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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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MULTIPLE HOMOCLINIC BIFURCATIONS FROM ORBIT-FLIP I: SUCCESSIVE HOMOCLINIC DOUBLINGS
International Journal of Bifurcation and Chaos, 1996The purpose of this and forthcoming papers is to obtain a better understanding of complicated bifurcations for multiple homoclinic orbits. We shall take one particular type of codimension two homoclinic orbits called orbit-flip and study bifurcations to multiple homoclinic orbits appearing in a tubular neighborhood of the original orbit-flip. The main
Kokubu, Hiroshi +2 more
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Chaos from orbit-flip homoclinic orbits generated in real systems
Proceedings of ISCAS'95 - International Symposium on Circuits and Systems, 2002A new class of chaotic systems is discovered that are generated in a practical, nonlinear, mutually coupled phase-locked loop (PLL) circuit. Presented theoretical results make it possible to understand experimental results of mutually coupled PLL's on the onset of chaos using the geometry of the invariant manifolds, while the resultant simple geometry ...
null Hisa-Aki Tanaka +2 more
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Codimension 3 Non-resonant Bifurcations of Rough Heteroclinic Loops with One Orbit Flip*
Chinese Annals of Mathematics, Series B, 2006This paper presents three bifurcation theorems from a non-principal rough heteroclinic loop of a four dimensional real autonomous differential system under a perturbation of codimension \(3\). These theorems investigate the bifurcation of a heteroclinic loop, a homoclinic loop and a periodic orbit. The main tool used to state and prove these results is
Shui, Shuliang, Zhu, Deming
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Bifurcations of heterodimensional cycles with one orbit flip and one inclination flip
Nonlinear Dynamics, 2009zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Xu, Yancong, Zhu, Deming
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International Journal of Bifurcation and Chaos, 2004
Bifurcations of homoclinic orbit with orbit-flip and resonant eigenvalues corresponding to the tangent directions are investigated in a four-dimensional system. The existence, number, coexistence and incoexistence of 1-homoclinic orbit, 1-periodic orbit, 2n-homoclinic orbit and 2n-periodic orbit are given, and the bifurcation surfaces and the ...
Zhang, Tiansi, Zhu, Deming
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Bifurcations of homoclinic orbit with orbit-flip and resonant eigenvalues corresponding to the tangent directions are investigated in a four-dimensional system. The existence, number, coexistence and incoexistence of 1-homoclinic orbit, 1-periodic orbit, 2n-homoclinic orbit and 2n-periodic orbit are given, and the bifurcation surfaces and the ...
Zhang, Tiansi, Zhu, Deming
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Chaos from Orbit-Flip Homoclinic Orbits Generated in a Practical Circuit
Physical Review Letters, 1995A new class of chaotic systems is generated in a practical, nonlinear, mutually coupled phase-locked loop (PLL) circuit. Theoretical results make it possible to understand experimental results of such PLL's on the onset of chaos using the geometry of the invariant manifolds, while the resultant simple geometry and complex dynamics is expected to have ...
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Journal of the Physical Society of Japan, 2018
The distribution of d-orbital valence electrons in volborthite [Cu3V2O7(OH)2 ∙ 2H2O] was investigated by charge density analysis of the multipole model refinement. Diffraction data were obtained by synchrotron radiation single-crystal X-ray diffraction experiments.
Kento Sugawara +6 more
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The distribution of d-orbital valence electrons in volborthite [Cu3V2O7(OH)2 ∙ 2H2O] was investigated by charge density analysis of the multipole model refinement. Diffraction data were obtained by synchrotron radiation single-crystal X-ray diffraction experiments.
Kento Sugawara +6 more
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Orbital Fluctuations and Orbital Flipping in
The effect of the average R-site ionic radius IR and variance on the orbital and magnetic order in R3+-doped YVO3 was studied in Y1-xLaxVO3 and Y1-x(La0.2337Lu0.7663)xVO3 with fixed IR. The orbital flipping temperature T{CG} increases nonlinearly with increasing R-site variance, indicating that the V-O-V bond angle is not the primary driving force ...
J-Q, Yan +13 more
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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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