具有阶段结构、时滞和捕获的渔业捕食系统动力学分析

Dynamic analysis of fishery predation system with stage structure,time delay and capture

通过假设两个捕食者以不同速度捕食同一类食饵,建立了具有阶段结构、时滞和捕获的渔业捕食-食饵模型,得到平凡平衡点、捕食者灭绝平衡点以及捕食者和食饵共存平衡点,并分析了这些平衡点的稳定性.结果表明:当捕获量大于某临界值时,捕食者灭绝平衡点渐近稳定;当捕获量小于此临界值时,捕食者和食饵共存平衡点存在.以时滞τ为分支参数,运用Hopf分支理论,在一定条件下得到当τ<τ_(0)时捕食者和食饵共存平衡点是局部渐近稳定的;当τ>τ_(0)时捕食者和食饵共存平衡点不稳定,即当τ经过临界值τ_(0)时系统出现Hopf分支;当τ过大时,系统的行为会变得极其复杂.MATLAB数值仿真验证了结论的正确性.

A fishery predator-prey model with stage structure, time delay and capture is established by assuming that two predators prey on the same type of prey at different speeds. The trivial equilibrium, predator extinction equilibrium and the coexistence equilibrium of predator and prey are obtained, and the stability of these equilibrium points is analyzed. The results show that the predator extinction equilibrium is asymptotically stable when the capture is greater than a critical value. When the capture is less than this critical value, the coexistence equilibrium point of predator and prey exists. Taking the time delay τ as the bifurcation parameter and using Hopf bifurcation theory, it is obtained that the coexistence equilibrium point of predator and prey is locally asymptotically stable when τ<τ_(0). When τ>τ_(0), the equilibrium point of the coexistence of predator and prey is unstable, that is, when τ passing the critical value τ_(0), the system appears Hopf bifurcation. When the time delay τ is too large, the behavior of the system will become extremely complex. MATLAB numerical simulation verifies the correctness of the conclusion.