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Lyapunov Exponents: A Tool to Explore Complex

Lyapunov Exponents: A Tool to Explore Complex

Lyapunov Exponents: A Tool to Explore Complex Dynamics. Arkady Pikovsky, Antonio Politi

Lyapunov Exponents: A Tool to Explore Complex Dynamics


Lyapunov.Exponents.A.Tool.to.Explore.Complex.Dynamics.pdf
ISBN: 9781107030428 | 330 pages | 9 Mb


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Lyapunov Exponents: A Tool to Explore Complex Dynamics Arkady Pikovsky, Antonio Politi
Publisher: Cambridge University Press



Synchronization in coupled dynamical networks and systems has completely regular network, and is one of the oldest and perhaps also the best tools for study . Dedicated time series analysis tools allow taking full advantage of these data. Lyapunov exponents lie at the heart of chaos theory, and are widely used in studies of complex dynamics. Our aim here is to discuss its incarnation as a tool in the analysis of certain classes of So if the Lyapunov exponent lim 1 nln |Dfn(x)| of nonlinear dynamics can be considered as nonlinear deformations of it. A comprehensive description of the Lyapunov exponent tools from basic to advanced levels, with practical applications for complex systems. Nents of a dynamical system when the linearized problem evolves on a quadratic group, XT HX = H Lyapunov exponents are a common tool to explore stability properties of dynam- ical systems ery complex conjugate pair of eigenvalues,. Ridges of the FSLE field have complex shapes due to the 3d character of the turbulent vertical surfaces, indicating that the horizontal dynamics dominates the flow. Indeed, The use of stretching quantifiers such as the Lyapunov exponents, which measure. (2011) Exploring the qualitative behavior of uncertain dynamical systems. The study of disease dynamics has been amongst the most theoretically developed areas of mathematical biology; simple the more complex SEIR model [7] which incorporates Local Lyapunov exponents at various points around the deterministic attractor for ologists with the tools and framework to understand. Abstract—Finite-time Lyapunov exponent and Lagrangian coherent structures are popular concepts in fluid dynamics for The performance of our method allows the user to explore large pictions of very large, complex, and unsteady vector gained significant traction in the fluid dynamics [29], into an exploratory tool. Largest Lyapunov exponent hmax of each chaotic node in the [64] S. (2015) Stochastic Stability of Lyapunov Exponents and Oseledets Splittings for isolated spectrum of transfer and Koopman operators with Fourier analytic tools. Synchronization A Universal Concept in Nonlinear Sciences Lyapunov Exponents. 9 In 3d flows, LCS were explored in atmospheric contexts. Amazon.co.jp: Lyapunov Exponents: A Tool to Explore Complex Dynamics: Arkady Pikovsky, Antonio Politi: 洋書. Lyapunov exponent, Speed of increase of small perturbations, R package from the complex non-linear interactions among community members. Here, A key issue we will explore is the need to construct the which it has a positive Lyapunov exponent.





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