具有非单调功能性反应的捕食系统的定性分析

Qualitative Analysis for Predator-Prey Systems with Simplified Holling Type-Ⅳ Functional Response

研究了捕食者自身设限、食饵具有非单调功能性反应的捕食系统.在全参数空间内系统的定性分析表明,系统具有复杂的动力学行为,包括全局稳定、双稳定等.变化参数可使得系统没有极限环、存在1个或者2个极限环,而最多可以从Hopf分支产生出2个极限环,并给出了相应的数值模拟.

A predator-prey model with simplified Holling type-Ⅳ functional response and predator＇s numerical response was considered. The qualitative analysis of the model depending on all parameters indicates that the model exhibits complicated dynamical phenomenon, such as a global attractor, two attractors etc. It is shown that there exist different parameter values for which the model has none limit cycle, one limit cycle, or two limit cycles, respectively and the model can have at most two limit cycles bifurcated from Hopf bifurcation. Some computer simulation was presented to illustrate the conclusions by XPPAUT.