ^ Greenhalgh, T.; Robert, G.; Macfarlane, F.; Bate, P.; and Kyriakidou, O. (2004). Diffusion Of Innovations In Service Organizations: Systematic Review And Recommendations. Milbank Quarterly. Volume 82, Issue 4, pages 581–629.
  6. ^ Ryan (1943), see above.
  7. ^ (Rogers, 1983. p. 11)
  8. ^ (Rogers, 1983. p. 17)
  9. ^ (Rogers 1983, p. 21)
  10. ^ (Rogers, 1983. p. 21, 23)
  11. ^ (Rogers, 1983. p. 24)
  12. ^ Abrahamson, E. (1991). Managerial Fads and Fashions: The Diffusion and Rejection of Innovation. California Management Review, 16: 586–612.
  13. ^ J. C. Fisher and R. H. Pry , "A Simple Substitution Model of Technological Change", Technological Forecasting & Social Change, vol. 3, no. 1 (1971)
  14. ^ Burt, R.S. (1973). The Differential Impact of Social Integration on Participation in the Diffusion of Innovations. Social Science Research, 2(2): 125–44.
  15. ^ a b (Rogers, 1983. p. 18)
  16. ^ a b c d e (Rogers, 1983. p. 19)
  17. ^ Katz, Elihu & Lazarsfeld, Paul (1955). Personal influence: The part played by people in the flow of mass communications, Glencoe: Free Press
  18. ^ Bell, W.E. (1963), "Consumer Innovators: A Unique Market for Newness," in Toward Scientific Marketing, ed. Stephen A. Greyser, Chicago: American Marketing Association, 90–93.
  19. ^ Economic policy making in evolutionary perspective, by Ulrich Witt, Max-Planck-Institute for Research into Economic Systems.
  20. ^ a b Valente, T.W. (1996). Social network thresholds in the diffusion of innovations. Social Networks. Volume 18, Issue 1, January 1996, Pages 69–89.
  21. ^ http://www.unc.edu/~fbaum/teaching/PLSC541_Fall08/berry_berry_1990.pdf
  22. ^ http://journals.cambridge.org/action/displayAbstract?fromPage=online&aid=205177
  23. ^ http://onlinelibrary.wiley.com/doi/10.1111/j.1540-5907.2010.00452.x/abstract
  24. ^ http://cps.sagepub.com/content/44/10/1343
  25. ^ Renana Peres, Eitan Muller, and Vijay Mahajan (2010), “Innovation Diffusion and New Product Growth Models: A Critical Review and Research Directions", International Journal of Research in Marketing, 27 (2) 91–106. Lead Article.
  26. ^ Eveland, J.D. (1986). Diffusion, Technology Transfer and Implementation. Knowledge: Creation, Diffusion, Utilization, 8(2): 303–22.
  27. ^ Moore, Stephen; Simon, Julian (Dec 15, 1999). The Greatest Century That Ever Was: 25 Miraculous Trends of the last 100 Years, The Cato Institute: Policy Analysis, No. 364. 
  28. ^ Grübler, Arnulf (1990). The Rise and Fall of Infrastructures: Dynamics of Evolution and Technological Change in Transport. Heidelberg and New York: Physica-Verlag. 
  29. ^ a b c d e f (Wejnert, "Integrating Models of Diffusion of Innovations," p. 299)
  30. ^ a b c d e f (Wejnert, "Integrating Models of Diffusion of Innovations," p. 301)
  31. ^ D.S. Hochbaum, E. Moreno-Centeno, P. Yelland, and R.A. Catena. Rating Customers According to Their Promptness to Adopt New Products, Operations Research 59(5): 1171–1183, 2011
  32. ^ What Math Can Tell Us About Technology's Spread Through Cities.
  33. ^ How does innovation take hold in a community? Math modeling can provide clues
  34. ^ D. J. Watts. "A Simple Model of Global Cascades on Random Networks"
  35. ^ N. J. McCullen, A. M. Rucklidge, C. S. E. Bale, T. J. Foxon, and W. F. Gale "Multiparameter Models of Innovation Diffusion on Complex Networks" SIAM J. Appl. Dyn. Syst., 12(1), 515–532.
  36. ^ Ayres, Robert (1989). Technological Transformations and Long Waves. 
  37. ^ Marchetti, Cesare (1996). Pervasive Long Waves: Is Society Cyclotymic. 
  38. ^ Grübler, Arnulf (1990). The Rise and Fall of Infrastructures: Dynamics of Evolution and Technological Change in Transport. Heidelberg and New York: Physica-Verlag. pp. 12–25. 
  39. ^ Veneris, Yannis (1984). The Informational Revolution, Cybernetics and Urban Modelling, PhD Thesis. University of Newcastle upon Tyne, UK.
  40. ^ Veneris, Yannis (1990). "Modeling the transition from the Industrial to the Informational Revolution". Environment and Planning A 22 (3): 399–416. doi:10.1068/a220399.

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