具有密度依赖的 Monod-Haldane 反应项的捕食模型共存解的存在性

摘要

文中研究了一类带有密度依赖项的Monod-Haldane反应项的捕食-食饵模型正平衡解的存在性、分歧和稳定性。利用极值原理、上下解方法、锥映射不动点指数得到平衡态方程正解存在的充分条件；利用局部分歧理论给出了分歧解的存在性，利用特征值谱分析法给出了正解的稳定性；通过数值模拟的方法研究了一维方程的平衡态解，验证了文中平衡解的所有结论的正确性，并使方程组的解可视化。%The existence ,bifurcation and stability of the positive steady-state solutions to the prey-predator model with ratio-dependent Monod-Haldane Response function are discussed .First ,by applying the maximum principle ,the low er-upper solution method and the index of fixed point of the compact map in cone ,the sufficient conditions for the existence of nonnegative steady-state solutions are obtained . Second ,the existence of the bifurcation solutions is obtained by the local bifurcation theory ,and the stability of the coexistence solutions is proved by the spectrum analysis of operators .Finally ,under the one-dimensional condition ,all the theorems ,including the existence ,bifurcation and the stability of the positive steady-state solutions to the prey-predator model ,are proved to be correct .And the solutions to the partial differential equations are visualized by the numerical simulation .