Stability of Heteroclinic Cycles: A New Approach Based on a Replicator Equation

Peixe, Telmo; Rodrigues, Alexandre A.

doi:10.1007/s00332-023-09953-7

J Nonlinear Sci

2023

DOI: 10.1007/s00332-023-09953-7

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Stability of Heteroclinic Cycles: A New Approach Based on a Replicator Equation

Telmo Peixe,

Alexandre A. Rodrigues

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Cited by 3 publications

References 36 publications

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Chaos, Solitons & Fractals

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Finite switching near heteroclinic networks

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Nonlinearity

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We address the level of complexity that can be observed in the dynamics near a robust heteroclinic network. We show that infinite switching, which is a path towards chaos, does not exist near a heteroclinic network such that the eigenvalues of the Jacobian matrix at each node are all real. Furthermore, for a path starting at a node that belongs to more than one heteroclinic cycle, we find a bound for the number of such nodes that can exist in any such path. This constricted dynamics is in stark contrast with examples in the literature of heteroclinic networks such that the eigenvalues of the Jacobian matrix at one node are complex.

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Stability of Heteroclinic Cycles: A New Approach Based on a Replicator Equation

Cited by 3 publications

References 36 publications

Dynamics near the three-point heteroclinic cycles with saddle-focus

Dynamics near the three-point heteroclinic cycles with saddle-focus

An escort replicator dynamic with a continuous action space and its application to resource management

Finite switching near heteroclinic networks

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