Stimulus, expectations, desires and response strategies: The building blocks of nonlinear interaction dynamics (Q1777561)

Summary: 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, \[ S_s(n+1)=f_s\bigl\{S_s (n)S_r(n)\bigr\}\quad\text{and}\quad S_r (n+1)=f_r\bigl\{S_r(n)S_s(n)\bigr\} \] 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.