HOPF BIFURCATION FOR NONSMOOTH LIÉNARD SYSTEMS

DOI10.1142/S0218127409024177zbMath1176.34047OpenAlexW2141079563MaRDI QIDQ3649646

Xia Liu, Mao'an Han

Publication date: 4 December 2009

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

Full work available at URL: https://doi.org/10.1142/s0218127409024177

zbMATH Keywords

limit cycleHopf cyclicitynonsmoothliapunov constant

Mathematics Subject Classification ID

Topological structure of integral curves, singular points, limit cycles of ordinary differential equations (34C05) Transformation and reduction of ordinary differential equations and systems, normal forms (34C20) Symmetries, invariants of ordinary differential equations (34C14) Bifurcation theory for ordinary differential equations (34C23)

Related Items (19)

Twenty Hopf-like bifurcations in piecewise-smooth dynamical systems ⋮ Linearly implicit Liénard systems ⋮ Hopf bifurcation of limit cycles in discontinuous Liénard systems ⋮ Bifurcations of small limit cycles in Liénard systems with cubic restoring terms ⋮ On Hopf bifurcations of piecewise planar Hamiltonian systems ⋮ The center problem on piecewise smooth differential systems with two zones ⋮ Cyclicity of periodic annulus and Hopf cyclicity in perturbing a hyper-elliptic Hamiltonian system with a degenerate heteroclinic loop ⋮ Bifurcation of limit cycles from generalized homoclinic loops in planar piecewise smooth systems ⋮ Isochronicity of centers in a switching Bautin system ⋮ Piecewise linear differential systems with two real saddles ⋮ Center condition and bifurcation of limit cycles for quadratic switching systems with a nilpotent equilibrium point ⋮ Degenerate Hopf bifurcations in a family of FF-type switching systems ⋮ On Hopf bifurcation in non-smooth planar systems ⋮ Hopf bifurcation for two types of Liénard systems ⋮ Hopf Bifurcation of Limit Cycles in Some Piecewise Smooth Liénard Systems ⋮ DEGENERATE HOPF BIFURCATION IN NONSMOOTH PLANAR SYSTEMS ⋮ Stability and Limit Cycle Bifurcation for Two Kinds of Generalized Double Homoclinic Loops in Planar Piecewise Smooth Systems ⋮ ON THE SLIDING BIFURCATION OF A CLASS OF PLANAR FILIPPOV SYSTEMS ⋮ Center conditions in a switching Bautin system

Cites Work

• Limit cycles for nonsmooth differential equations via Schwarzian derivative
• Generalized Hopf bifurcation for planar Filippov systems continuous at the origin
• Bifurcations of equilibria in non-smooth continuous systems
• On Hopf cyclicity of planar systems
• Bifurcation phenomena in non-smooth dynamical systems
• Generalized Hopf bifurcation for non-smooth planar systems
• Center-Focus Problem for Discontinuous Planar Differential Equations
• THE CENTER PROBLEM FOR DISCONTINUOUS LIÉNARD DIFFERENTIAL EQUATION
• Bifurcations in nonlinear discontinuous systems
• Degenerate Hopf bifurcations in discontinuous planar systems

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