带有时滞和非线性收获效应的捕食者-食饵系统的空间动力学

Spatial Dynamics in Predator-Prey System with Time Delay and Nonlinear Harvesting Effect

考虑一类带有时滞和非线性食饵收获效应的捕食者-食饵系统的空间动力学行为,先利用稳定性理论和分支理论得到Hopf分支和Turing分支的条件,再通过数值模拟展示系统存在丰富的动力学行为.数值结果表明,时滞和扩散不仅能影响点状、条状以及点条共存的Turing斑图的形成,而且还影响螺旋波斑图的形成.

We considered the spatial dynamic behavior of a predator-prey system with time delay and nonlinear prey harvesting effect.First,we obtained the condition of Hopf bifurcation and Turing bifurcation by using stability theory and bifurcation theory,and then numerical simulations show that the system has rich dynamic behavior.Numerical results show that time delay and diffusion can not only affect the formation of Turing patterns,such as spot,stripe and the coexistence of the two types,but also affect the formation of spiral patterns.