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Robust Heteroclinic Cycles in Pluridimensions. [PDF]
J Nonlinear SciAbstract Heteroclinic cycles are sequences of equilibria along with trajectories that connect them in a cyclic manner. We investigate a class of robust heteroclinic cycles that do not satisfy the usual condition that all connections between equilibria lie in flow-invariant subspaces of equal dimension. We refer to these as robust heteroclinic
Castro SBSD, Rucklidge AM.
europepmc +6 more sources
Examples and Counterexamples, 2022 Using a vector field in R4, we provide an example of a robust heteroclinic cycle between two equilibria that displays a mix of features exhibited by well-known types of low-dimensional heteroclinic structures, including simple, quasi-simple and pseudo ...
Sofia B.S.D. Castro, Alexander Lohse
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Multiplicity of Limit Cycle Attractors in Coupled Heteroclinic Cycles [PDF]
Progress of Theoretical Physics, 2002 A square lattice distribution of coupled oscillators that have heteroclinic cycle attractors is studied. In this system, we find a novel type of patterns that is spatially disordered and periodic in time.
Tachikawa, Masashi
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Dense heteroclinic tangencies near a Bykov cycle [PDF]
Journal of Differential Equations, 2014 This article presents a mechanism for the coexistence of hyperbolic and non-hyperbolic dynamics arising in a neighbourhood of a Bykov cycle where trajectories turn in opposite directions near the two nodes --- we say that the nodes have different ...
Labouriau, Isabel S. +1 more
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Simple heteroclinic cycles in R^4 [PDF]
Nonlinearity, 2015 In generic dynamical systems heteroclinic cycles are invariant sets of codimension at least one, but they can be structurally stable in systems which are equivariant under the action of a symmetry group, due to the existence of flow-invariant subspaces ...
Chossat, Pascal, Podvigina, Olga
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Heteroclinic Cycles in a Competitive Network [PDF]
International Journal of Bifurcation and Chaos, 2017 The competitive threshold linear networks have been recently developed and are typical examples of nonsmooth systems that can be easily constructed. Due to their flexibility for manipulation, they are used in several applications, but their dynamics (both local and global) are not completely understood.
Ulises Chialva, Walter Reartes
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Heteroclinic Cycles in Hopfield Networks [PDF]
Journal of Nonlinear Science, 2015 Learning or memory formation are associated with the strengthening of the synaptic connections between neurons according to a pattern reflected by the input. According to this theory a retained memory sequence is associated to a dynamic pattern of the associated neural circuit.
Chossat, Pascal, Krupa, Maciej
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Journal of Differential Equations, 2000 The paper presents a study of bifurcations from singular heteroclinic cycles in two parameter families of vector fields in \(\mathbb{R}^n\). The heteroclinic cycle consists of a hyperbolic singularity, a saddle-node singularity, and two heteroclinic orbits between them. The weak stable and weak unstable eigenvalues of the vector field at the hyperbolic
Ale Jan Homburg
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An Introduction to Coupled Heteroclinic Cycles [PDF]
Progress of Theoretical Physics Supplement, 2003 Coupled heteroclinic cycles are introduced as a new class of coupled oscillator systems. As an example, we study a square lattice distribution of heteroclinic cycles and show the emergence of non-chaotic disordered patterns. A short analysis of them is also reported.
Masashi Tachikawa
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Stability and bifurcations of heteroclinic cycles of type Z [PDF]
Nonlinearity, 2012 Dynamical systems that are invariant under the action of a non-trivial symmetry group can possess structurally stable heteroclinic cycles. In this paper we study stability properties of a class of structurally stable heteroclinic cycles in R^n which we ...
Podvigina, Olga
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