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Transient Chaos: Complex Dynamics on Finite Time Scales
Ying-Cheng Lai,Tamás Tél +1 more
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In this article, the transition from classical chaotic scattering to transient chaos is discussed in high dimensions and fractal basin boundary boundaries, and passive and active processes in open Chaotic Flows are discussed.Abstract:
Introduction.- Chaotic Saddles.- Transition to Transient Chaos.- Fractal Basin Boundaries.- Classical Chaotic Scattering.- Passive and Active Processes in open Chaotic Flows.- Quantum Chaotic Scattering and Transport in Nanosctructures.- Transient Chaos in High Dimensions.- Further Applications and Outlooks.- Appendix: Multifractal Properties of Transient Chaos.read more
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Data based identification and prediction of nonlinear and complex dynamical systems
TL;DR: The recent advances in this forefront and rapidly evolving field of reconstructing nonlinear and complex dynamical systems from measured data or time series are reviewed, aiming to cover topics such as compressive sensing, noised-induced dynamical mapping, perturbations, reverse engineering, synchronization, inner composition alignment, global silencing and Granger Causality.
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Data Based Identification and Prediction of Nonlinear and Complex Dynamical Systems
TL;DR: The problem of reconstructing nonlinear and complex dynamical systems from measured data or time series is central to many scientific disciplines including physical, biological, computer, and social sciences, as well as engineering and economics.
Book
Lyapunov Exponents: A Tool to Explore Complex Dynamics
Arkady Pikovsky,Antonio Politi +1 more
TL;DR: This chapter discusses high-dimensional systems: Lyapunov vectors and finite-size effects, as well as applications such as Coupled systems, random systems, and more.
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Finite-time Lyapunov dimension and hidden attractor of the Rabinovich system
Nikolay Kuznetsov,Nikolay Kuznetsov,Gennady A. Leonov,Timur N. Mokaev,Awadhesh Prasad,Manish Dev Shrimali +5 more
TL;DR: In this article, the Rabinovich system can exhibit a hidden attractor in the case of multistability as well as a classical self-excited attractor, and the concept of finite-time Lyapunov dimension is developed for numerical study of the dimension of attractors.
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Species fluctuations sustained by a cyclic succession at the edge of chaos
TL;DR: The findings show that natural ecosystems can sustain continued changes in species abundances and that seasonal forcing may push these nonequilibrium dynamics to the edge of chaos.