Discrete Dynamics in Nature and Society
Volume 7 (2002), Issue 3, Pages 133-149

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

Dimitrios S. Dendrinos

School of Architecture and Urban Design, The University of Kansas, Lawrence 66045-2250, KS, USA

Received 13 March 2001

Copyright © 2002 Dimitrios S. Dendrinos. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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)}andSr(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.