On Canard Homoclinic of a Liénard Perturbation System - Applied Mathematics

AM > Vol.2 No.10, October 2011

Applied Mathematics

Volume 2, Issue 10 (October 2011)

ISSN Print: 2152-7385 ISSN Online: 2152-7393

Google-based Impact Factor: 0.58 Citations

On Canard Homoclinic of a Liénard Perturbation System ()

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Download as PDF (Size: 156KB) PP. 1221-1224

DOI: 10.4236/am.2011.210170 5,331 Downloads 8,653 Views Citations

Author(s)

Makoto Hayashi

Affiliation(s)

ABSTRACT

The classification on the orbits of some Liénard perturbation system with several parameters, which is relation to the example in [1] or [2], is discussed. The conditions for the parameters in order that the system has a unique limit cycle, homoclinic orbits, canards or the unique equilibrium point is globally asymptotic stable are given. The methods in our previous papers are used for the proofs.

KEYWORDS

Liénard System, Canards, Limit Cycles, Homoclinic Orbits, Global Asymptotic Stability

Share and Cite:

M. Hayashi, "On Canard Homoclinic of a Liénard Perturbation System," Applied Mathematics, Vol. 2 No. 10, 2011, pp. 1221-1224. doi: 10.4236/am.2011.210170.

Cited by

[1]	On Non Liénard Type with One Limit Cycle
	2019

[2]	Boundedness of Solutions and Existence of Limits Cycle for Lienard's Systems
	2018

[3]	Explosions de cycles: analyses qualitatives, simulations numériques et modèles
	Thèse, 2016

[4]	Canard-induced loss of stability across a homoclinic bifurcation
	2015

[5]	Periodic steady-state analysis of nonlinear oscillators based on multivariate polynomial roots finding
	2014

[6]	Homoclinic orbits for the planar system of Liénard-type
	Qualitative Theory of Dynamical Systems, 2013

[7]	Limit Cycle Identification in Nonlinear Polynomial Systems
	Applied Mathematics, 2013

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