毒素影响下捕食种群具有脉冲投放的捕食系统的动力学研究

Dynamical Research of a Predator-Prey System of Predator Population with Impulse Release Rate under Toxin Influence

摘要: 本文建立毒素影响下捕食者具有脉冲投放的捕食–食饵模型，并运用Bendixson-Dulac定理、Poincaré-Bendixson定理等方法分析了无脉冲系统的全局动力学；接着证明了不同条件下阶一周期解的存在性与唯一性；其次利用类Poincaré准则，得到了阶一周期解稳定的条件；最后，分别选取不同的脉冲系数、阈值以及毒素系数，讨论不同参数对鱼类的可持续发展的影响，最后数值仿真结果验证了结论的合理性。

Abstract: In this paper, we establish a predator-prey model with a constant feeding rate of predators under the influence of toxins. The existence of the equilibrium point and the stability of the positive equilibrium point of the system are studied, combined with the theory of pulsed differential equa-tions. The pulse control of the pulseless system is carried out according to the actual situation, the persistence of the predation system is discussed, and the uniqueness of the order 1 periodic solu-tion of the system is proved by the following function method and interval set theorem, and finally, the conclusion is verified by numerical simulation.