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Codimension 2 reversible heteroclinic bifurcations with inclination flips [PDF]

Science in China Series A: Mathematics, 2009
In this paper, the heteroclinic bifurcation problem with real eigenvalues and two inclination-flips is investigated in a four-dimensional reversible system. We perform a detailed study of this case by using the method originally established in the papers “Problems in Homoclinic Bifurcation with Higher Dimensions” and “Bifurcation of Heteroclinic Loops,”
Deming Zhu, Yancong Xu, Yancong Xu, GuiFeng Deng   +3 more
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Codimension-3 Flip Bifurcation of a Class of Difference Equations

International Journal of Bifurcation and Chaos, 2018
In this paper, we consider a one-dimensional difference equation with three parameters, the derivative of which at a fixed point has an eigenvalue [Formula: see text] as the parameters are all zero. In the case that both nondegeneracy conditions of the flip bifurcation and the generalized flip bifurcation are not satisfied, by computing normal form ...
Jiyu Zhong, Xingwang Zhou
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Flip Bifurcation of a Class of Discrete-time Neural Networks

2009 WRI Global Congress on Intelligent Systems, 2009
In this paper, a class of discrete-time system modeling a network with two neurons is considered. Its flip bifurcations (also called period-doubling bifurcations for map) are demonstrated by deriving the equation describing the flow on the center manifold.
Xiaoliang Zhou, Rong Yu
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Homoclinic Bifurcation of Orbit Flip with Resonant Principal Eigenvalues

Acta Mathematica Sinica, English Series, 2005
Codimension–3 bifurcations of an orbit–flip homoclinic orbit with resonant principal eigenvalues are studied for a four–dimensional system. The existence, number, co–existence and non–coexistence of 1–homoclinic orbit, 1–periodic orbit, 2n–homoclinic orbit and 2n–periodic orbit are obtained. The bifurcation surfaces and existence regions are also given.
Tian Si Zhang, Deming Zhu
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Cascades of alternating pitchfork and flip bifurcations in H-bridge inverters

Physica D: Nonlinear Phenomena, 2017
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Viktor Avrutin, Zhanybai T. Zhusubaliyev, Erik Mosekilde   +2 more
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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.
Xuyang Zhang, Jingjing Li, Shuliang Shui
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Periodic solutions and flip bifurcation in a linear impulsive system

Chinese Physics B, 2008
In this paper, the dynamical behaviour of a linear impulsive system is discussed both theoretically and numerically. The existence and the stability of period-one solution are discussed by using a discrete map. The conditions of existence for flip bifurcation are derived by using the centre manifold theorem and bifurcation theorem.
Jiang Gui-Rong, Jiang Gui-Rong, Yang Qi-Gui   +2 more
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Homoclinic Flip Bifurcations in Conservative Reversible Systems [PDF]

, 2013
In this paper, flip bifurcations of homoclinic orbits in conservative reversible systems are analyzed. In such systems, orbit-flip and inclination-flip bifurcations occur simultaneously. It is shown that multi-pulses either do not bifurcate at all at flip bifurcation points or else bifurcate simultaneously to both sides of the bifurcation point.
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Cusp and generalized flip bifurcations under higher degree conditions

Nonlinear Analysis: Theory, Methods & Applications, 2003
The authors study local bifurcations generated by bi-parametric families of one-dimensional maps. It is about to define normal forms associated with codimension two bifurcations of cusp and flip types. Remind that a bifurcation is a qualitative change of a map (or an ODE) behavior under a small parameter variation.
Jose C. Valverde, Francisco Balibrea
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Non-resonance 3D homoclinic bifurcation with an inclination flip

Chaos, Solitons & Fractals, 2009
Abstract Local active coordinates approach is employed to study the bifurcation of a non-resonance three-dimensional smooth system which has a homoclinic orbit to a hyperbolic equilibrium point with three real eigenvalues - α , - β , 1 satisfying α > β > 0 . A homoclinic orbit is called an inclination-flip homoclinic orbit if
Qiuying Lu, Qiuying Lu
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