Discrete Dynamics in Nature and Society
Volume 7 (2002), Issue 3, Pages 133-149
doi:10.1155/S102602260200016X

Stimulus, expectations, desires and response strategies: The building blocks of nonlinear interaction dynamics

Abstract

Stimulus and response functions, as the fundamental blocks of nonlinear interaction dynamics, are analyzed and modeled here, under a variety of interaction strategies. The backbone of the suggested model is a simple iterative dynamical formulation: the magnitude of a signal sent at present is a function of a relevant signal sent—as well as of a signal received—in the past; in turn, a signal received at present is a function of a signal received—as well as of a signal sent—in the past; namely,Ss(n+1)=fs{Ss(n)Sr(n)}    and   Sr(n+1)=fr{Sr(n)Ss(n)} where Ss/r is the size of a signal sent/received, and n is a point in time.Expectations and desires by senders and receivers of signals are introduced in the analysis. As a result, a basic classification of individuals emerges, that of “dreamers” and “cynics.” Three fundamental response strategies are identified, all plays on a theoretically Newtonian action–reaction system. A pair of individual, as well as community, interaction end-states are the focus of the analysis here; their stability properties, under a tit-for-tat response strategy, are studied and their likelihood to occur is considered.