Critical behavior of a class of nonlinear stochastic models of diffusion of information

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Abstract
A theoretical analysis based on the concepts and techniques of statistical physics is carried out for two nonlinear models of diffusion of information—one in a closed population and the other in an open one. Owing to interpersonal contacts among the members of the population, the models exhibit a cooperative behavior when a certain parameter of the problem approaches a critical value. Mathematical similarities in the behavior of the two models, in the vicinity of the critical point, are so impelling that one is tempted to investigate the corresponding behavior of a generalized model, which can be done by carrying out a systematic system-size expansion of the master equation of the process and thereby deriving a nonlinear Fokker-Planck equation for the relevant probability distribution. This establishes a broader class of systems displaying identical behavior in the critical region and also elucidates the role played by fluctuations in bringing about the cooperative phenomenon.