\(Z_{2}\)-equivariant cubic system which yields 13 limit cycles

DOI10.1007/s10255-014-0420-xzbMath1311.34064OpenAlexW899012284MaRDI QIDQ477508

Ji-Bin Li, Yi-rong Liu

Publication date: 9 December 2014

Published in: Acta Mathematicae Applicatae Sinica. English Series (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10255-014-0420-x

zbMATH Keywords

bifurcationlimit cycleLyapunov constantplanar polynomial dynamical system

Mathematics Subject Classification ID

Topological structure of integral curves, singular points, limit cycles of ordinary differential equations (34C05) Symmetries, invariants of ordinary differential equations (34C14) Bifurcation theory for ordinary differential equations (34C23) Theory of limit cycles of polynomial and analytic vector fields (existence, uniqueness, bounds, Hilbert's 16th problem and ramifications) for ordinary differential equations (34C07)

Related Items (10)

Bifurcation of limit cycles by perturbing piecewise smooth integrable non-Hamiltonian systems ⋮ Simultaneity of centres in ℤ _q -equivariant systems ⋮ Isochronicity for a \(Z_{2}\)-equivariant cubic system ⋮ Center and isochronous center conditions for switching systems associated with elementary singular points ⋮ Complex integrability and linearizability of cubic \(Z_2\)-equivariant systems with two \(1:q\) resonant singular points ⋮ Limit cycles and invariant curves in a class of switching systems with degree four ⋮ Complex isochronous centers and linearization transformations for cubic \(Z_2\)-equivariant planar systems ⋮ Global Phase Portraits of ℤ2-Symmetric Planar Polynomial Hamiltonian Systems of Degree Three with a Nilpotent Saddle at the Origin ⋮ Integrability and linearizability of cubic \(Z_2\) systems with non-resonant singular points ⋮ Simultaneous integrability and non-linearizability at arbitrary double weak saddles and sole weak focus of a cubic Liénard system

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