Nonlinear Analysis on the Dynamical Model of Common Fishery Resource

摘要

In this paper, we formulate a dynamical model of common fishery resource harvested by multi-agents with heterogeneous rationality. We study the existence and stability of the positive equilibrium characterizing the sustainable use of the renewable resource. Then we investigate the local bifurcations of the system. Finally we show the influence of the adjusting speed for the harvesting quantity on the set of initial conditions which give non-negative trajectories converging to an equilibrium (called feasible set) though numerical simulation. When the players accelerate the adjusting speed in order to achieve initial advantage, we discover that it may cause instability of system and make the system sink into the chaotic state, and may lead to shrinkage of feasible set and thus make the resources extinct more easily.