Results 151 to 160 of about 3,010 (176)
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Homoclinic Bifurcation of Orbit Flip with Resonant Principal Eigenvalues
Acta Mathematica Sinica, English Series, 2005The authors consider the general 4-dimensional system in a resonant orbit flip situation. The resonance takes place between the two principal eigenvalues. This is a kind of codimension-3 bifurcation. The authors obtain the existence, number, coexistence of the 1-homoclinic orbit, 1-periodic orbit and 2-homoclinic orbit, etc.
Zhang, Tiansi, 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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Bifurcation analysis of the multiple flips homoclinic orbit
Chinese Annals of Mathematics, Series B, 2014zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Zhang, Tiansi, Zhu, Deming
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Degenerate bifurcations of heterodimensional cycle with orbit flip and inclination flip
SCIENTIA SINICA Mathematica, 2013We study the heterodimensional cycle with orbit flip and inclination flip in four-dimensional system. By setting up a new local coordinate system in small tubular neighborhood of unperturbed heterodimensional cycle, we construct a Poincare return map and further obtain the bifurcation equations.
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An equivariant, inclination-flip, heteroclinic bifurcation
Nonlinearity, 1996Summary: We examine a heteroclinic bifurcation occurring in families of equivariant vector fields. Within these families, the flows contain structurally stable heteroclinic cycles. The flow can twist around the cycle to produce what is the equivalent of an `inclination-flip' homoclinic orbit.
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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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Oscillation quenching and phase-flip bifurcation in coupled thermoacoustic systems
Chaos: An Interdisciplinary Journal of Nonlinear Science, 2019Oscillatory instabilities, although ubiquitous in nature, are undesirable in many situations such as biological systems, swaying of bridges and skyscrapers, aero-acoustic flutter, prey-predator and disease spread models, and thermoacoustic systems, where they exhibit large amplitude periodic oscillations.
Suraj Dange +5 more
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Simple diffusion can support the pitchfork, the flip bifurcations, and the chaos
Communications in Nonlinear Science and Numerical Simulation, 2017zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Lili Meng, Xinfu Li, Guang Zhang
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Pitchfork bifurcation and flip-flop operation with a coupled nonlinear system
Applied Optics, 1994A ring cavity system consisting of two hybrid Michelson interferometers coupled together with feedback is constructed. This system shows spatial bifurcation and can be utilized as an all-optical flip-flop device. We demonstrate experimentally a flip-flop operation by use of only a positive pulse in this system.
Y H, Yu, J M, Park, T K, Lim
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PERIOD-DOUBLING SCENARIO WITHOUT FLIP BIFURCATIONS IN A ONE-DIMENSIONAL MAP
International Journal of Bifurcation and Chaos, 2005In this work a one-dimensional piecewise-smooth dynamical system, representing a Poincaré return map for dynamical systems of the Lorenz type, is investigated. The system shows a bifurcation scenario similar to the classical period-doubling one, but which is influenced by so-called border collision phenomena and denoted as border collision period ...
Viktor Avrutin, Michael Schanz
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