具有交错扩散和恐惧效应的捕食系统解的性质  

The properties of solutions for predator-prey system with cross-diffusion and fear effects

作　　者：张莹 邢慧 ZHANG Ying;XING Hui(School of Science,Xi’an Polytechnic University,Xi’an 710048,China)

机构地区：[1]西安工程大学理学院,陕西西安710048

出　　处：《青海师范大学学报(自然科学版)》2024年第4期53-61,共9页Journal of Qinghai Normal University(Natural Science Edition)

基　　金：国家自然科学基金项目(11626182);陕西省自然科学基金项目(2021JQ-662)。

摘　　要：研究一类在Neumann边界条件下食饵具有恐惧因子、Allee效应和保护区的非线性交错扩散捕食-食饵系统的稳态问题.首先运用最大值原理、椭圆正则性理论和Sobolev嵌入定理得到了稳态解的先验估计.其次通过线性稳定性分析,确定了平凡解和捕食者灭绝的边界平衡点的局部稳定性.然后利用局部分歧理论,证明了系统在捕食者灭绝的边界平衡点处发生跨越式分歧,得到了正解的存在性.最后应用单边全局分歧理论,证明了系统从捕食者灭绝的边界平衡点处发生的全局分歧.并且进一步讨论了Allee效应常数和食饵扩散系数对该系统平衡态正解的渐近行为的影响.结果表明:非线性交错扩散项、恐惧效应和Allee效应共同促进食饵和捕食者的稳定共存.The steady-state problem of a nonlinear cross-diffusion predator-prey model with fear factor,Allee effect and protection zone under Neumann boundary conditions is studied.Firstly,a prior estimate of the steady-state solutions is obtained by using the maximum principle,elliptic regularity theory and Sobolev embedding theorem.Secondly,the local stability of trivial solutions and the semi-trivial solutions of predator extinction is given by linear stability analysis.Thirdly,by using the local bifurcation theory,it is proved that the system has transcritical bifurcation at the boundary equilibrium point of predator extinction.Finally,by applying uniateral global bifurcation theory,the global bifurcation of the system from the boundary equilibrium point of predator extinction is proved.The influence of Allee effect constant and prey diffusion coefficient on the asymptotic behavior of the equilibrium positive solutions of the system is further discussed.The results show that the nonlinear cross-diffusion term,fear effect and Allee effect can jointly promote the stable coexistence of prey and predators.

关 键 词：捕食-食饵系统 非线性交错扩散 保护区 ALLEE效应 恐惧因子 

分 类 号：O175.2[理学—数学]