Fold-flip and strong resonance bifurcations of a discrete-time mosquito model

In this paper we consider a two-dimensional discrete-time mosquito model, in which sterile mosquitoes are released into the wild at a nonlinear saturated rate. By reducing the discrete model into different normal forms, we prove that there exists a series of bifurcations of codimension two, including fold-flip bifurcation and strong resonance bifurcations (1:1, 1:2), when the values of two parameters vary. To verify theoretical analyses and confirm the chaotic behaviors of the discrete-time mosquito model, the bifurcation diagrams, phase portraits, time-series diagrams and maximum Lyapunov exponents diagrams are also showed for some special cases.