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

• Lyapunov Exponents: A Tool to Explore Complex Dynamics
• Arkady Pikovsky, Antonio Politi
• Page: 330
• Format: pdf, ePub, mobi, fb2
• ISBN: 9781107030428
• Publisher: Cambridge University Press

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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.

Lyapunov Exponents : A Tool to Explore Complex Dynamics
Download Lyapunov Exponents : A Tool to Explore Complex Dynamics book ( ISBN : 1107030420) by Arkady Pikovsky for free. Download or read online free  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. 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. Local predictability and nonhyperbolicity through finite Lyapunov
Nonlinear Dynamics, Chaos and Complex Systems Group, Departamento de By using finite Lyapunov exponent distributions, we get insight into both the local rithms must explore the phase space keeping in the same initial energy subspace. The search for invariants is one of the most common tools. Lyapunov Exponents: A Tool to Explore Complex Dynamics by
Available in: Hardcover. Lyapunov exponents lie at the heart of chaos theory, and are widely used in studies of complex dynamics. Utilising a pragmatic, Lyapunov Exponents A Tool to Explore Complex Dynamics
A comprehensive description of the Lyapunov exponent tools from basic to advanced levels, with practical applications for complex systems. Chaos in Dynamics of a Family of Transcendental Meromorphic
class of polynomials, is investigated in [4, 5, 11] to explore its global dy- namical that the nonlinear dynamics of functions in our family is little more chaotic Lyapunov exponent is an important tool to measure the chaos. Seasonally forced disease dynamics explored as switching between
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. Structural information content and Lyapunov exponent calculation in
Explore this journal > A lattice model with Monte Carlo dynamics is used to carry out computer information about the complex underlying protein dynamics. We calculate Lyapunov exponents for these unfolding runs and find If you can't find a tool you're looking for, please click the link at the top of  Artificial Ontogenies: A Computational Model of the Control and
The development of an organism involves complex patterns of dynamic behaviour 4.6 The Lyapunov exponents found using multiple initial conditions . . 69 5.4 A screenshot from TreeView: a tool for exploring ontogenetic space 104. Nonlinear dynamics and chaos methods in neurodynamics and
In this paper, we review modern nonlinear dynamical methods used in and methods: Lorenz attractor, Lyapunov exponents, and Kolmogorov–Sinai entropy. The main application of all presented tools is in various areas of medical diagnosis. exploring the onset of synchronization in populations of coupled oscillators. LYAPUNOV EXPONENTS OF SYSTEMS EVOLVING ON - CiteSeer
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,. Expectations and Chaotic Dynamics - WordPress.com
different currencies. Nonlinear dynamics in expectations can motivate complex dynamics in exchange rates Table 1: Tests on the Stability of the Largest Lyapunov Exponents. DIM2. DIM3 A central tool for the referred investigation is realized exchange rate is not fully explored and is thus a relevant research question. Onset and Synchronization of Complex Dynamic Behavior in the
Onset and Synchronization of Complex Dynamic Behavior in the Calculating the leading Lyapunov exponent confirms that this form of  ProjectOverview - PyDSTool Wiki
provide effective tools for exploring dynamical systems with minimial effort on the part of the user. Easy to build complex models using hierarchical object- oriented data Seamless use with tools in SciPy, Numpy, etc. through dynamic typing maps, Lyapunov exponent calculations, support for symbolic dynamics and 

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