Resumen de Takens–Bogdanov Bifurcation for a Ratio-Dependent Predation Interaction Involving Prey-Competition and Predator-Age

Peng Yang

• A large number of articles have been devoted to the study of age-dependent predation interaction. Most of them concentrate on the existence of the solution and the non-trivial periodic solution. The strength of this text is that we mainly investigate the long-time behavior of the solution for a general ratio-dependent predation interaction involving prey-competition and predator-age in the form of an ODE and a PDE.

  Firstly, we prove that there are some variable values such that this ratio-dependent predation interaction has a unique positive equilibrium age profile with Takens–Bogdanov singularity. Secondly, under fit tiny perturbation, the ratio-dependent predation interaction generates the Takens–Bogdanov bifurcation in a small domain of this positive equilibrium age profile.