具有B-D功能反应项和不连续收获的分数阶捕食食饵模型动力学分析

DynamicAnalysis of a Fractional Order Predation Model with B-D Functional Response Terms and Discontinuous Harvest

为了研究一类具有Beddington DeAnglis(B-D)功能反应项和不连续收获的分数阶捕食食饵模型,文中分析了系统的非负性和有界性,利用分数阶微分方程的李雅普诺夫函数法讨论了正平衡点的存在性和稳定性,利用Matlab模拟不同初值和不连续收获函数对系统解的影响。研究发现:系统在满足相应的初始条件下的解是非负且有界的,并给出了正平衡点存在和稳定的一些条件,且不连续收获项可能会导致系统出现周期解情况。

The paper studies a fractional predator model with Beddington DeAnglis(B-D)functional response terms and discontinuous harvest.The non negativity and boundedness of the system are analyzed.The existence and stability of the positive equilibrium point are discussed by the Lyapunov function method of the fractional differential equation.Finally,Matlab is used to simulate the effect of different initial values and discontinuous harvest functions on the solutions of the system.It is found that the solutions of the system are non negative and bounded when the corresponding initial conditions are satisfied.Some conditions for the existence and stability of positive equilibrium points are given,and discontinuous harvesting terms may lead to a periodic solution in the system.