Results 221 to 230 of about 180,188 (276)

Generalized Hopf Bifurcation and Its Dual Generalized Homoclinic Bifurcation

SIAM Journal on Applied Mathematics, 1988
We show the duality between the generalized Hopf bifurcation (GHB) and the generalized homoclinic bifurcation \((GHB^*)\). This duality is twofold: (1) the Poincaré normal forms at a weak focus and at a weak saddle, (2) the bifurcation diagrams of the GHB and the \(GHB^*\).
P. Joyal
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Homoclinic bifurcation at resonant eigenvalues

Journal of Dynamics and Differential Equations, 1990
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S. Chow, B. Deng, B. Fiedler
semanticscholar   +2 more sources

Resonant Homoclinic Flip Bifurcations

Journal of Dynamics and Differential Equations, 2000
Homoclinic bifurcations gained a lot of attention because they are closely related to transitions to chaotic dynamics. Many kinds of homoclinic bifurcations were studied (the best known is the Shil'nikov case of a homoclinic orbit to a saddle-focus equilibrium).
Homburg, A.J., Krauskopf, B.
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Chemical reaction systems with a homoclinic bifurcation: an inverse problem

Journal of Mathematical Chemistry, 2015
An inverse problem framework for constructing reaction systems with prescribed properties is presented. Kinetic transformations are defined and analysed as a part of the framework, allowing an arbitrary polynomial ordinary differential equation to be ...
Tomislav Plesa, T. Vejchodský, Radek Erban   +2 more
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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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