一类具有非线性捕获项的捕食-食饵扩散模型正解的稳定性和唯一性

Stability and Uniqueness of Positive Solutions for a Diffusive Predator-prey Model with Nonlinear Harvesting

研究了一类具有非线性捕获项和Crowley-Martin反应函数的捕食-食饵扩散模型.利用不动点指数理论得到了正解存在的充分条件.其次,采用线性算子的扰动理论、椭圆方程正则性理论和不动点指数理论考察了捕食者间干扰强度的影响,给出了正解的稳定性和唯一性.接着,运用比较原理讨论了抛物系统的灭绝性和全局吸引子的存在性.最后,通过数值模拟验证和补充了理论结果.研究结果表明捕食者间的干扰强度和捕获率对种群的共存具有非常重要的影响.

A diffusive predator-prey model with nonlinear harvesting and Crowley-Martin functional response is studied.By the fixed point index theory,the suficient conditions for the existence of positive solutions are obtained.Secondly,the effect of the magnitude of interference among predators is investigated by the combination of the linear operator perturbation theory,standard elliptic equations regularity theory and fixed point index theory,and the stability and uniqueness of positive solutions are determined.In addition,we discuss the extinction and existence of global attractor of the time-dependent system by means of the comparison principle.Finally,we make some numerical simulations to validate and complement the theoretical analysis.The findings suggest that the the magnitude of interference among predators and harvesting efforts have important effects on the coexistence of both species.