Coexistence and Dynamical Connections between Hyperchaos and Chaos in the 4D Rössler System: A Computer-Assisted Proof
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Publication:2790863
DOI10.1137/15M1039201zbMath1359.37144OpenAlexW2276585137MaRDI QIDQ2790863
Daniel Wilczak, Roberto Barrio, Sergio E. Serrano
Publication date: 8 March 2016
Published in: SIAM Journal on Applied Dynamical Systems (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1137/15m1039201
Attractors and repellers of smooth dynamical systems and their topological structure (37C70) Symbolic dynamics (37B10) Numerical chaos (65P20) Computational methods for ergodic theory (approximation of invariant measures, computation of Lyapunov exponents, entropy, etc.) (37M25) Homoclinic and heteroclinic orbits for dynamical systems (37C29)
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Uses Software
Cites Work
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- Extensive four-dimensional chaos in a mesoscopic model of the electroencephalogram
- A database of rigorous and high-precision periodic orbits of the Lorenz model
- A new image encryption algorithm based on hyper-chaos
- A topological horseshoe in the hyperchaotic Rössler attractor
- An equation for hyperchaos
- Period doubling in the Rössler system -- a computer assisted proof
- The existence of Shilnikov homoclinic orbits in the Michelson system: A computer assisted proof
- Covering relations, cone conditions and the stable manifold theorem
- Abundance of heteroclinic and homoclinic orbits for the hyperchaotic Rössler system
- The Lyapunov dimension of strange attractors
- Determining Lyapunov exponents from a time series
- Structural stability of Lorenz attractors
- Normally hyperbolic invariant manifolds in dynamical systems
- Topologically crossing heteroclinic connections to invariant tori.
- Topological-numerical approach to the existence of periodic trajectories in ODE's
- A rigorous ODE solver and Smale's 14th problem
- When chaos meets hyperchaos: 4D Rössler model
- An implicit algorithm for validated enclosures of the solutions to variational equations for ODEs
- \(C^1\) Lohner algorithm.
- Covering relations for multidimensional dynamical systems
- Bifurcations of quasi-periodic dynamics: torus breakdown
- Hyperchaotic set in continuous chaos-hyperchaos transition
- Qualitative analysis of the Rössler equations: bifurcations of limit cycles and chaotic attractors
- An equation for continuous chaos
- Transient chaos. Complex dynamics in finite-time scales
- Transition from Torus to Chaos Accompanied by Frequency Lockings with Symmetry Breaking: In Connection with the Coupled-Logistic Map
- Macro- and micro-chaotic structures in the Hindmarsh-Rose model of bursting neurons
- BEHAVIOR PATTERNS IN MULTIPARAMETRIC DYNAMICAL SYSTEMS: LORENZ MODEL
- Uniformly Hyperbolic Attractor of the Smale–Williams Type for a Poincaré Map in the Kuznetsov System
- How often are chaotic saddles nonhyperbolic?
- Bifurcations and strange attractors in the Lorenz-84 climate model with seasonal forcing
- Algorithm 924
- Periodic orbit analysis at the onset of the unstable dimension variability and at the blowout bifurcation
- Computer assisted proof of chaos in the Rössler equations and in the Hénon map
- Interval Methods for Systems of Equations
- Positive Definiteness and Stability of Interval Matrices
- Chaos in the Lorenz equations: a computer-assisted proof
- Complete Poincare sections and tangent sets
- Possible chaotic motion of comets in the Sun–Jupiter system—a computer-assisted approach based on shadowing
- Rigorous verification of cocoon bifurcations in the Michelson system
- Chaos
- Chaos-hyperchaos transition in coupled Rössler systems
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