Dynamics of coupled nonlinear maps and its application to ecological modeling

摘要

This paper investigates the behavior of coupled nonlinear dynamical systems. We take two such dynamical systems (or units), couple them together, and study the effect of coupling on the dynamics. We demonstrate that coupling two chaotic units can indeed stabilize both of them. Several results describing the global dynamics of the coupled nonlinear system are established. Using them, we show that, by-and-large, the presence of coupling appears to increase the orderliness of the coupled system's response, producing periodicity, synchronicity, and quasi-symmetry. Using exponential maps which are commonly used to simulate-population dynamics, we establish the applicability of our results to population dynamics.