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Dynamics analysis of a non-smooth Filippov pest-natural enemy system with time delay

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Abstract

In this paper, we propose a non-smooth Filippov system that describes the interaction of the pest and natural enemy with considering time delay, which represents the change in the growth rate of natural enemies before it is released to prey on pests. When the number of the pest is below the threshold, no control is applied; otherwise, control measures will be adopted. We discuss the stability of the equilibria and the existence of Hopf bifurcation. The results show that the Hopf bifurcation occurs when the time delay passes through some critical values. By applying the Filippov convex method, we obtain the dynamics of the sliding mode. The solutions of the system eventually tend toward the regular equilibrium, the pseudo-equilibrium or a standard periodic solution. Numerical simulations show that time delay plays an important role in local and global sliding bifurcations. We can obtain boundary focus bifurcations from boundary node bifurcations by varying time delay. Furthermore, touching, buckling and crossing bifurcations can be obtained frequently by increasing time delay. The results can provide some insights in pest control.

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  1. School of Mathematics and Statistics, Shandong Normal University, Jinan, 250014, People’s Republic of China

    Hui Wang & Youping Yang

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  1. Hui Wang
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  2. Youping Yang
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Correspondence to Youping Yang.

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Wang, H., Yang, Y. Dynamics analysis of a non-smooth Filippov pest-natural enemy system with time delay. Nonlinear Dyn 111, 9681–9698 (2023). https://doi.org/10.1007/s11071-023-08332-x

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