School of Mathematics and Information Science, Guangzhou University, Guangzhou, People's Republic of China.
Center for Applied Mathematics, Guangzhou University, Guangzhou, People's Republic of China.
J Biol Dyn. 2020 Dec;14(1):421-437. doi: 10.1080/17513758.2020.1772999.
In this paper, we consider a nonautonomous predator-prey system with Beddington-DeAngelis functional response and explore the global stability of boundary solution. Based on the dynamics of logistic equation, some new sufficient conditions on the global asymptotic stability of boundary solution are presented for general time-dependence case. Our main results indicate that (i) the long-term ineffective predation behaviour or high mortality of predator species will lead the predator species to extinction, even if the intraspecies competition of predator species is weak or no intraspecies competition; (ii) the long-term intense intraspecific competition may lead the predator species to extinction, even though the long-term accumulative predation benefit is higher than the death lose. When all parameters are periodic functions with common period, a necessary and sufficient condition on the global stability of boundary periodic solution is obtained. In addition, some numerical simulations are performed to illustrate the theoretical results.
本文考虑了一个具有 Beddington-DeAngelis 功能反应的非自治捕食者-被捕食者系统，并探讨了边界解的全局稳定性。基于 logistic 方程的动力学，我们针对一般的时变情况，给出了边界解全局渐近稳定性的一些新的充分条件。我们的主要结果表明：（i）长期无效的捕食行为或捕食者物种的高死亡率将导致捕食者物种灭绝，即使捕食者物种的种内竞争较弱或不存在种内竞争；（ii）长期激烈的种内竞争可能导致捕食者物种灭绝，即使长期累积的捕食收益高于死亡损失。当所有参数都是具有公共周期的周期函数时，得到了边界周期解全局稳定性的一个充分必要条件。此外，还进行了一些数值模拟以说明理论结果。
