PSEUDO-DETERMINISTIC CHAOTIC SYSTEMS

DOI10.1142/S0218127403008636zbMath1057.37033MaRDI QIDQ4655526

Celso Grebogi, José R. R. Barbosa, Sandro E. de Souza Pinto, Ricardo L. Viana

Publication date: 8 March 2005

Published in: International Journal of Bifurcation and Chaos (Search for Journal in Brave)

zbMATH Keywords

hyperbolic systemsChaotic systemsLyapunov exponentsshadowing

Mathematics Subject Classification ID

Strange attractors, chaotic dynamics of systems with hyperbolic behavior (37D45) Approximate trajectories (pseudotrajectories, shadowing, etc.) in smooth dynamics (37C50) Dynamical aspects of attractors and their bifurcations (37G35)

Related Items (5)

Synchronization threshold in coupled logistic map lattices ⋮ The Lorenz system: hidden boundary of practical stability and the Lyapunov dimension ⋮ Crisis-induced unstable dimension variability in a dynamical system ⋮ Milnor and Topological Attractors in a Family of Two-Dimensional Lotka–Volterra Maps ⋮ Periodic orbit analysis at the onset of the unstable dimension variability and at the blowout bifurcation

Cites Work

• Unnamed Item
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• The dynamics of the Hénon map
• Characterization of transition to chaos with multiple positive Lyapunov exponents by unstable periodic orbits
• Nonlinear oscillations, dynamical systems, and bifurcations of vector fields
• Absolutely continuous invariant measures for one-parameter families of one-dimensional maps
• \(\omega\)-limit sets for axiom A diffeomorphisms
• Variation of Lyapunov exponents on a strange attractor
• Unstable dimension variability: A source of nonhyperbolicity in chaotic systems
• Scaling laws for invariant measures on hyperbolic and nonhyperbolic attractors.
• Bubbling of attractors and synchronisation of chaotic oscillators
• Rigorous verification of trajectories for the computer simulation of dynamical systems
• From attractor to chaotic saddle: a tale of transverse instability
• Pas de “Shadowing lemma” pour les dynamiques partiellement hyperboliques
• Shadowing of physical trajectories in chaotic dynamics: Containment and refinement
• Multistability and the control of complexity
• Synchronization in chaotic systems
• Crises, sudden changes in chaotic attractors, and transient chaos
• SUPER PERSISTENT CHAOTIC TRANSIENTS IN PHYSICAL SYSTEMS: EFFECT OF NOISE ON PHASE SYNCHRONIZATION OF COUPLED CHAOTIC OSCILLATORS
• RIDDLED BASINS AND UNSTABLE DIMENSION VARIABILITY IN CHAOTIC SYSTEMS WITH AND WITHOUT SYMMETRY
• Controlling chaotic dynamical systems

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