不同理性两个体捕捞公共渔业资源的非线性分析

Nonlinear Analysis of Common Fishery Resource Competed by Two Players with Heterogeneous Expectations

在假设不同理性两个体博弈公共渔业资源的基础上,建立了不同理性两个体捕捞渔业资源的模型,重点研究了该系统不动点的存在性和稳定性,并且通过数值模拟分析了该系统在不同参数下的动态行为,研究发现:当市场参与者为了使自己在竞争中处于有利位置,加快捕捞调整速度时,就会使系统出现复杂的动力学行为,即可能出现Neimark分叉和反向的倍周期分叉.资源储量可能出现不可预测的准周期波动甚至随机的混沌波动.

This paper builds a duopoly game model with heterogeneous expections on the basis of assuming that two players with different expections harvest fish from a common fish ground. We mainly study the existence and stability of this system＇s positive equilibria,and analyze the dynamics in different parameters through numerical simulation. We discover that ,when the players accelerate the adjustment speed of harvesting fish in order to make oneself win in the competition,it may lead to complicated dynamics such as the Neimark or flip （double period） bifurcations. Thus the fishery resources may unpredictably fluctuate in a semi-periodic form or a chaotic form.