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Codimension-2 bifurcation analysis and control of a discrete mosquito model with a proportional release rate of sterile mosquitoes. (English) Zbl 1445.92292

Summary: This paper concerns a discrete wild and sterile mosquito model with a proportional release rate of sterile mosquitoes. It is shown that the discrete model undergoes codimension-2 bifurcations with \(1:2\), \(1:3\), and \(1:4\) strong resonances by applying the bifurcation theory. Some numerical simulations, including codimension-2 bifurcation diagrams, maximum Lyapunov exponents diagrams, and phase portraits, are also presented to illustrate the validity of theoretical results and display the complex dynamical behaviors. Moreover, two control strategies are applied to the model.

MSC:

92D40 Ecology
92D25 Population dynamics (general)
34H20 Bifurcation control of ordinary differential equations
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