The diffusion of an innovation traditionally has been defined as the process by which that innovation is “communicated through certain channels over time among the members of a social system” (Rogers, 1983, p. 5). As such, the diffusion process consists of four key elements: innovation, communication channels, time, and the social system.

New Product Diffusion Models in Marketing: A Review and Directions for Research:

The diffusion theory literature offers a fairly well-developed conceptual framework for the study of communications. As developed across a number of disciplines, diffusion applies to the flow of information, ideas, and products; its uniqueness is its focus on interpersonal communication transfer. This paper offers new theoretical propositions to advance consumer diffusion research and to provide a foundation for diffusion modeling.

A Propositional Inventory for New Diffusion Research

Preface. Introduction. Part I: Overview. 1. New Product Diffusion Models: From Theory to Practice V. Mahajan, et al. Part II: Strategic, Global and Digital Environment for Diffusion Analysis. 2. Firm Strategy and Speed of Diffusion S. Kuester, et al. 3. Multi-Market and Global Diffusion M. Dekimpe, et al. 4. Innovation Adoption and Diffusion in the Digital Environment: Some Research Opportunities A. Rangaswamy, S. Gupta. Part III: Diffusion Models. 5. Modeling the Marketing Mix Influence in New Product Diffusion F. Bass, et al. 6. Diffusion Models with Replacement and Multiple Purchases B. Ratchford, et al. 7. Growth Models for Multi-Product Interactions: Current Status and New Directions B. Bayus, et al. 8. Dynamic Models Incorporating Competition R. Chatterjee, et al. 9. Disaggregate Level Diffusion Models J. Roberts, J. Lattin. 10. Operations Planning in the Presence of Innovation Diffusion Dynamics M.A. Cohen, et al. Part IV: Estimation. 11. Estimation Techniques for Macro Diffusion Models W.P. Putsis, V. Srinivasan. Part V: Applications and Software. 12. Diffusion Models: Managerial Applications and Software G.L. Lilien, et al. List of Contributors. About The Editors. References. Index.

Chapter 8 New-product diffusion models

The population dynamics underlying the diffusion of ideas hold many qualitative similarities to those involved in the spread of infections. In spite of much suggestive evidence this analogy is hardly ever quantified in useful ways. The standard benefit of modeling epidemics is the ability to estimate quantitatively population average parameters, such as interpersonal contact rates, incubation times, duration of infectious periods, etc. In most cases such quantities generalize naturally to the spread of ideas and provide a simple means of quantifying sociological and behavioral patterns. Here we apply several paradigmatic models of epidemics to empirical data on the advent and spread of Feynman diagrams through the theoretical physics communities of the USA, Japan, and the USSR in the period immediately after World War II. This test case has the advantage of having been studied historically in great detail, which allows validation of our results. We estimate the effectiveness of adoption of the idea in the three communities and find values for parameters reflecting both intentional social organization and long lifetimes for the idea. These features are probably general characteristics of the spread of ideas, but not of common epidemics.

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The power of a good idea: Quantitative modeling of the spread of ideas from epidemiological models

Preface 1. Nonlinear behavior in the physical sciences and biology: some typical examples 2. Quantitative formulation 3. Dynamical systems with a finite number of degrees of freedom 4. Linear stability analysis of fixed points 5. Nonlinear behavior around fixed points: bifurcation analysis 6. Spatially distributed systems, broken symmetries, pattern formation 7. Chaotic dynamics Appendices References Index.

Introduction to Nonlinear Science

This book is dedicated to Prof. J. Kapur and his contributions to the field of entropy measures and maximum entropy applications. Eminent scholars in various fields of applied information theory have been invited to contribute to this Festschrift, collected on the occasion of his 75th birthday. The articles cover topics in the areas of physical, biological, engineering and social sciences such as information technology, soft computing, nonlinear systems or molecular biology with a thematic coherence. The volume will be useful to researchers working in these different fields enabling them to see the underlying unity and power of entropy optimization frameworks.

Entropy Measures, Maximum Entropy Principle and Emerging Applications

A theoretical method based on the concept of “system‐sized expansion” is applied to a generalization of Bartholomew's model of diffusion of information in a population of size N. The model considers a combination of mass‐mediated and interactively mediated messages, with the provision that the spreaders of information may not remain active for an indefinite period of time; it also takes into account the possibility that the parameters governing the process be time‐dependent. Explicit expressions for the time evolution of the diffusion process (including the probability distribution of the relevant variable, its mean value and variance) are derived in the asymptotic regime N ≫ 1. The nonlinear character of the model enables us to exploit our asymptotic expressions for studying finite‐size effects as well; the resulting expressions turn out to be reliable for N as low as 10.

Stochastic evolution of a nonlinear model of diffusion of information

The dynamical behavior of domestic political hostility is modeled in terms of the interaction between hostile (challenger) and ruling (regime) groups. The conditions under which the conflict situat...

A Dynamic Model of Domestic Political Conflict Process

Diffusion of innovation occupies a central place as an instrument of social change. Numerous attempts have been made to model this phenomenon in disciplines such as economics, sociology, marketing, geography etc. Considerable research effort has been devoted to the mathematical modelling in the field, focusing mainly on temporal aspects of diffusion of innovations in the form of growth curves in a given social system. These models have been constructed within both deterministic and stochastic frameworks. Some of the recent modelling efforts have analyzed the process as an evolutionary phenomenon in the framework of self-organizing systems. Such models offer considerable insight into the dynamics of the success of an innovation in the form of niche acquisition and the self-reinforcing ’lock-in’ mechanism. The framework employed in these models makes it possible to enlarge the scope of enquiry by their ability to examine the critical phenomenon in the form of phase transformation characterizing take off and sustainability of an innovation. In this chapter we present a brief review of the literature in the field of mathematical modelling of temporal aspects of innovation diffusion.

Modelling Innovation Diffusion

A comparative study of three demographic models of urbanization is carried out and their consequences are compared with empirically validated patterns of urbanization resulting from the ‘replacement dynamics’. The United Nations projections of world urbanization over the period 1950–2000 are also found to follow the same pattern. It is noted that, with appropriate changes in the parameters of the UN model of urbanization, the predictions obtained from this modified model are much closer to reality. An interesting feature which emerges from the analysis is the constancy of the replacement rate parameter (which turns out to be a linear combination of the time-dependent demographic parameters) over a considerable length of time.

Karmeshu

Papers

Entropy Measures, Maximum Entropy Principle and Emerging Applications

Stochastic evolution of a nonlinear model of diffusion of information

A Dynamic Model of Domestic Political Conflict Process

Modelling Innovation Diffusion

Demographic Models of Urbanization