The Equilibria of KSIM Models: Existence, Stability, and Implications

The asymptotic behavior of the KSIM cross-impact model is investigated. A nonlinear state-variable representation of the continuous time model is developed and applied to determine conditions for the existence and stability of model equilibria. Results of this analysis confirm the empirical observation that KSIM model behavior is biased towards extremal equilibrium states, i.e., towards states in which all variables individually assume either minimum (zero) or maximum (unity) values. The implications of this result are considered. It is argued that the KSIM model is not a universally valid representational form for exploring system behavior, even for qualitative and heuristic purposes. The KSIM model is inherently inappropriate for representation of the broad class of systems exhibiting homeostasis in the usual sense, i. e., systems which tend to be stable and self-regulating at states which do not necessarily coincide with limiting conditions.