Results 141 to 150 of about 1,118,392 (164)

On the Heteroclinic Connections in the 1:3 Resonance Problem

International Journal of Bifurcation and Chaos, 2016
Analytical predictions of the triangle and clover heteroclinic bifurcations in the problem of self-oscillations stability loss near 1:3 resonance are provided using the method of nonlinear time transformation. The analysis was carried out considering the slow flow of a self-excited nonlinear Mathieu oscillator corresponding to the normal form near ...
Bo-Wei Qin, Kwok-Wai Chung, Abdelhak Fahsi, Mohamed Belhaq   +3 more
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Attractors for Robust Heteroclinic Cycles with Continua of Connections

Journal of Nonlinear Science, 1998
The paper studies heteroclinic and homoclinic cycles in continuous dynamical systems with symmetry, with an emphasis on the case when there are multidimensional submanifolds of connecting orbits between fixed points in the cycle. The multidimensionality introduces some new features not present when the sets of connecting orbits are one-dimensional, in ...
Ashwin, P., Chossat, P.
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Heteroclinic Connections in the Kuramoto-Sivashinsky Equation: a Computer Assisted Proof

Reliable Computing, 1997
The authors investigate the system of differential equations \(\dot x_0= x_1\), \(\dot x_1= x_2\), \(\dot x_2= -\lambda x_1- 0,5x^2_0+ 1\) with parameter \(\lambda\) (for \(\lambda=1\) this system can be considered as a finite-dimensional approximation of the Kuramoto-Sivashinsky equation, well known from the nonlinear theory of hydrodynamical ...
Marian Mrozek, Marcin Zelawski
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Geometry of Basins of Attraction and Heteroclinic Connections in Coupled Bistable Systems

International Journal of Bifurcation and Chaos, 2014
The fundamental principle of bistability is widely used across various disciplines, including biology, chemistry, mechanics, physics, electronics and materials science. As the need for more powerful, efficient and sensitive complex-engineered systems grow, networks of coupled bistable systems have gained significant attention in recent years. Modeling
Daniel Lyons, Joseph M. Mahaffy, Sára Wang, Antonio Palacios, Visarath In   +4 more
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The Bifurcations of Countable Connections from a Twisted Heteroclinic Loop

SIAM Journal on Mathematical Analysis, 1991
Codimension-two bifurcation phenomena associated with a non-degenerate heteroclinic loop between two relatively contracting saddles in a \(d \geq 2\)-dimensional system are studied. The bifurcation curves of homoclinic loops in the parameter space are characterized in terms of the twist properties of the heteroclinic loop at the bifurcation point.
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Identifying heteroclinic connections using artificial neural networks

Acta Astronautica, 2019
Abstract This paper demonstrates the usage of artificial neural networks (ANN) to identify heteroclinic connections in astrodynamical systems. The ANN architecture is applied to find heteroclinic connections, or lack thereof, in the Earth-Moon circular restricted three body problem from L 1 to L 2 Lyapunov orbits for ...
Stijn De Smet, Daniel J. Scheeres
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Saddle connections and heteroclinic orbits for standard maps

Nonlinearity, 1996
Summary: We consider a family of standard maps that have saddle connections. After perturbation, we give sufficient conditions for these connections to break up into transversal heteroclinic connections. We use a generalization of the Melnikov method for twist maps in any number of dimensions.
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Heteroclinic connections in a realistic model of laser sustained plasma

Nonlinear Analysis: Theory, Methods & Applications, 1997
The paper is devoted to the proof of the existence of travelling wave solutions to the equations of a two temperature model describing laser sustained plasma. Previously [\textit{B. Kaźmierczak} and \textit{Z. Peradzyński}, Math. Methods Appl. Sci. 19, No.
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Cascades of heteroclinic connections in hyperbolic balance laws

2010
The Dissertation investigates the relation between global attractors of hyperbolic balance laws and viscous balance laws on the circle. Hence it is thematically located at the crossroads of hyperbolic and parabolic partial differential equations with one-dimensional space variable and periodic boundary conditions given by: (H): u_t + [f(u)]_x = g(u ...
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Identification of Intermittent Ordered Patterns as Heteroclinic Connections

Physical Review Letters, 1996
, Stone, , Gorman, , el-Hamdi, , Robbins
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