一类比率依赖种群模型在常数收获下的分岔

Bifurcations of a ratio-dependent population model with constant rate harvesting

利用微分方程定性理论以及规范型理论研究了一类具有常数收获项的生物模型.首先,考虑常数收获项对该模型非负平衡点的影响,讨论平衡点的稳定性情况.其次,选取常数收获项作为参数,给出系统存在鞍结点分岔、Hopf分岔以及极限环的充分条件.进一步地,考虑双参数分岔,给出系统存在余维2的Bogdanov-Takens分岔的充分条件.结果表明,由于添加了常数收获项,系统具有丰富的动力学行为.最后,通过数值仿真验证了所得结果的正确性.

This paper investigates a class of biological model with constant rate harvesting by using the qualitative theories of differential equations and theories of normal form.Firstly,considering the effect of constant rate harvesting on the nonnegative equilibria of the model,the problem of stability of the equilibria is discussed.Secondly,choosing the constant rate harvesting as the bifurcation parameter,the sufficient conditions of existence for the saddle node bifurcation,the Hopf bifurcation and the limit cy...