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MOdulation-Guided ENcoding (MOGEN) Scheme for Vessel-Encoded Arterial Spin Labeling
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Resonant Homoclinic Flip Bifurcations
Journal of Dynamics and Differential Equations, 2000Homoclinic bifurcations gained a lot of attention because they are closely related to transitions to chaotic dynamics. Many kinds of homoclinic bifurcations were studied (the best known is the Shil'nikov case of a homoclinic orbit to a saddle-focus equilibrium).
Homburg, A.J., Krauskopf, B.
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Flip-Flip Bifurcation in a Mathematical Cardiac System
International Journal of Bifurcation and Chaos, 2019We study the intersection of double-flip (period-doubling) bifurcations in a parameter plane. We derive normal forms for discrete-time and continuous-time systems. Using these normal forms, we clarify the bifurcation structure around the flip-flip bifurcation point. We apply these analytical results to a system of coupled ventricular cell models.
Hiroyuki Kitajima, Toru Yazawa
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Phase-flip bifurcation induced by time delay
Physical Review E, 2006We present a general bifurcation in the synchronized dynamics of time-delay-coupled nonlinear oscillators. The relative phase between the oscillators jumps from zero to pi as a function of the coupling; this phase-flip bifurcation is accompanied by a discontinuous change in the frequency of the synchronized oscillators.
Awadhesh, Prasad +3 more
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CODIMENSION 3 BIFURCATIONS OF HOMOCLINIC ORBITS WITH ORBIT FLIPS AND INCLINATION FLIPS
Chinese Annals of Mathematics, 2004zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Shui, Shuliang, Zhu, Deming
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BIFURCATION OF ROUGH HETEROCLINIC LOOP WITH ORBIT FLIPS
International Journal of Bifurcation and Chaos, 2012In 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.
Liu, Xingbo, Wang, Zhenzhen, Zhu, Deming
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DEGENERATE BIFURCATIONS OF HETERODIMENSIONAL CYCLES WITH ORBIT FLIP
International Journal of Bifurcation and Chaos, 2013In this paper, nongeneric bifurcation analysis near heterodimensional cycles with orbit flip is investigated for three-dimensional systems. With the aid of a suitable local coordinate system, the Poincaré map is constructed. By means of the bifurcation equations, the existence, nonexistence, coexistence and uniqueness of homoclinic orbit, periodic ...
Liu, Xingbo, Liu, Junying, Zhu, Deming
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Degenerate Orbit Flip Homoclinic Bifurcations with Higher Dimensions
Acta Mathematica Sinica, English Series, 2006For higher dimensional systems, bifurcations of a degenerate homoclinic orbit with orbit flip are studied. By establishing local coordinates near the homoclinic orbit, conditions are given sufficient for the existence and uniqueness of a 1-homoclinic orbit and a 1-periodic orbit.
Wu, Ran Chao, Sun, Jian Hua
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Heterodimensional cycle bifurcation with two orbit flips
Nonlinear Dynamics, 2014zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Liu, Xingbo, Xu, Yancong, Wang, Sisi
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Flip bifurcations of two systems of difference equations
Mathematical Methods in the Applied Sciences, 2020This paper investigates the bifurcations of the following difference equations where a,b,c, and d are positive constants and the initial conditions x0 and y0 are positive numbers. Psarros, Papaschinopoulos, and Schinas (Math. Methods Appl. Sci., 2016, 39: 5216–5222) presented the semistability of the fixed point (0,0) when one eigenvalue is equal to ...
Qi Cheng, Shengfu Deng
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