ASYMPTOTIC EXPANSIONS OF MELNIKOV FUNCTIONS AND LIMIT CYCLE BIFURCATIONS (Q4908405)

scientific article; zbMATH DE number 6141703

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English	ASYMPTOTIC EXPANSIONS OF MELNIKOV FUNCTIONS AND LIMIT CYCLE BIFURCATIONS	scientific article; zbMATH DE number 6141703

Statements

instance of

scholarly article

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title

ASYMPTOTIC EXPANSIONS OF MELNIKOV FUNCTIONS AND LIMIT CYCLE BIFURCATIONS (English)

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publication date

5 March 2013

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zbMATH Keywords

center

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cusp

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nilpotent saddle

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homoclinic loop

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Melnikov function

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limit cycle bifurcation

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Degenerate Hopf bifurcations in discontinuous planar systems

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Melnikov method for homoclinic bifurcation in nonlinear impact oscillators

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Cyclicity of planar homoclinic loops and quadratic integrable systems

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On Hopf cyclicity of planar systems

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On the stability of double homoclinic and heteroclinic cycles.

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ON THE NUMBER AND DISTRIBUTION OF LIMIT CYCLES IN A CUBIC SYSTEM

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A new cubic system having eleven limit cycles

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The loop quantities and bifurcations of homoclinic loops

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Bifurcation of limit cycles near equivariant compound cycles

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LIMIT CYCLE BIFURCATIONS IN NEAR-HAMILTONIAN SYSTEMS BY PERTURBING A NILPOTENT CENTER

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Limit cycles near homoclinic and heteroclinic loops

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HOPF BIFURCATIONS FOR NEAR-HAMILTONIAN SYSTEMS

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Limit cycle bifurcations by perturbing a cuspidal loop in a Hamiltonian system

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On Hopf bifurcation in non-smooth planar systems

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On the Number of Limit Cycles in Perturbations of Quadratic Hamiltonian Systems

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Centennial History of Hilbert's 16th Problem

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Melnikov functions and perturbation of a planar Hamiltonian system

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Bifurcation set and limit cycles forming compound eyes in a perturbed Hamiltonian system

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Global bifurcations in a perturbed cubic system with \(Z_ 2\)-symmetry

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INVESTIGATIONS OF BIFURCATIONS OF LIMIT CYCLES IN Z2-EQUIVARIANT PLANAR VECTOR FIELDS OF DEGREE 5

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HILBERT'S 16TH PROBLEM AND BIFURCATIONS OF PLANAR POLYNOMIAL VECTOR FIELDS

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Bifurcations of limit cycles in a \(Z_8\)-equivariant planar vector field of degree 7

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Melnikov functions for period annulus, nondegenerate centers, heteroclinic and homoclinic cycles.

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BIFURCATIONS OF LIMIT CYCLES IN A Z2-EQUIVARIANT PLANAR POLYNOMIAL VECTOR FIELD OF DEGREE 7

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Limit cycles near generalized homoclinic and double homoclinic loops in piecewise smooth systems

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Bifurcation of limit cycles by perturbing a piecewise linear Hamiltonian system with a homoclinic loop

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Limit cycles of a \(Z_3\)-equivariant near-Hamiltonian system

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On the number of limit cycles which appear by perturbation of separatrix loop of planar vector fields

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Dynamics retrospective: Great problems, attempts that failed

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Bifurcation of limit cycles from a heteroclinic loop with a cusp

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Existence of 121 limit cycles in a perturbed planar polynomial Hamiltonian vector field of degree 11

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BIFURCATION OF LIMIT CYCLES IN Z10-EQUIVARIANT VECTOR FIELDS OF DEGREE 9

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ON THE STUDY OF LIMIT CYCLES OF THE GENERALIZED RAYLEIGH–LIENARD OSCILLATOR

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On the study of limit cycles of a cubic polynomial system under \(\mathbb Z_{4}\)-equivariant quintic perturba\-tion

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Limit cycle bifurcations of some Liénard systems with a cuspidal loop and a homoclinic loop

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Limit cycle bifurcations of some Liénard systems

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On Melnikov functions of a homoclinic loop through a nilpotent saddle for planar near-Hamiltonian systems

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Bifurcations of limit cycles in a cubic system

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Bifurcations of limit cycles for a cubic Hamiltonian system under quartic perturbations

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full work available at URL

https://doi.org/10.1142/s0218127412502963

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published in

International Journal of Bifurcation and Chaos in Applied Sciences and Engineering

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Identifiers

zbMATH Open document ID

1258.34054

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DOI

10.1142/S0218127412502963

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Mathematics Subject Classification ID

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Sitelinks

Mathematics(1 entry)

mardi Publication:4908405