Symmetry in planar dynamical systems

DOI10.1006/jsco.2001.0502zbMath1003.34026OpenAlexW1967464745MaRDI QIDQ1599554

Jane M. Pearson, Noel G. Lloyd

Publication date: 11 June 2002

Published in: Journal of Symbolic Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1006/jsco.2001.0502

zbMATH Keywords

symmetryGröbner basiscritical pointplanar dynamical systemcentre

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)

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LOCAL AND GLOBAL BIFURCATIONS TO LIMIT CYCLES IN A CLASS OF LIÉNARD EQUATION ⋮ Quantities at infinity in translational polynomial vector fields ⋮ Limit cycle bifurcations in a kind of perturbed Liénard system ⋮ Symmetric centers on planar cubic differential systems ⋮ A new method to determine isochronous center conditions for polynomial differential systems. ⋮ LIMIT CYCLE BIFURCATIONS OF A KIND OF LIÉNARD SYSTEM WITH A HYPOBOLIC SADDLE AND A NILPOTENT CUSP ⋮ Center and isochronous center at infinity for differential systems. ⋮ Limit cycles of the generalized polynomial Liénard differential equations ⋮ Limit cycles in generalized Liénard systems ⋮ Computation of invariant curves and identifying the type of critical point ⋮ On limit cycles of the Liénard equation with \(Z_2\) symmetry ⋮ A polynomial differential system with nine limit cycles at infinity ⋮ Limit cycle bifurcations of some Liénard systems ⋮ ON THE MAXIMUM NUMBER OF LIMIT CYCLES OF A CLASS OF GENERALIZED LIÉNARD DIFFERENTIAL SYSTEMS ⋮ Bifurcation of Limit Cycles for Some Liénard Systems with a Nilpotent Singular Point

Cites Work

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• REDUCE and the bifurcation of limit cycles
• Computing centre conditions for certain cubic systems
• Five limit cycles for a simple cubic system
• Polynomial systems from certain differential equations
• A cubic Kolmogorov system with six limit cycles
• An algorithmic approach to the center problem for homogeneous perturbations
• Bifurcation of limit cycles and integrability of planar dynamical systems in complex form
• The centres in the reduced Kukles system
• Algorithmic Derivation of Centre Conditions

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