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.


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


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