一类具有恐怖因子和羊群效应的捕食者–食饵模型的动力学行为

Dynamic Behavior of a Predator-Prey Model with Fear Factor and Herding Effect

在生物种群中,由于食饵会对天敌的捕食产生恐惧,所以他们会降低自身出生率来抵抗捕食者的捕抓,针对这一情况研究了一类具有恐怖因子和羊群效应的捕食者–食饵模型,首先证明了解的一致有界性;然后由Routh-Hurwitz准则讨论了系统平衡点的存在性和存在时平衡点的类型,以及稳定性;并且根据Poincare’-Andronov-Hopf分支定理得到了系统产生Hopf分支的条件。最后,通过Matlab软件仿生所得到的定理,并得出了只要选取恰当的参数便可使系统中的两类种群一直稳定存在下去的结论。

In the biological population, the prey will be afraid of the predator, so they will reduce their own natality to prevent being caught. Considering this situation, a predator-prey model with fear factor and herd effect is studied. Firstly, we discuss uniform boundedness of this model. Then Routh-Hurwitz criterion is used to discuss the existence of the equilibrium point of the system, the type of the equilibrium point and its stability. Moreover, according to the Poincare’-Andronov-Hopf branch theorem, conditions for the generation of Hopf branch were obtained. Finally, the theoretical results are verified by numerical simulation, and a conclusion is drawn that the predator and the prey in the system can be kept stable as long as appropriate parameters are chosen.