一类比率依赖的捕食者-食饵扩散系统的动力学性质分析  

Dynamical analysis in a diffusive predator-prey model with ratio-dependent functional response

作　　者：陈美瑶 魏新 CHEN Meiyao;WEI Xin(School of Mathematical Sciences,Heilongjiang University,Harbin 150080,China)

机构地区：[1]黑龙江大学数学科学学院,哈尔滨150080

出　　处：《黑龙江大学自然科学学报》2024年第3期288-301,共14页Journal of Natural Science of Heilongjiang University

基　　金：国家自然科学基金资助项目(11901172);黑龙江省省属高等学校基本科研业务费项目(2022-KYYWF-1043,2021-KYYWF-0017)。

摘　　要：研究了一类具比率依赖型功能反应的捕食者-食饵系统的时空动力学行为。为了探讨食饵的内禀增长率和扩散系数比值对系统动力学性质的影响,进行了以下分析:平衡解的稳定性分析;Hopf分支、Turing分支和Turing-Hopf分支出现的充分条件;Turing-Hopf分支点附近规范型的推导和计算。结果表明,食饵内禀增长率和扩散系数比值的微小变化会破坏系统常值稳态解的稳定性,引起复杂的时空行为,包括空间齐次周期解、空间非齐次周期解和非常值稳态解。此外,结合数值模拟对理论分析的结果进行了解释,数值模拟的结果和理论分析完全吻合。The spatiotemporal dynamics of a predator-prey model with ratio-dependent functional responses has been studied.To explore the joint effect of prey growth rate and the ratio of diffusion coefficients on the dynamics of the system,the following analyses are performed,including the stability analysis of constant steady states;sufficient conditions for the occurrence of Hopf bifurcation,Turing bifurcation,and Turing-Hopf bifurcation;the derivation and calculation of the normal form near the Turing-Hopf singularity.The results demonstrate that the small change in prey growth rate and the ratio of diffusion coefficients can destabilize the constant steady states,and lead to the complex spatiotemporal behaviors,including spatially homogeneous and spatially inhomogeneous periodic solutions,and non-constant steady states solutions.The numerical simulations to demonstrate the theoretical analysis are provided,and the numerical simulations coincide with our theoretical results.

关 键 词：Turing-Hopf分支 HOPF分支 比率依赖 捕食者-食饵系统 

分 类 号：O193[理学—数学]