Results 131 to 140 of about 7,371 (144)

Homoclinic bifurcations in radiating diffusion flames

Combustion Theory and Modelling, 2013
We analyse the dynamics of a model describing a planar diffusion flame with radiative heat losses incorporating a single step kinetic using timestepping techniques for Lewis number equal to one. We construct the full bifurcation diagram with respect to the Damköhler number including the branches of oscillating solutions. Based on this analysis we found,
Michail E Kavousanakis, Lucia Russo, Francesco Saverio Marra, Constantinos Siettos   +3 more
openaire   +5 more sources

Secondary homoclinic bifurcation theorems

Chaos: An Interdisciplinary Journal of Nonlinear Science, 1995
We develop criteria for detecting secondary intersections and tangencies of the stable and unstable manifolds of hyperbolic periodic orbits appearing in time-periodically perturbed one degree of freedom Hamiltonian systems. A function, called the ‘‘Secondary Melnikov Function’’ (SMF) is constructed, and it is proved that simple (resp. degenerate) zeros
openaire   +3 more sources

DEGENERATED HOMOCLINIC BIFURCATIONS WITH HIGHER DIMENSIONS

Chinese Annals of Mathematics, 2000
The authors study periodic and homoclinic orbits produced from the degenerate homoclinic bifurcations, that is, they assume \[ \text{codim}(T_{r(t)} W^u+T_{r(t)} W^s)=2, \] where \(\Gamma= \{z=r(t): t\in\mathbb{R}, r(\pm\infty)=0\}\) is a homoclinic loop. They present results corresponding to the nonresonant and resonant cases and a method to establish
Yinlai Jin, Deming Zhu
openaire   +3 more sources

Homoclinic bifurcation with nonhyperbolic equilibria

Nonlinear Analysis: Theory, Methods & Applications, 2007
Abstract The problem of homoclinic bifurcation is studied for a high dimensional system with nonhyperbolic equilibria. By constructing local coordinate systems near the unperturbed homoclinic orbit, Poincare maps for the new system are established. Then the persistence of the homoclinic orbit and the bifurcation of the periodic orbit for the system ...
Deming Zhu, Xianlong Fu, Xingbo Liu
openaire   +2 more sources

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.
openaire   +2 more sources

N-Homoclinic bifurcations for homoclinic orbits changing their twisting

Journal of Dynamics and Differential Equations, 1996
The author considers two-parameter families of vector fields possessing a homoclinic orbit along a path in the parameter plane. These homoclinic orbits are homoclinic to a hyperbolic singularity that has a one-dimensional unstable manifold. The weakest stable and unstable eigenvalues of the linearized vector field at the singularity are supposed to be ...
openaire   +3 more sources

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.
D. G. Aronson, Martin Krupa, S. A. van Gils   +2 more
openaire   +3 more sources

Homoclinic flip bifurcations accompanied by transcritical bifurcation [PDF]

Chinese Annals of Mathematics, Series B, 2011
The bifurcations of orbit flip homoclinic loop with nonhyperbolic equilibria are investigated. By constructing local coordinate systems near the unperturbed homoclinic orbit, Poincare maps for the new system are established. Then the existence of homoclinic orbit and the periodic orbit is studied for the system accompanied with transcritical ...
openaire   +1 more source

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 ...
M. Lizana, L. Niño
openaire   +2 more sources

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.
openaire   +3 more sources