Homoclinic bifurcation of limit cycles in near-Hamiltonian systems on the cylinder

DOI10.1016/j.jde.2021.09.036OpenAlexW3205518979MaRDI QIDQ2235665

Yixia Shi, Li-jun Zhang, Mao'an Han

Publication date: 21 October 2021

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jde.2021.09.036

zbMATH Keywords

Melnikov functiondouble homoclinic loopkey words cylinder near-Hamiltonian systemlimit cycle of type II

Mathematics Subject Classification ID

Topological structure of integral curves, singular points, limit cycles of ordinary differential equations (34C05) Bifurcation theory for ordinary differential equations (34C23) Perturbations of finite-dimensional Hamiltonian systems, normal forms, small divisors, KAM theory, Arnol'd diffusion (37J40) Perturbations, asymptotics of solutions to ordinary differential equations (34E10) Homoclinic and heteroclinic solutions to ordinary differential equations (34C37)

Related Items

General study on limit cycle bifurcation near a double homoclinic loop ⋮ Bifurcation of multiple periodic solutions for a class of nonlinear dynamical systems in \((m+4)\)-dimension ⋮ Limit cycle bifurcations near a double 2-polycycle on the cylinder ⋮ Global-in-time existence of unbounded separatrices and blow-up time of solutions for Liénard systems whose restoring force is an odd power function

Cites Work

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• On the number of limit cycles for perturbed pendulum equations
• Hopf and homoclinic bifurcations for near-Hamiltonian systems
• Limit cycles near homoclinic and heteroclinic loops
• Nonlinear oscillations, dynamical systems, and bifurcations of vector fields
• Limit cycles and chaos in equations of the pendulum type
• Bifurcations of invariant tori and subharmonic solutions for periodic perturbed systems
• Bifurcation theory of invariant tori of planar periodic perturbed systems
• Limit cycles in the equation of whirling pendulum with autonomous perturbation.
• Existence and uniqueness of the periodic orbits of a class of cylinder equations
• Dulac-Cherkas test for determining the exact number of limit cycles of autonomous systems on the cylinder
• On the number of limit cycles of some systems on the cylinder
• Some bifurcation methods of finding limit cycles
• Limit Cycles in the Josephson Equation
• On the number of limit cycles which appear by perturbation of separatrix loop of planar vector fields
• ON THE MAXIMUM NUMBER OF PERIODIC SOLUTIONS OF PIECEWISE SMOOTH PERIODIC EQUATIONS BY AVERAGE METHOD