Poincaré Bifurcation of Some Nonlinear Oscillator of Generalized Liénard Type Using Symbolic Computation Method (Q4583272)

scientific article; zbMATH DE number 6928082

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English	Poincaré Bifurcation of Some Nonlinear Oscillator of Generalized Liénard Type Using Symbolic Computation Method	scientific article; zbMATH DE number 6928082

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scholarly article

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title

Poincaré Bifurcation of Some Nonlinear Oscillator of Generalized Liénard Type Using Symbolic Computation Method (English)

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28 August 2018

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zbMATH Keywords

nonlinear oscillator of Liénard type

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limit cycle

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heteroclinic loop

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Bifurcations of limit cycles from quintic Hamiltonian systems with an eye-figure loop

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Bifurcations of limit cycles for a quintic Hamiltonian system with a double cuspidal loop

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A note on existence and uniqueness of limit cycles for Liénard systems

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AN APPLICATION OF REGULAR CHAIN THEORY TO THE STUDY OF LIMIT CYCLES

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The center conditions for a Liénard system

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Alien limit cycles in Liénard equations

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Strongly nonlinear oscillators. Analytical solutions

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Perturbations from an elliptic Hamiltonian of degree four. I: Saddle loop and two saddle cycles

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Perturbations from an elliptic Hamiltonian of degree four. II: Cuspidal loop

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Perturbation from an elliptic Hamiltonian of degree four. III: global centre.

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Perturbation from an elliptic Hamiltonian of degree four. IV: Figure eight-loop.

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A Chebyshev criterion for Abelian integrals

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HOPF BIFURCATIONS FOR NEAR-HAMILTONIAN SYSTEMS

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Normal forms, Melnikov functions and bifurcations of limit cycles

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Small-amplitude limit cycles of polynomial Liénard systems

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Q5416050

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A criterion for determining the monotonicity of the ratio of two Abelian integrals

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On the hyperelliptic limit cycles of Liénard systems

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Bounding the number of zeros of certain abelian integrals

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Q4234243

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On period functions of Liénard systems

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Bifurcation of limit cycles from a heteroclinic loop with a cusp

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Bifurcation of limit cycles from a Liénard system with a heteroclinic loop connecting two nilpotent saddles

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On the number of zeros of abelian integral for some Liénard system of type \((4,3)\)

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Multiple limit cycles of some strongly nonlinear Liénard-van der Pol oscillator

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The sharp bound on the number of zeros of Abelian integral for a perturbation of hyper-elliptic Hamiltonian system

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Perturbations of a class of hyper-elliptic Hamiltonian systems of degree seven with nilpotent singular points

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Perturbation of a period annulus bounded by a heteroclinic loop connecting two hyperbolic saddles

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Bounding the number of limit cycles for a polynomial Liénard system by using regular chains

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Global Existence and Uniqueness of Periodic Waves in a Population Model with Density-Dependent Migrations and Allee Effect

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Hopf bifurcation for two types of Liénard systems

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Bifurcation of small limit cycles in cubic integrable systems using higher-order analysis

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On the number of limit cycles in small perturbations of a class of hyper-elliptic Hamiltonian systems with one nilpotent saddle

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Bound the number of limit cycles bifurcating from center of polynomial Hamiltonian system via interval analysis

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On the existence and uniqueness of limit cycles for generalized Liénard systems

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New lower bounds for the Hilbert number of polynomial systems of Liénard type

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Q5496561

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LOCAL AND GLOBAL BIFURCATIONS TO LIMIT CYCLES IN A CLASS OF LIÉNARD EQUATION

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The hyperelliptic limit cycles of the Liénard systems

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The perturbations of a class of hyper-elliptic Hamilton systems with a double homoclinic loop through a nilpotent saddle

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full work available at URL

https://doi.org/10.1142/s0218127418500967

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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

1397.34071

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DOI

10.1142/S0218127418500967

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Mathematics Subject Classification ID

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Sitelinks

Mathematics(1 entry)

mardi Publication:4583272