Limit cycle bifurcations near a generalized homoclinic loop in piecewise smooth systems with a hyperbolic saddle on a switch line

DOI10.1016/j.amc.2014.05.041zbMath1335.34074OpenAlexW2042172743MaRDI QIDQ279908

Lijun Wei, Shiping Lu, Feng Liang

Publication date: 29 April 2016

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

Full work available at URL: https://doi.org/10.1016/j.amc.2014.05.041

zbMATH Keywords

Melnikov functiongeneralized homoclinic looppiecewise smooth systemlimit cycle bifurcationnear-Hamiltonian system

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) Homoclinic and heteroclinic orbits for dynamical systems (37C29) Local and nonlocal bifurcation theory for dynamical systems (37G99)

Related Items (8)

Limit cycle bifurcations in a class of piecewise smooth systems with a double homoclinic loop ⋮ Limit Cycle Bifurcations by Perturbing a Piecewise Hamiltonian System with a Double Homoclinic Loop ⋮ Limit cycle bifurcations near generalized homoclinic loop in piecewise smooth systems with a cusp ⋮ ON THE NUMBER OF LIMIT CYCLES BY PERTURBING A PIECEWISE SMOOTH HAMILTON SYSTEM WITH TWO STRAIGHT LINES OF SEPARATION ⋮ Limit Cycle Bifurcations Near a Piecewise Smooth Generalized Homoclinic Loop with a Saddle-Fold Point ⋮ Some Bifurcation Analysis in a Family of Nonsmooth Liénard Systems ⋮ On limit cycles in regularized Filippov systems bifurcating from homoclinic-like connections to regular-tangential singularities ⋮ Limit cycle bifurcations near generalized homoclinic loop in piecewise smooth differential systems

Cites Work

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• Limit cycles near homoclinic and heteroclinic loops
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• Non-smooth dynamical systems
• On the number of limit cycles in double homoclinic bifurcations
• Bifurcation of limit cycles from a hyper-elliptic Hamiltonian system with a double heteroclinic loops
• Piecewise-smooth dynamical systems. Theory and applications
• Bifurcations of limit cycles from quintic Hamiltonian systems with an eye-figure loop. II
• Limit cycles near generalized homoclinic and double homoclinic loops in piecewise smooth systems
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• Center-Focus Problem for Discontinuous Planar Differential Equations
• ASYMPTOTIC EXPANSIONS OF MELNIKOV FUNCTIONS AND LIMIT CYCLE BIFURCATIONS
• Unnamed Item

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