Time-periodic perturbation of a Liénard equation with an unbounded homoclinic loop

DOI10.1016/j.physd.2011.06.006zbMath1237.34095OpenAlexW2016191982MaRDI QIDQ720706

Marcelo Messias, Márcio R. Alves Gouveia

Publication date: 11 October 2011

Published in: Physica D (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.physd.2011.06.006

zbMATH Keywords

chaotic dynamicshomoclinic bifurcationMelnikov methodPoincaré compactificationforced Liénard equation

Mathematics Subject Classification ID

Bifurcation theory for ordinary differential equations (34C23) Perturbations of ordinary differential equations (34D10) Complex behavior and chaotic systems of ordinary differential equations (34C28) Homoclinic and heteroclinic solutions to ordinary differential equations (34C37)

Related Items

Exact solutions of the Liénard- and generalized Liénard-type ordinary nonlinear differential equations obtained by deforming the phase space coordinates of the linear harmonic oscillator, A class of exact solutions of the Liénard-type ordinary nonlinear differential equation, On the integrability of the Abel and of the extended Liénard equations

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Periodic perturbation of quadratic systems with two infinite heteroclinic cycles
• Nonlinear oscillations, dynamical systems, and bifurcations of vector fields
• An example of bifurcation to homoclinic orbits
• The existence of transverse homoclinic points in the Sitnikov problem
• The integration of polynomial Liénard systems by elementary functions
• Mathematical problems for the next century
• Qualitative theory of planar differential systems
• Transversal homoclinic orbits in the collinear restricted three-body problem
• A stable manifold theorem for degenerate fixed points with applications to celestial mechanics
• Extending Geometric Singular Perturbation Theory to Nonhyperbolic Points---Fold and Canard Points in Two Dimensions
• More limit cycles than expected in Liénard equations
• Interaction of damping and forcing in a second order equation
• CHAOS AND CHAOTIC TRANSIENTS IN A FORCED MODEL OF THE ECONOMIC LONG WAVE: THE ROLE OF HOMOCLINIC BIFURCATION TO INFINITY
• Ordinary Differential Equations with Applications
• Extending Melnikov theory to invariant manifolds on non-compact domains
• Canard cycles and center manifolds
• Relaxation oscillation and canard explosion