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

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, S s ( n + 1 ) = f s { S s ( n ) S r ( n ) } and S r ( n + 1 ) = f r { S r ( n ) S s ( n ) } where S s / 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.