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Global phase portraits for a planar \(\mathbb Z_2\)-equivariant Kukles systems of degree 3. (English) Zbl 1452.37031

Summary: We provide normal forms and the global phase portraits on the Poincaré disk of all planar Kukles systems of degree \(3\) with \(\mathbb Z_2\)-equivariant symmetry. Moreover, we also provide the bifurcation diagrams for these global phase portraits.

MSC:

37C81 Equivariant dynamical systems
37G40 Dynamical aspects of symmetries, equivariant bifurcation theory
37G05 Normal forms for dynamical systems
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