一类有平方根功能反应、食饵避难及互相干扰的脉冲食物链系统研究(英文)

An Impulsive Food Chain System with Square Root Functional Response and Both Prey Refuge and Mutual Interference

本文构建一类具有平方根功能反应,食饵避难与捕食者相互干扰的脉冲食物链系统;证明系统的一致有界性;利用小振幅扰动技术,弗洛凯理论和比较定理,研究食饵和顶端捕食者灭绝周期解的存在性和全局渐进稳定性;通过构造李雅普诺夫函数,得到系统持久的充分条件;然后通过数值模拟验证了理论结果,进一步揭示了系统复杂的动力学性质;最后分析所得结果的生物意义,并就相关控制策略提出了一些可行的意见与建议.

In this paper, an impulsive food chain system with square root functional response, prey refuge and mutual interference for predator is constructed. We show that this system is uniformly bounded. By using small perturbations skills, Floquet theory and comparison theorem, we investigate the existence and globally asymptotical stability of the prey and top predator-eradication periodic solution. Moreover, we obtain sufficient conditions for the system to be permanent via the comparison theorem and multiple Lyapunov functions. Numerical simulations are given to portray the complex behaviors of this system. Finally, we analyze the biological meanings of these results and give some suggestions for feasible control strategies.