Results 11 to 20 of about 648 (183)
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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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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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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Stable heteroclinic cycles and symbolic dynamics [PDF]
Chaos: An Interdisciplinary Journal of Nonlinear Science, 1994 Let S10, S11,...,S1n−1 be n circles. A rotation in n circles is a map f:∪i=0n−1S1i→∪ i=0n−1S1i which maps each circle onto another by a rotation. This particular type of interval exchange map arises naturally in bifurcation theory. In this paper we give a full description of the symbolic dynamics associated to such maps.
Lluı́s Alsedà +2 more
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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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Sharp Bound of the Number of Zeros for a Liénard System with a Heteroclinic Loop
Discrete Dynamics in Nature and Society, 2021 In the presented paper, the Abelian integral Ih of a Liénard system is investigated, with a heteroclinic loop passing through a nilpotent saddle. By using a new algebraic criterion, we try to find the least upper bound of the number of limit cycles ...
Junning Cai, Minzhi Wei, Guoping Pang
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Dynamics of a plant-herbivore model with a chemically-mediated numerical response
Mathematics in Applied Sciences and Engineering, 2021 A system of two ordinary differential equations is proposed to model chemically-mediated interactions between plants and herbivores by incorporating a toxin-modified numerical response.
Lin Wang, James Watmough, Fang Yu
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Scalar Field Evolution at Background and Perturbation Levels for a Broad Class of Potentials
Fortschritte der Physik, Volume 71, Issue 10-11, November 2023., 2023 Abstract In this paper, a non‐interacting scalar field cosmology with an arbitrary potential using the f‐deviser method that relies on the differentiability properties of the potential is investigated. Using this alternative mathematical approach, a unified dynamical system analysis at a scalar field's background and perturbation levels with arbitrary ...
Genly Leon +5 more
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Building modern coexistence theory from the ground up: The role of community assembly
Ecology Letters, Volume 26, Issue 11, Page 1840-1861, November 2023., 2023 Modern coexistence theory (MCT) is limited by its dependence on the naive invasion growth rate criterion. We extend the applicability of MCT by using permanence theory. We use this newly developed method to gain new insights into community coexistence and its limits.
Jurg W. Spaak, Sebastian J. Schreiber
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