独特性
捕食
单调多边形
稳态(化学)
功能性反应
Dirichlet边界条件
应用数学
不动点指数
理论(学习稳定性)
最大值原理
捕食者
消光(光学矿物学)
数学
数学分析
边界(拓扑)
边值问题
数学优化
物理
计算机科学
最优控制
古生物学
化学
几何学
物理化学
机器学习
生物
光学
作者
Xiao Yan,Yanling Li,Yane Wang
标识
DOI:10.1142/s0218127420502247
摘要
This paper is dedicated to a study of a diffusive one-prey and two-cooperative-predators model with C–M functional response subject to Dirichlet boundary conditions. We first discuss the existence of positive steady states by the fixed point index theory and the degree theory. In the meantime, we analyze the uniqueness and stability of coexistence states under conditions that one predator’s consumer rate is small and the effect of interference intensity of another predator is large. Then, steady-state bifurcations from two strong semi-trivial steady states (provided that they uniquely exist under some conditions) and from one weak semi-trivial steady state are investigated in detail by the Crandall–Rabinowitz bifurcation theorem, the technique of space decomposition and the implicit function theorem. In addition, we study the asymptotic behaviors including the extinction and permanence of the time-dependent system by the comparison principle, upper-lower solution method and monotone iteration scheme. Finally, numerical simulations are done not only to validate the theoretical conclusions, but also to further clarify the impacts of parameters on the three species.
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