Remarks on a class of generalized Liénard planar systems
DOI10.13137/2464-8728/32864zbMath1506.34048OpenAlexW3215481548MaRDI QIDQ5087778
Gabriele Villari, Fabio Zanolin
Publication date: 1 July 2022
Full work available at URL: https://flore.unifi.it/handle/2158/1247193?mode=full.2226
limit cyclesgeneralized Liénard equationsqualitative theory of planar dynamical systemsaveraging and bifurcation
Periodic solutions to ordinary differential equations (34C25) Topological structure of integral curves, singular points, limit cycles of ordinary differential equations (34C05) Bifurcation theory for ordinary differential equations (34C23) Averaging method for ordinary differential equations (34C29) Theory of limit cycles of polynomial and analytic vector fields (existence, uniqueness, bounds, Hilbert's 16th problem and ramifications) for ordinary differential equations (34C07) Nonautonomous smooth dynamical systems (37C60)
Cites Work
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- An extension of Dragilev's theorem for the existence of periodic solutions of the Liénard equation
- A note on existence and uniqueness of limit cycles for Liénard systems
- Chaos in periodically perturbed planar Hamiltonian systems using linked twist maps
- Stability by Liapunov's direct method. With applications
- A necessary and sufficient condition for oscillation of the generalized Liénard equation
- On the qualitative behaviour of solutions of Liénard equation
- On a continuation lemma for the study of a certain planar system with applications to Liénard and Rayleigh equations
- Reversible systems
- Boundedness of solutions of nonlinear differential equations
- Every period annulus is both reversible and symmetric
- A geometric approach to periodically forced dynamical systems in presence of a separatrix
- Periodic solutions of the Liénard equation with one-sided growth restrictions
- On the qualitative behavior of a class of generalized Liénard planar systems
- Effectiveness of the Bendixson-Dulac theorem
- Chaotic dynamics in a periodically perturbed Liénard system.
- On the bifurcation of limit cycles due to polynomial perturbations of Hamiltonian centers
- On periodic solutions of the system \(\dot x = y - F(x),\dot y = - g(x)\)
- On the generalized Lienard equation with negative damping
- A continuation theorem with applications to periodically forced Liénard equations in the presence of a separatrix
- Stable and Random Motions in Dynamical Systems
- Stability and Chaos in Celestial Mechanics
- Systems of Differential Equations Which Are Competitive or Cooperative: I. Limit Sets
- Subshifts of Finite Type in Linked Twist Mappings
- Chaos in periodically forced reversible vector fields
- Foundations of chaotic mixing
- On the non-uniqueness of periodic solutions for an asymmetric Liénard equation
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