Hopf Bifurcation of Limit Cycles in Some Piecewise Smooth Liénard Systems

DOI10.1142/S0218127420502491zbMath1452.37057OpenAlexW3092419439MaRDI QIDQ4971073

Weijiao Xu, Mao'an Han

Publication date: 8 October 2020

Published in: International Journal of Bifurcation and Chaos (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1142/s0218127420502491

zbMATH Keywords

Liénard systemHopf bifurcationcyclicitypiecewise smooth 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) Theory of limit cycles of polynomial and analytic vector fields (existence, uniqueness, bounds, Hilbert's 16th problem and ramifications) for ordinary differential equations (34C07) Dynamics induced by flows and semiflows (37C10) Bifurcations of limit cycles and periodic orbits in dynamical systems (37G15)

Cites Work

• Unnamed Item
• Limit cycle bifurcations by perturbing piecewise smooth Hamiltonian systems with multiple parameters
• Bifurcation of limit cycles by perturbing a piecewise linear Hamiltonian system with a homoclinic loop
• Limit cycle bifurcations in a class of near-Hamiltonian systems with multiple parameters
• On Hopf bifurcations of piecewise planar Hamiltonian systems
• Uniqueness of limit cycles for Liénard differential equations of degree four
• Bifurcation of periodic orbits in a class of planar Filippov systems
• On Hopf bifurcation in non-smooth planar systems
• Estimating the number of limit cycles in polynomial systems
• Hopf bifurcation of limit cycles in discontinuous Liénard systems
• Bifurcation of limit cycles from generalized homoclinic loops in planar piecewise smooth systems
• Limit cycles in discontinuous classical Liénard equations
• Finiteness theorems for limit cycles
• HOPF BIFURCATION FOR NONSMOOTH LIÉNARD SYSTEMS
• BIFURCATION OF LIMIT CYCLES IN PIECEWISE SMOOTH SYSTEMS VIA MELNIKOV FUNCTION