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On the existence of heteroclinic connections
Sao Paulo Journal of Mathematical Sciences, 2017Let \( W : \mathbb R^m \longrightarrow \mathbb R\) be a smooth nonnegative function that vanishes on a finite set \(A\), with \(\sharp A\geq 2\) and \(a_-, a_+ \) two distinct points in \(A\). The paper is concerned with the existence of heteroclinic connections between \(a_-\) and \( a_+\) for the equation \[ \ddot{u}+ \nabla W(u)=0, \;\;x \in \mathbb
Matteo Novaga +2 more
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Attractors for Robust Heteroclinic Cycles with Continua of Connections
Journal of Nonlinear Science, 1998The 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 ...
Peter Ashwin, P Chossat
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Twin Heteroclinic Connections of Reversible Systems
Regular and Chaotic DynamicszbMATH Open Web Interface contents unavailable due to conflicting licenses.
Lev Lerman
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The Bifurcations of Countable Connections from a Twisted Heteroclinic Loop
SIAM Journal on Mathematical Analysis, 1991Codimension-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.
Bo Deng
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Identifying heteroclinic connections using artificial neural networks
Acta Astronautica, 2019Abstract 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 ...
D J Scheeres, Stijn de Smet
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Saddle connections and heteroclinic orbits for standard maps
Nonlinearity, 1996Summary: 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.
Hector E Lomeli
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Cascades of heteroclinic connections in hyperbolic balance laws [PDF]
, 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 ...
Ehrt, Julia
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On the Heteroclinic Connections in the 1:3 Resonance Problem
International Journal of Bifurcation and Chaos, 2016Analytical 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 +3 more
openaire +3 more sources