Results 171 to 180 of about 13,882 (205)

Homoclinic flip bifurcations accompanied by transcritical bifurcation

Chinese Annals of Mathematics, Series B, 2011
The author investigates the bifurcation of a homoclinic loop with a nonhyperbolic equilibrium by constructing a suitable Poincaré map. Using the fundamental solutions to linear variational equations as an active coordinate system, he constructs a global map which is composed of a regular map in the tubular neighborhood of the homoclinic orbit and a ...
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Homoclinic flip bifurcation with a nonhyperbolic equilibrium

Nonlinear Dynamics, 2011
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Liu, Xingbo, Shi, Lina, Zhang, Dongmei
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Homoclinic Bifurcation of Orbit Flip with Resonant Principal Eigenvalues

Acta Mathematica Sinica, English Series, 2005
The 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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NONRESONANT BIFURCATIONS OF HETEROCLINIC LOOPS WITH ONE INCLINATION FLIP

International Journal of Bifurcation and Chaos, 2011
Heteroclinic bifurcations in four-dimensional vector fields are investigated by setting up local coordinates near a heteroclinic loop. This heteroclinic loop consists of two principal heteroclinic orbits, but there is one stable foliation that involves an inclination flip.
Shui, Shuliang, Li, Jingjing, Zhang, Xuyang   +2 more
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Bifurcations of heterodimensional cycles with one orbit flip and one inclination flip

Nonlinear Dynamics, 2009
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Xu, Yancong, Zhu, Deming
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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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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 analysis of the multiple flips homoclinic orbit

Chinese Annals of Mathematics, Series B, 2014
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Zhang, Tiansi, Zhu, Deming
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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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Numerical analysis of the flip bifurcation of maps

Applied Mathematics and Computation, 1991
Discrete dynamical systems depending on a paramter \(\alpha\) are considered: \(x(t+1)=f_{\alpha}(t).\) It is assumed that an \(n\times n\) matrix \(A_{\alpha}\) and a smooth map \(g_{\alpha}\) with \(f_{\alpha}(x)=A_{\alpha}x+g_{\alpha}(x)\) and \(g_{\alpha}(0)=0\), \(\partial g/\partial x|_{\alpha =0}=0\) exists. Problems of this type are of interest
Kuznetsov, Yu. A., Rinaldi, S.
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