BIFURCATIONS OF LIMIT CYCLES CREATED BY A MULTIPLE NILPOTENT CRITICAL POINT OF PLANAR DYNAMICAL SYSTEMS

DOI10.1142/S0218127411028544zbMath1210.34056MaRDI QIDQ2994872

Yi-rong Liu, Ji-Bin Li

Publication date: 29 April 2011

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

zbMATH Keywords

Lyapunov constantplanar dynamical systemnilpotent critical pointbifurcation of limit cyclemultiple critical point

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) Bifurcations of singular points in dynamical systems (37G10)

Related Items (12)

Bi-center problem and bifurcation of limit cycles from nilpotent singular points in \(Z_{2}\)-equivariant cubic vector fields ⋮ Nilpotent Center in a Continuous Piecewise Quadratic Polynomial Hamiltonian Vector Field ⋮ Nilpotent bi-center in continuous piecewise \(\mathbb{Z}_2\)-equivariant cubic polynomial Hamiltonian systems ⋮ Limit cycle bifurcations from a nilpotent focus or center of planar systems ⋮ Nilpotent center conditions in cubic switching polynomial Liénard systems by higher-order analysis ⋮ LIMIT CYCLE BIFURCATION FOR A NILPOTENT SYSTEM IN <i>Z</i>₃-EQUIVARIANT VECTOR FIELD ⋮ A KIND OF BIFURCATION OF LIMIT CYCLES FROM A NILPOTENT CRITICAL POINT ⋮ Center condition and bifurcation of limit cycles for quadratic switching systems with a nilpotent equilibrium point ⋮ ANALYTIC CENTER OF NILPOTENT CRITICAL POINTS ⋮ Double bifurcation for a cubic Kolmogorov model ⋮ Double Bifurcation of Nilpotent Focus ⋮ New Double Bifurcation of Nilpotent Focus

Cites Work

• Generating limit cycles from a nilpotent critical point via normal forms
• NEW STUDY ON THE CENTER PROBLEM AND BIFURCATIONS OF LIMIT CYCLES FOR THE LYAPUNOV SYSTEM (II)
• NEW STUDY ON THE CENTER PROBLEM AND BIFURCATIONS OF LIMIT CYCLES FOR THE LYAPUNOV SYSTEM (I)
• MONODROMY AND STABILITY FOR NILPOTENT CRITICAL POINTS

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