Theoretical and numerical bifurcation analysis of a predator–prey system with ratio-dependence

The present paper investigates the critical normal form coefficients for the one-parameter and two-parameter bifurcations of a two-dimensional discrete-time ratio-dependence predator–prey model. The discrete-time ratio-dependence predator–prey model exhibits the period-doubling, Neimark-Sacker, and strong resonance bifurcations. Based on the critical coefficients, it can be determined which scenario corresponds to each bifurcation. This paper investigates the complex dynamics of the model numerically by using MatcotM which is a MATLAB package.