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Bifurcations of heteroclinic loop accompanied by pitchfork bifurcation [PDF]

Nonlinear Dynamics, 2012
In this paper, using the local coordinate moving frame approach, we investigate bifurcations of generic heteroclinic loop with a hyperbolic equilibrium and a nonhyperbolic equilibrium which undergoes a pitchfork bifurcation. Under some generic hypotheses, the existence of homoclinic loop, heteroclinic loop, periodic orbit and three or four heteroclinic
Yancong Xu, Yancong Xu, Fengjie Geng
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Bifurcations of Heteroclinic Orbits

Journal of Dynamics and Differential Equations, 2010
Thesearchfortravelingwavesolutionsofasemilineardiffusionpartialdifferen- tialequationcanbereducedtothesearchforheteroclinicsolutionsoftheordinarydifferential equation ¨ u − c ˙ u + f (u) = 0, where c is a positive constant and f is a nonlinear function. A heteroclinic orbit is a solution u(t) such that u(t) → γ1 as t →− ∞and u(t) → γ2 as t →∞ where γ1 ,
Patrick D. McSwiggen, Xiaojie Hou, Kenneth R. Meyer   +2 more
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Homoclinic and Heteroclinic Bifurcations Close to a Twisted Heteroclinic Cycle

International Journal of Bifurcation and Chaos, 1998
We study the interaction of a transcritical (or saddle-node) bifurcation with a codimension-0/codimension-2 heteroclinic cycle close to (but away from) the local bifurcation point. The study is motivated by numerical observations on the traveling wave ODE of a reaction–diffusion equation.
Mario A. Natiello, Martin Zimmermann
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Observing a codimension-two heteroclinic bifurcation

Chaos: An Interdisciplinary Journal of Nonlinear Science, 1993
This paper reports experimental observations of codimension-two heteroclinic bifurcations in an autonomous third-order electrical circuit. The paper also reports confirmations by computer simulations. In the laboratory experiments, a pair of programmable resistors are used in order to adjust two bifurcation parameters.
Ryuji Tokunaga, Yasushi Abe, Takashi Matsumoto   +2 more
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Resonance and bifurcation of fractional quintic Mathieu-Duffing system.

Chaos, 2023
In this paper, the main subharmonic resonance of the Mathieu-Duffing system with a quintic oscillator under simple harmonic excitation, the route to chaos, and the bifurcation of the system under the influence of different parameters is studied.
Jiale Zhang, Jiaquan Xie, Wei Shi, Yiting Huo, Z. Ren, Dongping He   +5 more
semanticscholar   +1 more source

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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Singularly Degenerate Heteroclinic Cycles with Nearby Apple-Shape Attractors

International Journal of Bifurcation and Chaos in Applied Sciences and Engineering, 2023
Compared with most known singularly degenerate heteroclinic cycles consisting of two different equilibria of a line or a curve, or two parallel lines of semi-hyperbolic equilibria, little seems to be noticed about the one that connects two perpendicular ...
Haijun Wang, Guiyao Ke, G. Dong, Qifang Su, Jun Pan   +4 more
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Approximations of the Heteroclinic Orbits Near a Double-Zero Bifurcation with Symmetry of Order Two. Application to a Liénard Equation

International Journal of Bifurcation and Chaos in Applied Sciences and Engineering, 2019
A dynamical system possessing an equilibrium point with two zero eigenvalues is considered. We assume that a degenerate Bogdanov–Takens bifurcation with symmetry of order two is present and, in the parameter space, a curve of heteroclinic bifurcation ...
C. Rocsoreanu, Mihaela Sterpu
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Heteroclinic Trajectory and Hopf Bifurcation in an Extended Lorenz System

International Journal of Bifurcation and Chaos in Applied Sciences and Engineering, 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].
Xianyi Li, Haijun Wang
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On the extinction route of a stochastic population model under heteroclinic bifurcation

Acta Mechanica Sinica, 2022
Qing Yu, Yang Li, Xianbin Liu
semanticscholar   +2 more sources