Results 201 to 210 of about 13,646 (248)

Codimension-4 resonant homoclinic bifurcations with orbit flips and inclination flips

Acta Mathematica Sinica, English Series, 2015
The paper studies a codimension-4 resonant homoclinic bifurcation with one orbit flip and two inclination flips, where the resonance takes place in the tangent direction of homoclinic orbit. Local active coordinate system is introduced to construct the Poincare returning map, and also the associated successor functions.
Deming Zhu, Tian Si Zhang
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Bifurcations of heterodimensional cycles with one orbit flip and one inclination flip

Nonlinear Dynamics, 2009
In this paper, the bifurcations of heterodimensional cycles are investigated by setting up a suitable local coordinate system in a four-dimensional system. Under some ungeneric conditions—one orbit flip and one inclination flip—the persistence of heterodimensional cycles, the existence of homoclinic orbit and a family of periodic orbits, the ...
Yancong Xu, Yancong Xu, Deming Zhu
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An equivariant, inclination-flip, heteroclinic bifurcation

Nonlinearity, 1996
Summary: 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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BIFURCATION OF ROUGH HETEROCLINIC LOOP WITH ORBIT FLIPS

International Journal of Bifurcation and Chaos, 2012
In 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.
Zhenzhen Wang, Deming Zhu, Xingbo Liu
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Heterodimensional cycle bifurcation with two orbit flips

Nonlinear Dynamics, 2014
In this paper, we consider a heteroclinic cycle consisting of two hyperbolic equilibria with different indices, one robust heteroclinic connection and a heteroclinic connection within a codimension-2 intersection of the corresponding manifolds of the equilibria, which is called the heterodimensional cycle.
Xingbo Liu, Yancong Xu, Sisi Wang
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Bifurcation analysis of the multiple flips homoclinic orbit

Chinese Annals of Mathematics, Series B, 2014
A high-codimension homoclinic bifurcation is considered with one orbit flip and two inclination flips accompanied by resonant principal eigenvalues. A local active coordinate system in a small neighborhood of homoclinic orbit is introduced. By analysis of the bifurcation equation, the authors obtain the conditions when the original flip homoclinic ...
Tiansi Zhang, Deming Zhu
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DEGENERATE BIFURCATIONS OF HETERODIMENSIONAL CYCLES WITH ORBIT FLIP

International Journal of Bifurcation and Chaos, 2013
In 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 ...
Deming Zhu, Junying Liu, Xingbo Liu
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Degenerate bifurcations of heterodimensional cycle with orbit flip and inclination flip

SCIENTIA SINICA Mathematica, 2013
We 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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Flip bifurcation and Neimark–Sacker bifurcation in a discrete predator–prey model with harvesting

International Journal of Biomathematics, 2019
In this paper, a difference-algebraic predator–prey model is proposed, and its complex dynamical behaviors are analyzed. The model is a discrete singular system, which is obtained by using Euler scheme to discretize a differential-algebraic predator–prey model with harvesting that we establish.
Wei Liu, Yaolin Jiang
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Bifurcation of rough heteroclinic loop with orbit and inclination flips

Nonlinear Analysis: Real World Applications, 2009
Abstract In this paper, we are concerned with the heteroclinic loop bifurcations accompanied by one orbit flip and one inclination flip under some roughness conditions. The existence of one 1-periodic orbit, one 1-homoclinic orbit, two 1-periodic orbits, one double 1-periodic orbit is obtained, respectively, approximate expressions of the ...
Qiuying Lu, Deming Zhu, Zhiqin Qiao
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