Bifurcations and periodic solutions for an algae-fish semicontinuous system. (English) Zbl 1470.34115

Summary: We propose an algae-fish semicontinuous system for the Zeya Reservoir to study the control of algae, including biological and chemical controls. The bifurcation and periodic solutions of the system were studied using a Poincaré map and a geometric method. The existence of order-1 periodic solution of the system is discussed. Based on previous analysis, we investigated the change in the location of the order-1 periodic solution with variable parameters and we described the transcritical bifurcation of the system. Finally, we provided a series of numerical results to illustrate the feasibility of the theoretical results. These results may help to facilitate a better understanding of algal control in the Zeya Reservoir.


34C25 Periodic solutions to ordinary differential equations
34A36 Discontinuous ordinary differential equations
34C60 Qualitative investigation and simulation of ordinary differential equation models
92D40 Ecology
34A37 Ordinary differential equations with impulses
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