Results 161 to 170 of about 8,177 (202)

Homoclinic bifurcations in heterogeneous market models

Chaos, Solitons & Fractals, 2003
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FORONI, ILARIA, Gardini, L.
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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
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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
Jin, Yinlai, Zhu, Deming
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Homoclinic Cycle Bifurcations in Planar Maps

International Journal of Bifurcation and Chaos, 2017
In this study, bifurcations of an invariant closed curve (ICC) generated from a homoclinic connection of a saddle fixed point are analyzed in a planar map. Such bifurcations are called homoclinic cycle (HCC) bifurcations of the saddle fixed point. We examine the HCC bifurcation structure and the properties of the generated ICC.
Kamiyama, Kyohei, Komuro, Motomasa, Aihara, Kazuyuki   +2 more
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Homoclinic-Hopf interaction: an autoparametric bifurcation

Proceedings of the Royal Society of Edinburgh: Section A Mathematics, 2000
Bifurcation of periodic and chaotic solutions is investigated for coupled perturbed autonomous ordinary differential equations (ODEs) when the first unperturbed ODE has a homoclinic solution and the second unperturbed ODE possesses a Hopf singularity.
Fečkan, M., Gruendler, J.
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MULTIPLE HOMOCLINIC BIFURCATIONS FROM ORBIT-FLIP I: SUCCESSIVE HOMOCLINIC DOUBLINGS

International Journal of Bifurcation and Chaos, 1996
The purpose of this and forthcoming papers is to obtain a better understanding of complicated bifurcations for multiple homoclinic orbits. We shall take one particular type of codimension two homoclinic orbits called orbit-flip and study bifurcations to multiple homoclinic orbits appearing in a tubular neighborhood of the original orbit-flip. The main
Kokubu, Hiroshi, Komuro, Motomasa, Oka, Hiroe   +2 more
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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 ...
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Bifurcation of degenerate homoclinics

Results in Mathematics, 1992
The continuation and bifurcation of homoclinic orbits near a given degenerate homoclinic orbit is analyzed. It is shown that the existence of such degenerate homoclinic orbits is a codimension three phenomenon and that generically the set of parameter values at which a homoclinic solution exists forms a codimension one surface which shows a singularity
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Poincaré sequences, homoclinic bifurcation, and chaos

1999
Abstract Important features can be totally obscured in such a diagram, but Poincare maps can be used to detect underlying structure, such as periodic solutions having the forcing or a subharmonic frequency. In this context the investigation of periodic solutions, nearly periodic solutions, and similar phenomena is to a considerable ...
D W Jordan, P Smith
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Homoclinic bifurcation with nonhyperbolic equilibria

Nonlinear Analysis: Theory, Methods & Applications, 2007
The authors study the bifurcation of a homoclinic or heteroclinic orbit with a nonhyperbolic equilibrium, which is a pitchfork bifurcation point. The unperturbed system is assumed to possess a homoclinic orbit \(\Gamma\). Combining two discrete maps in the vicinity of \(\Gamma\), one of which describes the flow close to the equilibrium, while the other
Liu, Xingbo, Fu, Xianlong, Zhu, Deming
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