一类植物-草食动物扩散系统的动力学分析

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.

Dynamic Analysis of a Class of Plant-Herbivore Diffusion System

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.