Results 171 to 180 of about 8,177 (202)

Cascades of Homoclinic Doubling Bifurcations

2001
We present an overview of the theory of homoclinic doubling cascades, describing bifurcation theory and discussing universal scaling properties obtained from a renormalization theory.
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Low-Dimensional Homoclinic Bifurcations of Repellers

International Journal of Bifurcation and Chaos, 2014
We study the relationship between homoclinic orbits associated with repellers, usually called snap-back repellers, and expanding sets of smooth endomorphisms. We also consider critical homoclinic orbits and prove that the bifurcations they create constitute a codimension one phenomenon.
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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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Transverse bifurcations of homoclinic cycles

Physica D: Nonlinear Phenomena, 1997
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Chossat, P., Krupa, M., Melbourne, I., Scheel, A.   +3 more
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Homoclinic Bifurcations in n Dimensions

Studies in Applied Mathematics, 1990
Bifurcations near homoclinic orbits in n dimensions are described. Depending on the eigenvalues of the Jacobian at the fixed point whose real parts are closest to zero, a strange invariant set of periodic and aperiodic orbits can be produced, which can be described by a Bernoulli shift on a finite set of symbols.
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Homoclinic Bifurcation in a Predator-Prey Model

Acta Mathematica Hungarica, 1997
The authors deal with predator-prey models \[ N' = N \Biggl[ \frac{\varepsilon}{K}(K - N) - \frac{aP}{\beta + N}\Biggr], \quad P' = P \Biggl[-M(P) + \frac{bN}{\beta + N}\Biggr], \tag{1} \] where \(N(t)\) and \(P(t)\) are the quantities of prey and predator, respectively, the function \(M(P) = (\gamma + \delta P) / (1 + P)\) describes the specific ...
Lizana, M., Niño, L.
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Hopf bifurcations and homoclinic tangencies

Nonlinearity, 1999
A general programme stated by Palis [see the book ``Hyperbolicity and sensitive chaotic dynamics at homoclinic bifurcations'' by \textit{F. Takens} and \textit{J. Palis} [Cambridge Studies in Advanced Mathematics 35, Cambridge University Press (1993; Zbl 0790.58014] and for further views the article of \textit{J.
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Bifurcation of Homoclinic Solutions for Hamiltonian Systems

Zeitschrift für Analysis und ihre Anwendungen, 2002
We consider the Hamiltonian system Ju'(x) + Mu(x) – \bigtriangledown _u F(x,u(x)) = \lambda u(x). Using variational methods obtained by Stuart on the one hand and by Giacomoni and Jeanjean on the other, we get bifurcation results for homoclinic solutions by imposing ...
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Spatial Unfolding of Homoclinic Bifurcations

2002
We consider solutions which are homogeneous in space, periodic in time, and close to being homoclinic for a partial differential equation. We show that such solutions are generically unstable with respect to large wavelength perturbations, and that the instability can be of two different types: either the well-known Kuramoto phase insta- bility, or a ...
P. Coullet, E. Risler, N. Vanderberghe
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The homoclinic twist bifurcation point

1992
We analyze bifurcations occurring in the vicinity of a homoclinic twist point for a generic two parameter family of Z 2 equivariant ODE’s in four dimensions. The results are compared with numerical results for a system of two coupled Josephson junctions with pure capacitive load.
Aronson, D.G., van Gils, S.A., Krupa, M.
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