Dynamic complexity of a predator-prey model with nonlinear pulse and periodic factor

Based on an integrated pest control strategy, a class of nonlinear impulse predator-prey models with a sinusoidal function as the periodicity factor is qualitatively analyzed. Using the Comparison Theorem for Differential Equations and the Floquet Lemma, sufficient condition for the global asymptotic stability of the pest-eradication periodic solution of the system is obtained. The condition for the persistence of the system is proved through the Comparison Theorem, and the system has very complex dynamic properties when intermediate between the two conditions obtained. By using branching theory, the existence of non-trivial periodic solutions of the system is analyzed and further conditions for supercritical bifurcation are obtained, and finally the obtained conditions are verified by numerical simulations.