Results 1 to 10 of about 3,877 (218)
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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Persistence of Heteroclinic Cycles Connecting Repellers in Banach Spaces [PDF]
Journal of Mathematics, 2022 This paper is concerned with persistence of heteroclinic cycles connecting repellers in Banach spaces. It is proved that if a map with a regular and nondegenerate heteroclinic cycle connecting repellers undergoes a small perturbation, then the perturbed ...
Zongcheng Li
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Exploring Limit Cycle Bifurcations in the Presence of a Generalized Heteroclinic Loop [PDF]
Mathematics, 2023 This work revisits the number of limit cycles (LCs) in a piecewise smooth system of Hamiltonian with a heteroclinic loop generalization, subjected to perturbed functions through polynomials of degree m.
Erli Zhang, Stanford Shateyi
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Simple heteroclinic cycles in R^4 [PDF]
, 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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Stability of heteroclinic cycles in ring graphs [PDF]
Chaos: An Interdisciplinary Journal of Nonlinear Science, 2022 Networks of interacting nodes connected by edges arise in almost every branch of scientific inquiry. The connectivity structure of the network can force the existence of invariant subspaces, which would not arise in generic dynamical systems. These invariant subspaces can result in the appearance of robust heteroclinic cycles, which would otherwise be ...
Claire Postlethwaite, Rob Sturman
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Heteroclinic Dynamics of Localized Frequency Synchrony: Stability of Heteroclinic Cycles and Networks [PDF]
Journal of Nonlinear Science, 2019 In the first part of this paper, we showed that three coupled populations of identical phase oscillators give rise to heteroclinic cycles between invariant sets where populations show distinct frequencies. Here, we now give explicit stability results for these heteroclinic cycles for populations consisting of two oscillators each.
Christian Bick, Alexander Lohse
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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.
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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.
Pascal Chossat, Maciej Krupa
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Dense heteroclinic tangencies near a Bykov cycle [PDF]
, 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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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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