Towards complete detection of unstable periodic orbits in chaotic systems

DOI10.1016/S0375-9601(01)00463-7zbMath0971.37041OpenAlexW2070111669MaRDI QIDQ5941671

Ruslan L. Davidchack, Aaron Klebanoff, Ying-Cheng Lai, Erik M. Bollt

Publication date: 21 August 2001

Published in: Physics Letters. A (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0375-9601(01)00463-7

zbMATH Keywords

initial conditionsattraction basinefficient convergence

Mathematics Subject Classification ID

Computational methods for bifurcation problems in dynamical systems (37M20) Random dynamical systems (37H99)

Related Items (13)

The q-deformed Tinkerbell map ⋮ Firefly algorithm approach based on chaotic tinkerbell map applied to multivariable PID controller tuning ⋮ COUNTING LOW-PERIOD CYCLES FOR FLOWS ⋮ A new method for finding cycles by semilinear control ⋮ Unstable periodic orbit detection for ODEs with periodic forcing ⋮ AN EXACT MAP FOR A CHAOTIC BILLIARD ⋮ BIFURCATION AND CHAOS IN THE TINKERBELL MAP ⋮ Recent Developments in Chaotic Time Series Analysis ⋮ On comparing dynamical systems by defective conjugacy: A symbolic dynamics interpretation of commuter functions ⋮ Dynamical mechanisms for sensitive response of aperiodic firing cells to external stimulation ⋮ Simulated annealing algorithm for finding periodic orbits of multi-electron atomic systems ⋮ Algebraic Analysis of Bifurcations and Chaos for Discrete Dynamical Systems ⋮ On the use of stabilizing transformations for detecting unstable periodic orbits in high-dimensional flows

Uses Software

• Dynamics

Cites Work

• Unnamed Item
• A two-dimensional mapping with a strange attractor
• Finding all periodic orbits of maps using Newton methods: Sizes of basins
• How often are chaotic saddles nonhyperbolic?
• A NEW AND SIMPLE CHAOS TOY

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