The stability of a degenerate fixed point for Guzowska–Luís–Elaydi model

Qualitative properties and bifurcations of a leaf-eating herbivores model

“…In the cases that (k, b) lies at one of the points (1,4), (2,1) and (3,1), the qualitative properties of E are not given because the proofs involve computing the normal forms of some strong resonances, the Takens theorem, which shows that the analysis of dynamics for a map can be reduced to the discussion of a differential equation, and the blowing-up techniques. The specific processes can be referred to the references [24,26]. Furthermore, the system may produce 1:2 resonance, 1:4 resonance and 1:3 resonance respectively.…”