LIMIT CYCLE BIFURCATIONS IN NEAR-HAMILTONIAN SYSTEMS BY PERTURBING A NILPOTENT CENTER
From MaRDI portal
Publication:5322560
DOI10.1142/S0218127408022226zbMath1165.34333OpenAlexW1995731991MaRDI QIDQ5322560
Jiao Jiang, Huai-Ping Zhu, Mao'an Han
Publication date: 21 July 2009
Published in: International Journal of Bifurcation and Chaos (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1142/s0218127408022226
Topological structure of integral curves, singular points, limit cycles of ordinary differential equations (34C05) Bifurcation theory for ordinary differential equations (34C23) Bifurcations of limit cycles and periodic orbits in dynamical systems (37G15)
Related Items
Bifurcation of limit cycles in a cubic-order planar system around a nilpotent critical point, Computation of expansion coefficients of Melnikov functions near a nilpotent center, On the number of zeros of abelian integral for some Liénard system of type \((4,3)\), Limit cycle bifurcations of some Liénard systems with a cuspidal loop and a homoclinic loop, Limit Cycle Bifurcations from an Order-3 Nilpotent Center of Cubic Hamiltonian Systems Perturbed by Cubic Polynomials, On the Number of Limit Cycles Bifurcated from a Near-Hamiltonian System with a Double Homoclinic Loop of Cuspidal Type Surrounded by a Heteroclinic Loop, Limit cycle bifurcations in a class of quintic \(Z_2\)-equivariant polynomial systems, LIMIT CYCLE BIFURCATION FOR A NILPOTENT SYSTEM IN <i>Z</i><sub>3</sub>-EQUIVARIANT VECTOR FIELD, On Melnikov functions of a homoclinic loop through a nilpotent saddle for planar near-Hamiltonian systems, Nine limit cycles around a singular point by perturbing a cubic Hamiltonian system with a nilpotent center, A KIND OF BIFURCATION OF LIMIT CYCLES FROM A NILPOTENT CRITICAL POINT, LIMIT CYCLE BIFURCATIONS NEAR A DOUBLE HOMOCLINIC LOOP WITH A NILPOTENT SADDLE, HOPF BIFURCATION OF LIÉNARD SYSTEMS BY PERTURBING A NILPOTENT CENTER, ASYMPTOTIC EXPANSIONS OF MELNIKOV FUNCTIONS AND LIMIT CYCLE BIFURCATIONS, Limit cycle bifurcations near a double homoclinic loop with a nilpotent saddle of order \(m\), BIFURCATION OF LIMIT CYCLES AT A NILPOTENT CRITICAL POINT IN A SEPTIC LYAPUNOV SYSTEM, On the Melnikov functions and limit cycles near a double homoclinic loop with a nilpotent saddle of order \(\hat{m} \), On the Distribution of Limit Cycles in a Liénard System with a Nilpotent Center and a Nilpotent Saddle, LIMIT CYCLE BIFURCATIONS OF SOME LIÉNARD SYSTEMS WITH A NILPOTENT CUSP, Bifurcations in a Cubic System with a Degenerate Saddle Point, LIMIT CYCLE BIFURCATIONS FROM CENTERS OF SYMMETRIC HAMILTONIAN SYSTEMS PERTURBED BY CUBIC POLYNOMIALS, Bifurcation of Limit Cycles for Some Liénard Systems with a Nilpotent Singular Point
Cites Work
- Unnamed Item
- Unnamed Item
- Loss of stability of self-oscillations close to resonance and versal deformations of equivariant vector fields
- Hilbert's 16th problem for quadratic vector fields
- Degenerate and non-trivial hyperbolic polycycles with two vertices
- PP-graphics with a nilpotent elliptic singularity in quadratic systems and Hilbert's 16th problem.
- On Hopf cyclicity of planar systems
- Finite cyclicity of graphics with a nilpotent singularity of saddle or elliptic type
- Bifurcations of cuspidal loops
- Linear estimate for the number of zeros of Abelian integrals with cubic Hamiltonians
- Elementary graphics of cyclicity 1 and 2
- Hilbert's 16-th problem for quadratic vector fields and cyclicity of graphics
- Hilbert's 16th problem for quadratic systems and cyclicity of elementary graphics
- HILBERT'S 16TH PROBLEM AND BIFURCATIONS OF PLANAR POLYNOMIAL VECTOR FIELDS
- THE SAME DISTRIBUTION OF LIMIT CYCLES IN FIVE PERTURBED CUBIC HAMILTONIAN SYSTEMS
- Existence of at most 1, 2, or 3 zeros of a Melnikov function and limit cycles
