May 16 2020
Lyapunov Exponents: A Tool to Explore Complex Dynamics
Lyapunov exponents lie at the heart of chaos theory, and are widely used in studies of complex dynamics. Utilising a pragmatic, physical approach, this self-contained book provides a comprehensive description of the concept. Beginning with the basic properties and numerical methods, it then guides readers through to the most recent advances in applications to complex systems. Practical algorithms are thoroughly reviewed and their performance is discussed, while a broad set of examples illustrate the wide range of potential applications. The description of various numerical and analytical techniques for the computation of Lyapunov exponents offers an extensive array of tools for the characterization of phenomena such as synchronization, weak and global chaos in low and high-dimensional set-ups, and localization. This text equips readers with all the investigative expertise needed to fully explore the dynamical properties of complex systems, making it ideal for both graduate students and experienced researchers.
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Lyapunov Exponents: A Tool to Explore Complex Dynamics by Arkady Pikovsky High-dimensional systems: Lyapunov vectors and finite-size effects; 12. Chaos and Coarse Graining in Statistical Mechanics - Cambridge
While statistical mechanics describe the equilibrium state of systems with new tools are needed to study the evolution of systems with many degrees of Firstly, the basic concepts of chaotic dynamics are introduced, moving on to explore the Nonlinear Dynamics, Chaotic and Complex Systems Lyapunov Exponents. Lyapunov Exponent and Surrogation Analysis of Patterns of
The Lyapunov Exponent (LyE) is one specific nonlinear tool that has been used to We explored different surrogation techniques to address the inherently noisy We used the Tools for Dynamics software (Applied Nonlinear Sciences, LLC Mapping time series into networks as a tool to assess the complex
Official Full-Text Publication: Mapping time series into networks as a tool to assess the complex dynamics of tourism systems on ResearchGate, Lyapunov Exponents - Cambridge University Press
Lyapunov Exponents, Arkady Pikovsky, Antonio Politi, 9781107030428, Cambridge University Press. A Tool to Explore Complex Dynamics. Arkady Pikovsky. Synchronization | Nonlinear Science and Fluid Dynamics
Synchronization A Universal Concept in Nonlinear Sciences Lyapunov Exponents. A Tool to Explore Complex Dynamics Perturbation Analysis - Thinking Systems - The University - School of
Patterns are a tool that enables the collective knowledge of a particular community and visualisation tools to quantify and explore the stability of dynamic systems. A complex dynamic system is one consisting of multiple elements, where the future The Lyapunov exponents of a system measure the exponential rate of
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