Limit cycles for perturbing a piecewise linear Hamiltonian system with one or two saddles

DOI10.1016/j.chaos.2014.05.010zbMath1349.37059OpenAlexW1968629527MaRDI QIDQ340465

Mohammad Hasan, M. Dambrine

Publication date: 14 November 2016

Published in: Chaos, Solitons and Fractals (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.chaos.2014.05.010

zbMATH Keywords

bifurcations of limit cyclesnumbers of limit cyclespiecewise linear Hamiltonian system

Mathematics Subject Classification ID

Topological structure of integral curves, singular points, limit cycles of ordinary differential equations (34C05) Perturbations of finite-dimensional Hamiltonian systems, normal forms, small divisors, KAM theory, Arnol'd diffusion (37J40) Bifurcations of limit cycles and periodic orbits in dynamical systems (37G15)

Related Items (14)

Limit cycle bifurcations in a class of perturbed piecewise smooth systems ⋮ On the Number of Limit Cycles by Perturbing a Piecewise Smooth Liénard Model ⋮ The center problem on piecewise smooth differential systems with two zones ⋮ The Maximal Number of Limit Cycles in Perturbations of Piecewise Linear Hamiltonian Systems with Two Saddles ⋮ Bifurcation Analysis in a Class of Piecewise Nonlinear Systems with a Nonsmooth Heteroclinic Loop ⋮ BIFURCATION OF LIMIT CYCLES IN PIECEWISE SMOOTH SYSTEMS VIA MELNIKOV FUNCTION ⋮ On the number of limit cycles of a piecewise quadratic near-Hamiltonian system ⋮ Limit cycle bifurcations near homoclinic and heteroclinic loops via stability-changing of a homoclinic loop ⋮ Limit Cycles Near a Piecewise Smooth Generalized Homoclinic Loop with a Nonelementary Singular Point ⋮ Limit cycles in small perturbations of a planar piecewise linear Hamiltonian system with a non-regular separation line ⋮ Limit Cycles from Perturbing a Piecewise Smooth System with a Center and a Homoclinic Loop ⋮ Limit Cycle Bifurcations Near a Piecewise Smooth Generalized Homoclinic Loop with a Saddle-Fold Point ⋮ Limit Cycles of a Kind of Nonsmooth Differential Systems with Two Switching Lines ⋮ Limit Cycle and Boundary Equilibrium Bifurcations in Continuous Planar Piecewise Linear Systems

Cites Work

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• Limit cycle bifurcations in a class of perturbed piecewise smooth systems
• Bifurcation of limit cycles by perturbing a piecewise linear Hamiltonian system with a homoclinic loop
• Non-smooth dynamical systems
• Limit cycles for discontinuous quadratic differential systems with two zones
• Piecewise-smooth dynamical systems. Theory and applications
• Limit cycles near generalized homoclinic and double homoclinic loops in piecewise smooth systems
• The sliding bifurcations in planar piecewise smooth differential systems
• LOWER BOUNDS FOR THE MAXIMUM NUMBER OF LIMIT CYCLES OF DISCONTINUOUS PIECEWISE LINEAR DIFFERENTIAL SYSTEMS WITH A STRAIGHT LINE OF SEPARATION
• Introduction to the Qualitative Theory of Differential Systems
• Bifurcation of limit cycles by perturbing a piecewise linear Hamiltonian system
• Degenerate Hopf bifurcations in discontinuous planar systems

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