A Polycycle and Limit Cycles in a Non-Differentiable Predator-Prey Model

Proceedings Mathematical Sciences

I Szántó¹  E Sáez² 

[1] $$;Departamento de Matemática, Universidad Técnica Federico Santa María, Casilla 0-V, Valparaíso, Chile$$

关键词: Stability;    limit cycles;    bifurcations;    predator-prey model.;   

DOI  :  

学科分类：数学（综合）

来源: Indian Academy of Sciences

【 摘 要 】

For a non-differentiable predator-prey model, we establish conditions for the existence of a heteroclinic orbit which is part of one contractive polycycle and for some values of the parameters, we prove that the heteroclinic orbit is broken and generates a stable limit cycle. In addition, in the parameter space, we prove that there exists a curve such that the unique singularity in the realistic quadrant of the predator-prey model is a weak focus of order two and by Hopf bifurcations we can have at most two small amplitude limit cycles.

【 授权许可】

Unknown