## Coexistence of small and large amplitude limit cycles of polynomial differential systems of degree four.(English)Zbl 1168.92319

Summary: A class of degree four differential systems with an invariant conic $$x^2+Cy^2=1$$, $$C\in {\mathbb R}$$, is examined. We show the coexistence of small amplitude limit cycles, large amplitude limit cycles, and invariant algebraic curves under perturbations of the coefficients of the systems.

### MSC:

 92D25 Population dynamics (general) 34C05 Topological structure of integral curves, singular points, limit cycles of ordinary differential equations 34C60 Qualitative investigation and simulation of ordinary differential equation models

### Keywords:

stability; limit cycles; center; bifurcations

Mathematica
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### References:

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