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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.

MSC:

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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