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Resonant Homoclinic Flip Bifurcations [PDF]

Journal of Dynamics and Differential Equations, 2000
Homoclinic 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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Phase-flip bifurcation induced by time delay [PDF]

Physical Review E, 2006
We 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, Jürgen Kurths, Ramakrishna Ramaswamy, Syamal K. Dana   +3 more
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Flip-Flip Bifurcation in a Mathematical Cardiac System

International Journal of Bifurcation and Chaos, 2019
We 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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Homoclinic flip bifurcations accompanied by transcritical bifurcation [PDF]

Chinese Annals of Mathematics, Series B, 2011
The bifurcations of orbit flip homoclinic loop with nonhyperbolic equilibria are investigated. By constructing local coordinate systems near the unperturbed homoclinic orbit, Poincare maps for the new system are established. Then the existence of homoclinic orbit and the periodic orbit is studied for the system accompanied with transcritical ...
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CODIMENSION 3 BIFURCATIONS OF HOMOCLINIC ORBITS WITH ORBIT FLIPS AND INCLINATION FLIPS

Chinese Annals of Mathematics, 2004
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Deming Zhu, Shuliang Shui
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Lorenz attractors in unfoldings of homoclinic-flip bifurcations

Dynamical Systems, 2010
Lorenz-like attractors are known to appear in unfoldings from certain codimension two homoclinic bifurcations for differential equations in 3 that possess a reflectional symmetry. This includes homoclinic loops under a resonance condition and the inclination-flip homoclinic loops.
Golmakani, A., Homburg, A.J.
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Flip bifurcations of two systems of difference equations

Mathematical Methods in the Applied Sciences, 2020
This 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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HETERODIMENSIONAL CYCLE BIFURCATION WITH ORBIT-FLIP

International Journal of Bifurcation and Chaos, 2010
The local moving frame approach is employed to study the bifurcation of a degenerate heterodimensional cycle with orbit-flip in its nontransversal orbit. Under some generic hypotheses, we provide the conditions for the existence, uniqueness and noncoexistence of the homoclinic orbit, heteroclinic orbit and periodic orbit.
Zhiqin Qiao, Deming Zhu, Qiuying Lu, Tiansi Zhang   +3 more
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Homoclinic flip bifurcation with a nonhyperbolic equilibrium

Nonlinear Dynamics, 2011
In this paper, the problem of homoclinic bifurcation accompanied by a transcritical bifurcation is investigated for high-dimensional systems. With the aid of a suitable local coordinate system, the Poincare map is constructed. Under certain nongeneric conditions (orbit flip and inclination flip homoclinic orbits), the existence, nonexistence ...
Dongmei Zhang, Lina Shi, Xingbo Liu
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Numerical analysis of the flip bifurcation of maps

Applied Mathematics and Computation, 1991
A numerical procedure for the analysis of the flip bifurcation of maps in R^n is described. The procedure is based on normal forms and the center-manifold approach and can be applied to study period doubling of limit cycles in autonomous systems as well as period doubling of periodic solutions of time-periodic systems. The procedure has been programmed
Sergio Rinaldi, Yu. A. Kuznetsov
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