Results 171 to 180 of about 5,108 (187)

Exponential trichotomy and heteroclinic bifurcations

Nonlinear Analysis: Theory, Methods & Applications, 1997
This paper is devoted to the study of bifurcation/perturbation problems derived from the existence of homoclinic/heteroclinic orbits of flows in \(\mathbb{R}^n\). The technique used here is based on the exponential trichotomy theory for linear systems to establish principal normal coordinates.
openaire   +1 more source

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.
Liu, Xingbo, Wang, Zhenzhen, Zhu, Deming
openaire   +2 more sources

Homoclinic and heteroclinic bifurcations of Vector fields

Japan Journal of Applied Mathematics, 1988
The author studies a bifurcation of homoclinic and heteroclinic orbits in a k-parameter family of \((m+n)\)-dimensional ODES: \(\dot x=f(x)+g(x,\mu)\), \(x\in {\mathbb{R}}^{m+n}\), \(\mu \in {\mathbb{R}}^ k\) (k\(\geq 2)\), where f and g are smooth and \(g(x,0)=0\). Suppose that the system has three saddle equilibria \(0_ i(\mu)\), \(i=1,2,3\), and the
openaire   +2 more sources

T-points: A codimension two heteroclinic bifurcation

Journal of Statistical Physics, 1986
The local bifurcation structure of a heteroclinic bifurcation which has been observed in the Lorenz equations is analyzed. The existence of a particular heteroclinic loop at one point in a two-dimensional parameter space (a ``T point'') implies the existence of a line of heteroclinic loops and a logarithmic spiral of homoclinic orbits, as well as ...
Glendinning, Paul, Sparrow, Colin
openaire   +2 more sources

Bifurcations of Rough Heteroclinic Loops with Three Saddle Points

Acta Mathematica Sinica, English Series, 2002
The perturbed \(C^r\)-system \[ \dot z=f(z)+g(z,\mu)\tag{1} \] is considered with \(r\geq 4\), \(z\in \mathbb{R}^{m}\), \(\mu \in \mathbb{R}^k\), \(k\geq 3\), \(0\leq |\mu |\ll 1\), \(g(z,0)=0\). The unperturbed system (1) with \(\mu =0\) has a heteroclinic loop \(\Gamma \) connecting three hyperbolic critical points.
Jin, Yin Lai, Zhu, De Ming
openaire   +1 more source

A heteroclinic bifurcation of Anosov diffeomorphisms

Ergodic Theory and Dynamical Systems, 1998
We study some diffeomorphisms in the boundary of the set of Anosov diffeomorphisms mainly from the ergodic viewpoint. We prove that these diffeomorphisms, obtained by isotopy from an Anosov $f:M \mapsto M$ through a heteroclinic tangency, determine a manifold ${\cal M}$ of finite codimension in the set of $C^r$ diffeomorphisms.
openaire   +1 more source

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.
openaire   +1 more source

Theory and Application of a Nongeneric Heteroclinic Loop Bifurcation

SIAM Journal on Applied Mathematics, 1999
Summary: Homoclinic and heteroclinic bifurcations from a heteroclinic loop are considered. The system under consideration has three parameters, two of which are not suitable for generic unfoldings. Analytical criteria in terms of derivatives to Melnikov's functions are given for nongeneric parameters.
Chow, Shui-Nee, Deng, Bo, Friedman, Mark J.   +2 more
openaire   +1 more source

GLOBAL AND LOCAL CONTROL OF HOMOCLINIC AND HETEROCLINIC BIFURCATIONS

International Journal of Bifurcation and Chaos, 2005
A comprehensive resonant optimal control method is developed and discussed for suppressing homoclinic and heteroclinic bifurcations of a general one-degree-of-freedom nonlinear oscillator. Based on an adjustable phase shift, the primary resonant optimal control method is presented.
Cao, Hongjun, Chen, Guanrong
openaire   +1 more source

Heteroclinic bifurcation in a ratio-dependent predator-prey system

Journal of Mathematical Biology, 2004
In this paper we study the heteroclinic bifurcation in a general ratio-dependent predator-prey system. Based on the results of heteroclinic loop obtained in [J. Math. Biol. 43(2001): 221-246], we give parametric conditions of the existence of the heteroclinic loop analytically and describe the heteroclinic bifurcation surface in the parameter space, so
Tang, Yilei, Zhang, Weinian
openaire   +2 more sources