Results 141 to 150 of about 401 (174)

BIFURCATION OF ROUGH HETEROCLINIC LOOP WITH ORBIT FLIPS

International Journal of Bifurcation and Chaos, 2012
In this paper, heteroclinic loop bifurcations with double orbit flips are investigated in four-dimensional vector fields. We obtain the bifurcation equations by setting up a local coordinate system near the rough heteroclinic orbit and establishing the Poincaré map.
Xingbo Liu, Zhenzhen Wang, Deming Zhu
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GLOBAL AND LOCAL CONTROL OF HOMOCLINIC AND HETEROCLINIC BIFURCATIONS

International Journal of Bifurcation and Chaos, 2005
A comprehensive resonant optimal control method is developed and discussed for suppressing homoclinic and heteroclinic bifurcations of a general one-degree-of-freedom nonlinear oscillator. Based on an adjustable phase shift, the primary resonant optimal control method is presented.
Hongjun Cao, Guanrong Chen
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Heteroclinic bifurcation in a ratio-dependent predator-prey system

Journal of Mathematical Biology, 2004
In this paper we study the heteroclinic bifurcation in a general ratio-dependent predator-prey system. Based on the results of heteroclinic loop obtained in [J. Math. Biol. 43(2001): 221-246], we give parametric conditions of the existence of the heteroclinic loop analytically and describe the heteroclinic bifurcation surface in the parameter space, so
Yilei Tang, Weinian Zhang, Zhang Weinian   +2 more
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Theory and Application of a Nongeneric Heteroclinic Loop Bifurcation

SIAM Journal on Applied Mathematics, 1999
Summary: Homoclinic and heteroclinic bifurcations from a heteroclinic loop are considered. The system under consideration has three parameters, two of which are not suitable for generic unfoldings. Analytical criteria in terms of derivatives to Melnikov's functions are given for nongeneric parameters.
Bo Deng, Mark J. Friedman, Shui-Nee Chow
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Heteroclinic Bifurcation of Strongly Nonlinear Oscillator

Chinese Physics Letters, 2008
Analytical prediction of heteroclinic bifurcation of the strongly nonlinear oscillator is presented by using the extended normal form method. We consider the approximate periodic solution of the system subject to the quintic nonlinearity by introducing the undetermined fundamental frequency.
Zhang Qi-Chang, Wang Wei, Li Wei-Yi
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ANALYTICAL APPROXIMATION OF HETEROCLINIC BIFURCATION IN A 1:4 RESONANCE

International Journal of Bifurcation and Chaos, 2012
Bifurcation of heteroclinic cycle near 1:4 resonance in a self-excited parametrically forced oscillator with quadratic nonlinearity is investigated analytically in this paper. This bifurcation mechanism leads to the disappearance of a slow flow limit cycle giving rise to frequency-locking near the resonance. The analytical approach used to approximate
Abdelhak Fahsi, Mohamed Belhaq
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NONRESONANT BIFURCATIONS OF HETEROCLINIC LOOPS WITH ONE INCLINATION FLIP

International Journal of Bifurcation and Chaos, 2011
Heteroclinic bifurcations in four-dimensional vector fields are investigated by setting up local coordinates near a heteroclinic loop. This heteroclinic loop consists of two principal heteroclinic orbits, but there is one stable foliation that involves an inclination flip.
Shuliang Shui, Jingjing Li, Xuyang Zhang
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Heteroclinic Trajectory and Hopf Bifurcation in an Extended Lorenz System

International Journal of Bifurcation and Chaos, 2018
This note revisits an extended Lorenz system, which was presented in the paper entitled “Hopf bifurcations in an extended Lorenz system” by Zhou et al. [2017]. On the one hand, one points out and corrects some wrong results in that paper on the Hopf bifurcation at the symmetric equilibria [Formula: see text] and [Formula: see text].
Xianyi Li, Haijun Wang
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Exponential trichotomy and heteroclinic bifurcations

Nonlinear Analysis: Theory, Methods & Applications, 1997
This paper is devoted to the study of bifurcation/perturbation problems derived from the existence of homoclinic/heteroclinic orbits of flows in \(\mathbb{R}^n\). The technique used here is based on the exponential trichotomy theory for linear systems to establish principal normal coordinates.
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Analytics of heteroclinic bifurcation in a 3:1 subharmonic resonance

Nonlinear Dynamics, 2010
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Mohamed Belhaq, Belhaq Mohamed
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