一类植物-草食动物扩散系统的动力学分析  

Dynamic Analysis of a Class of Plant-Herbivore Diffusion System

作　　者：麻晓琦 赵治涛[1] MA Xiaoqi;ZHAO Zhitao(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：《吉林大学学报（理学版）》2021年第5期1057-1065,共9页Journal of Jilin University:Science Edition

基　　金：国家自然科学基金(批准号:11201128);黑龙江省自然科学基金(批准号:LH2019A022).

摘　　要：考虑一类植物-草食动物扩散系统的动力学性质.首先,用上下解方法和抛物方程的比较定理,证明该系统解的全局存在性、耗散性和持续性;其次,基于椭圆算子主特征值理论和Lyapunov函数方法,给出常值稳态解的存在性、局部和全局渐近稳定性,并建立系统产生图灵不稳定的判别准则;最后,通过数值模拟验证所得结果的有效性.We considered the dynamical properties of a class of plant-herbivore diffusion system.Firstly,we proved the global existence,dissipation and persistence of the solutions of system by using the method of upper and lower solutions and the comparison theorem of parabolic equations.Secondly,based on the principle eigenvalue theory of elliptic operator and Lyapunov function method,we gave the existence,the local and global asymptotic stability of constant steady state solutions,and established the criterion of the Turing instability of the system.Finally,the effectiveness of results was verified by some numerical simulations.

关 键 词：植物-草食动物扩散系统 常值稳态解 LYAPUNOV函数 图灵不稳定 数值模拟 

分 类 号：O175.21[理学—数学]