Qualitative Structures Near a Degenerate Fixed Point of a Discrete Ratio-Dependent Predator–Prey System

This paper investigates the qualitative structures of a discrete ratio-dependent predator–prey model near a degenerate fixed point whose eigenvalues are \(\pm 1\) $\pm 1$ . By the normal form theory, Picard iteration and Takens’s theorem, this model is transformed into an ordinary differential system. Then the qualitative structures of this differential system near the highly degenerate equilibrium are analyzed with the blowing-up method, which yields the ones of the discrete model near the fixed point by the conjugacy between the discrete model and the time-one mapping of the vector field.