一类具有B-D功能反应项的捕食系统的定性分析

(西安工业大学 理学院,西安 710021

周期解; 持续生存; 脉冲; 混沌

Qualitative Analysis of the Predator-Prey Model with B-D Functional Response
LI Changtong,FENG Xiaozhou

(School of Science,Xi'an Technological University,Xi'an 710021,China)

periodic solution; permanence; impulse; chaos

DOI: 10.16185/j.jxatu.edu.cn.2020.01.001 http://xb.xatu.edu.cn

备注

为了解决害虫防防治策略因农业资源有限引起的非线性影响,文中对具有非线性脉冲控制的捕食系统进行了定性分析.利用脉冲微分方程中的Floquet理论,证明了当脉冲周期小于某临界值时,系统的害虫根除周期解是局部渐近稳定的,并利用分支理论得到非平凡周期解的存在性的条件.数值上验证了具有非线性脉冲的系统有非常丰富的动力学性质.

Pest control strategies are inevitably affected by limited agricultural resources, in order to simulate the nonlinear effect since the resource limitation.The predator-prey system with B-D functional response is proposed and analyzed.It is proved that there exists a local stable pest-free periodic solution when impulsive period is less than a certain critical value.The existence of nontrivial periodic solution is established on the bifurcation theory.The numerical results show that the system with limited resource has complex dynamical behavior.