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Qualitative analysis on a diffusive predator-prey model with toxins
Journal of Mathematical Analysis and Applications ( IF 1.3 ) Pub Date : 2020-06-01 , DOI: 10.1016/j.jmaa.2020.123868
Xiao Yan , Yanling Li , Gaihui Guo

Abstract This paper is concerned with the diffusive predator-prey model with toxins subject to Dirichlet boundary conditions. The uniform persistence of positive solution is given under certain conditions. In addition, by the Liapunov-Schmidt method, the existence and stability of the bifurcation solution from a double eigenvalues are investigated. Moreover, by the fixed point index theory and perturbation theory of eigenvalues, the uniqueness, stability and multiplicity of coexistence states are analyzed when some key parameter changes. Finally, some numerical simulations are presented to verify the theoretical conclusions and further to reflect the importance of parameters to the number of coexistence states.

中文翻译:

含毒素的扩散捕食-猎物模型的定性分析

摘要 本文研究了受狄利克雷边界条件约束的具有毒素的扩散捕食者-猎物模型。正溶液的均匀持久性是在一定条件下给出的。此外,通过Liapunov-Schmidt方法,研究了双特征值分岔解的存在性和稳定性。此外,通过特征值的不动点指数理论和微扰理论,分析了当一些关键参数发生变化时共存状态的唯一性、稳定性和多重性。最后,给出了一些数值模拟来验证理论结论,并进一步反映参数对共存态数量的重要性。
更新日期:2020-06-01
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