Stability and bifurcation of a reaction-diffusion predator-prey model with non-local delay and Michaelis-Menten-type prey-harvesting

作者：Zhang, Xuebing; Zhao, Hongyong^*

来源：International Journal of Computer Mathematics, 2016, 93(9): 1447-1469.

DOI：10.1080/00207160.2015.1056169

• non-local delay
• stability
• Hopf bifurcation
• harvesting
• global stability

We investigate a reaction-diffusion predator-prey system with homogeneous Neumann boundary conditions and non-local delay due to predator gestation. By analysing the corresponding characteristic equations, we establish the local stability of the positive steady state. We also discuss the existence of Hopf bifurcations at the positive steady state. We derive sufficient conditions for the global stability of the positive steady state of the proposed problem using the Lyapunov functional. Numerical simulations illustrate the results and reveal that as the discrete delay tau increases, the species may tend to extinction. Changes in the harvesting effort E and non-local delay beta can transform an unstable system into a stable one.

• 出版日期2016
• 单位南京航空航天大学