Cycles homoclinic to chaotic sets; robustness and resonance

DOI10.1063/1.166221zbMath1012.37020OpenAlexW2062080269WikidataQ73463534 ScholiaQ73463534MaRDI QIDQ4935810

Peter Ashwin

Publication date: 17 January 2000

Published in: Chaos: An Interdisciplinary Journal of Nonlinear Science (Search for Journal in Brave)

Full work available at URL: http://epubs.surrey.ac.uk/1497/1/fulltext.pdf

zbMATH Keywords

Lyapunov exponentsnumerical simulationschaotic attractorschaotic setcycling chaoshomoclinic cycleapproximately periodicskew-product structure

Mathematics Subject Classification ID

Strange attractors, chaotic dynamics of systems with hyperbolic behavior (37D45) Nonuniformly hyperbolic systems (Lyapunov exponents, Pesin theory, etc.) (37D25) Computational methods for ergodic theory (approximation of invariant measures, computation of Lyapunov exponents, entropy, etc.) (37M25)

Related Items

Stability of cycling behaviour near a heteroclinic network model of Rock–Paper–Scissors–Lizard–Spock ⋮ Cycling chaotic attractors in two models for dynamics with invariant subspaces ⋮ Phase resetting effects for robust cycles between chaotic sets ⋮ Coherence properties of cycling chaos ⋮ Cycling chaos: Its creation, persistence and loss of stability in a model of nonlinear magnetoconvection

Uses Software

• DSTool

Cites Work

• Time averages for unpredictable orbits of deterministic systems
• Homoclinic bifurcation at resonant eigenvalues
• On the concept of attractor
• Bubbling of attractors and synchronisation of chaotic oscillators
• Structurally stable heteroclinic cycles
• An example of a nonasymptotically stable attractor
• Time Averages for Heteroclinic Attractors
• Heteroclinic attractors: Time averages and moduli of topological conjugacy
• RIDDLED BASINS
• From attractor to chaotic saddle: a tale of transverse instability
• Heteroclinic cycles involving periodic solutions in mode interactions with O(2) symmetry