Fractal Dependence on Initial Conditions of Coupled Inverted Pendula Model of Competition and Cooperation

抄録

A coupled inverted pendula model of competition and cooperation is proposed to obtain a purely mechanical implementation of dynamics comparable with the Lotka-Volterra competition dynamics. It is shown numerically that the proposed model can produce the four equilibria that can be compared to ecological coexistence, dominance, and scramble. It is also shown that the proposed model exhibits fractal dependence on initial conditions. The result implies that selection of the equilibria will be uncertain under finite accuracy of knowledge on initial conditions.