Results 51 to 60 of about 3,278 (95)
Heteroclinic Dynamics of Localized Frequency Synchrony: Heteroclinic Cycles for Small Populations [PDF]
Journal of Nonlinear Science, 2019 Many real-world systems can be modeled as networks of interacting oscillatory units. Collective dynamics that are of functional relevance for the oscillator network, such as switching between metastable states, arise through the interplay of network structure and interaction.
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Heteroclinic Cycles Imply Chaos and Are Structurally Stable [PDF]
Discrete Dynamics in Nature and Society, 2021 This paper is concerned with the chaos of discrete dynamical systems. A new concept of heteroclinic cycles connecting expanding periodic points is raised, and by a novel method, we prove an invariant subsystem is topologically conjugate to the one-side symbolic system. Thus, heteroclinic cycles imply chaos in the sense of Devaney.
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Abstract and Applied Analysis, 2013 A delayed Leslie-Gower predator-prey model with nonmonotonic functional response is studied. The existence and local stability of the positive equilibrium of the system with or without delay are completely determined in the parameter plane.
Jiao Jiang, Yongli Song
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Network Inoculation: Heteroclinics and phase transitions in an epidemic model [PDF]
, 2016 In epidemiological modelling, dynamics on networks, and in particular adaptive and heterogeneous networks have recently received much interest. Here we present a detailed analysis of a previously proposed model that combines heterogeneity in the ...
Anderson R. M. +7 more
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, 2018 Using a vector field in $\mathbb{R}^4$, 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-simple cycles.
Castro, Sofia, Lohse, Alexander
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Electronic Journal of Qualitative Theory of Differential Equations, 2017 In this work, we analyze a bi-dimensional differential equation system obtained by considering Holling type II functional response in prey–predator model with strong Allee effect in prey.
Partha Mandal, Aadil Lahrouz
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Stability and bifurcations of heteroclinic cycles of type Z
, 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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Heteroclinic connections between periodic orbits and resonance transitions in celestial mechanics [PDF]
, 2000 In this paper we apply dynamical systems techniques to the problem of heteroclinic connections and resonance transitions in the planar circular restricted three-body problem.
Koon, Wang Sang +3 more
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Stability of quasi-simple heteroclinic cycles [PDF]
Dynamical Systems, 2018 The stability of heteroclinic cycles may be obtained from the value of the local stability index along each connection of the cycle. We establish a way of calculating the local stability index for quasi-simple cycles: cycles whose connections are 1-dimensional and contained in flow-invariant spaces of equal dimension.
Garrido-da-Silva, Liliana +1 more
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Robust Heteroclinic Cycles in Pluridimensions
Journal of Nonlinear ScienceAbstract 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
Sofia B. S. D. Castro +1 more
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