Two-dimensional nonlinear dynamic system model of interspecific interaction and numerical simulation research on it

Abstract

The mechanism and the course of two-dimensional nonlinear dynamic system of interspecific interaction were dealt with systematically. By extending the Lotka-Volterra model from the viewpoint of biomechanics, it developed new models of two-dimensional nonlinear autonomous and nonautonomous dynamic systems, with its equilibrium point's stability and the existence and stability of its periodical solutions analyzed, and did numerical simulation experiments on its dynamics course. The results show that efficiency of interaction between two populations, time-varying effort, and change direction of action coefficient and reaction coefficient have important influences on the stability of dynamic system, that too large or too small interspecific interaction efficiency and contrary change direction of action coefficient and reaction coefficient may result in the nonstability of the system, and thus it is difficult for two populations to coexist, and that time-varying active force contributes to system stability.