Uniqueness of limit cycles in polynomial systems with algebraic invariants

DOI10.1017/S0004972700016026zbMath0802.34030OpenAlexW2058491446MaRDI QIDQ4290989

André Zegeling, Robert E. Kooij

Publication date: 5 May 1994

Published in: Bulletin of the Australian Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1017/s0004972700016026

zbMATH Keywords

transformationsplanar systemsuniqueness of limit cyclesBogdanov-Takens systemgeneralized Liénard systemsZhang Zhifen's Lemma

Mathematics Subject Classification ID

Periodic solutions to ordinary differential equations (34C25) Topological structure of integral curves, singular points, limit cycles of ordinary differential equations (34C05)

Related Items (10)

Qualitative and bifurcation analysis in a Leslie-Gower model with Allee effect ⋮ Number of limit cycles for planar systems with invariant algebraic curves ⋮ The application of Liénard transformations to predator-prey systems ⋮ Qualitative properties of two-dimensional predator-prey systems ⋮ Liénard systems for quadratic systems with invariant algebraic curves ⋮ Several bifurcation mechanisms for limit cycles in a predator-prey system ⋮ Permanency in predator-prey models of Leslie type with ratio-dependent simplified Holling type-IV functional response ⋮ Irreducibility of the Picard-Fuchs equation related to the Lotka-Volterra polynomial \(x^2y^2(1-x-y)\) ⋮ Poincaré bifurcations of two classes of polynomial systems ⋮ The distribution of limit cycles in quadratic systems with four finite singularities

Cites Work

• A new class of quadratic systems
• Nonlinear oscillations, dynamical systems, and bifurcations of vector fields
• Bifurcations of certain family of planar vector fields tangent to axes
• Uniqueness of periodic orbits of some vector fields with codimension two singularities
• ON THE VERSALITY OF A FAMILY OF SYMMETRIC VECTOR FIELDS IN THE PLANE
• Proof of the uniqueness theorem of limit cycles of generalized liénard equations

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