Transcritical Bifurcation and Flip Bifurcation of a New Discrete Ratio-Dependent Predator-Prey System

After a discrete two-species predator-prey system with ratio-dependent functional response is topologically and equivalently reduced, some new dynamical properties for the are formulated. The one existence local stability all equilibria of this system. Although corresponding results equilibrium $$E_3$$ have been presented in known literature, our more complete. other is, what’s important difficult, to derive sufficient conditions transcritical bifurcation period-doubling at $$E_1$$ , $$E_2$$ occur, which completely new. Numerical simulations performed not only illustrate theoretical obtained but also find dynamics—chaos occuring. Our sufficiently display that very sensitive its parameters. Namely, perturbations different parameters will produce bifurcations.