非线性出生率对双斑块模型动力学行为的影响

考虑一类具有非线性出生率的单种群双斑块扩散模型，研究非线性出生率和扩散对生物种群的影响.探讨系统平衡点的存在性、局部稳定性和全局稳定性，运用数值模拟分析非线性出生率和扩散常数D₁、D₂对种群动力学的影响.研究结果表明，在一些适当的假设下，绝灭平衡点或唯一正平衡点可能全局渐近稳定，且非线性出生率和扩散会使得两个斑块内种群持久生存或灭绝.通过数值模拟，当出生率(a₁)增大或密度依赖系数(A)减小时，种群总密度会增加.当D₁减小或D₂增大时，种群总密度也会增加.以上结果表明，物种的出生率和扩散对系统动力学行为起重要的作用.

Influence of nonlinear birth rate on dynamic behavior of a two-patch model

In this paper, a two-patch model with nonlinear birth rate is considered, and the influence of nonlinear birth rate and dispersal is studied. The existence and stability of equilibrium of the system is discussed. The influence of nonlinear birth rate and dispersal rate is simulated. We show that under some suitable assumptions, the extinction or the unique positive equilibrium may be globally asymptotically stable. Dispersal and nonlinear birth rate can lead to the persistence or extinction of the population in both patches. Combining mathematical analysis with the numerical simulation, we verify that the total population density will increase when a increases or A decreases. And the total population abundance increases when the dispersal rate decreases or the dispersal rate increases. The above results indicate that the birth rate and dispersal of species play important role on the dynamic behaviors of the system.