Limit cycle bifurcations in a class of piecewise smooth systems with a double homoclinic loop

DOI10.1016/j.amc.2014.09.125zbMath1338.34071OpenAlexW1995373224MaRDI QIDQ298440

F. Blanchet-Sadri, M. Dambrine

Publication date: 20 June 2016

Published in: Applied Mathematics and Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.amc.2014.09.125

zbMATH Keywords

limit cycleMelnikov functionHamiltonian systemdouble homoclinic loop

Mathematics Subject Classification ID

Topological structure of integral curves, singular points, limit cycles of ordinary differential equations (34C05) Bifurcations of limit cycles and periodic orbits in dynamical systems (37G15)

Related Items (10)

Bifurcation of limit cycles from a parabolic-parabolic type critical point in a class of planar piecewise smooth quadratic systems ⋮ Limit Cycle Bifurcations by Perturbing a Piecewise Hamiltonian System with a Double Homoclinic Loop ⋮ On the Number of Limit Cycles by Perturbing a Piecewise Smooth Liénard Model ⋮ Bifurcation diagrams of global connections in Filippov systems ⋮ Bifurcation of Nonhyperbolic Limit Cycles in Piecewise Smooth Planar Systems with Finitely Many Zones ⋮ Limit cycle bifurcations near a double 2-polycycle on the cylinder ⋮ ON THE NUMBER OF LIMIT CYCLES BY PERTURBING A PIECEWISE SMOOTH HAMILTON SYSTEM WITH TWO STRAIGHT LINES OF SEPARATION ⋮ Limit Cycles from Perturbing a Piecewise Smooth System with a Center and a Homoclinic Loop ⋮ Bifurcation of Periodic Orbits Crossing Switching Manifolds Multiple Times in Planar Piecewise Smooth Systems ⋮ Limit Cycles of Planar Piecewise Smooth Quadratic Systems with Focus-Parabolic Type Critical Points

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Limit cycle bifurcations near a generalized homoclinic loop in piecewise smooth systems with a hyperbolic saddle on a switch line
• Bifurcation of limit cycles by perturbing a piecewise linear Hamiltonian system with a homoclinic loop
• Isochronicity of centers in a switching Bautin system
• Limit cycles near homoclinic and heteroclinic loops
• On Hopf bifurcation in non-smooth planar systems
• Non-smooth dynamical systems
• Bifurcation of periodic orbits with multiple crossings in a class of planar Filippov systems
• Piecewise-smooth dynamical systems. Theory and applications
• Dynamical analysis of a delayed ratio-dependent Holling-Tanner predator-prey model
• Limit cycles near generalized homoclinic and double homoclinic loops in piecewise smooth systems
• On the existence and uniqueness of limit cycles for generalized Liénard systems
• The cusp of order n
• EIGHT LIMIT CYCLES AROUND A CENTER IN QUADRATIC HAMILTONIAN SYSTEM WITH THIRD-ORDER PERTURBATION
• On the number of limit cycles which appear by perturbation of separatrix loop of planar vector fields
• HILBERT'S 16TH PROBLEM AND BIFURCATIONS OF PLANAR POLYNOMIAL VECTOR FIELDS
• Center-Focus Problem for Discontinuous Planar Differential Equations
• ASYMPTOTIC EXPANSIONS OF MELNIKOV FUNCTIONS AND LIMIT CYCLE BIFURCATIONS
• The Focus-Center-Limit Cycle Bifurcation in Symmetric 3D Piecewise Linear Systems
• Viral Blips May Not Need a Trigger: How Transient Viremia Can Arise in Deterministic In-Host Models
• Degenerate Hopf bifurcations in discontinuous planar systems

This page was built for publication: Limit cycle bifurcations in a class of piecewise smooth systems with a double homoclinic loop