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

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Abstract

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.

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Acknowledgements

We are very grateful to the editors and the anonymous reviewers for their very valuable comments and suggestions which led to a significant improvement of this study. This work was partially supported by the Doctoral Scientific Research Foundation of Northwest Normal University (202203101201), the Young Teachers’ Scientific Research Ability Promotion Project of Northwest Normal University (NWNU-LKQN2023-01).

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  1. Colloge of Mathematics and Statistics, Northwest Normal University, Lanzhou, 730070, Gansu, People’s Republic of China

    Peng Yang

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Yang, P. Takens–Bogdanov Bifurcation for a Ratio-Dependent Predation Interaction Involving Prey-Competition and Predator-Age. Qual. Theory Dyn. Syst. 22, 151 (2023). https://doi.org/10.1007/s12346-023-00845-5

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