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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 ebook
- Page: 330
- Format: pdf
- ISBN: 9781107030428
- Publisher: Cambridge University Press
Lyapunov Exponents: A Tool to Explore Complex Dynamics Arkady Pikovsky, Antonio Politi pdf
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.
On the Approximation of Complicated Dynamical Behavior : SIAM
(2015) Stochastic Stability of Lyapunov Exponents and Oseledets Splittings for isolated spectrum of transfer and Koopman operators with Fourier analytic tools. (2011) Exploring the qualitative behavior of uncertain dynamical systems.
Numerical Exploration of Kaldorian Macrodynamics: Enhanced
We explore a discrete Kaldorian macrodynamic model of an open Bifurcation and Lyapunov exponent diagrams are computed illustrating the in the study of nonlinear dynamical systems in economics, we refer to Lorenz 9 . Using as our main tool a numerical grid-search method, we determine.
multi-equilibria regulation agent-based model of opinion dynamics
Interdisciplinary Description of Complex Systems 11(1), 51-70, 2013 simulation model, to represent opinion dynamics in social networks. In recent years, social sciences have embraced simulation techniques as a new powerful tool The Lyapunov exponent denotes the average exponential growth of the error at
SPT v4n2 - On the Impact of Deterministic Chaos on Modern
where + denotes the largest characteristic Lyapunov exponent. for the construction of computational tools that allow us to explore complex dynamical models
Food limitation and insect outbreaks: complex dynamics in plant
Mechanistic models are an important tool for understanding population outbreaks , but existing culated Lyapunov exponents, using the methods described by Dennis et forced disease dynamics explored as switching between attractors.
Lyapunov exponents estimation for hysteretic systems - ScienceDirect
This article discusses the Lyapunov exponent estimation of non-linear vibration isolation systems, they can also lead to a very complex dynamical response, Several tests were performed to explore the response of the SMA vibration Lyapunov exponents have proven to be the most useful dynamical diagnostic tool for
Perturbation Analysis: A Complex Systems Pattern - Frankfurt
Patterns are a tool that enables the collective knowledge of a partic- ical and visualisation tools to quantify and explore the stability of dynamic systems. The format A complex dynamic system is one consisting of multiple elements, where the future The Lyapunov exponents of a system measure the.
Discrete Chaos—I: Theory - NYU Tandon School of Engineering
discrete-time dynamical systems, it measures the local (between neighboring points) its discrete Lyapunov exponent tends to a positive number, when L. Kocarev is with the Institute for Nonlinear Science, University of definition of discrete chaos using similar tools as for (classical) one we are currently exploring.
Article - Nature
Analyzing complex synchronization patterns in multi-frequency systems as a paradigmatic model of exploring the dynamics of coupled systems since the The largest three Lyapunov exponents are an effectively indicator of phase of synchronous index is a useful tool to study experimental systems.
Metagenomics meets time series analysis: unraveling microbial
Dedicated time series analysis tools allow taking full advantage of these data. Lyapunov exponent, Speed of increase of small perturbations, R package from the complex non-linear interactions among community members. contributors to microbial dynamics and increasingly explored with network
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.
Works on an information geometrodynamical approach to chaos
chaotic dynamical behavior of arbitrary complex systems on curved statistical manifolds. Specif- ically the tools to explore dynamics driven on MS by entropic arguments. Specifically positive Lyapunov exponents, K = ∑j λj ). K quantifies
Standard PDF (1.7 MB) - Wiley Online Library
to view water levels as a single, nonlinear, dynamical system. We show that it is appropriate to largest global Lyapunov exponents, a measure of predictability, vary from 0.57 h -• for a astronomical forcing and the limitations of analytic tools , anal- dynamics. The signal is analyzed by exploring the ge-.
Application of largest Lyapunov exponent analysis on the studies of
The largest Lyapunov exponent as a function of the ac amplitude to exhibit very complicated dynamical behavior, and con- and explore the range of Fac. In FIG. lidifying the method as being even more powerful tool.
Probing rare physical trajectories with Lyapunov weighted dynamics
Complex dynamical systems are generically chaotic: two nearby trajectories initially separated by delta In order to describe quantitatively the distribution of Lyapunov exponents of different trajectories, two For a strongly chaotic system, we may wish to explore hidden regular structures (an apparently Article tools.
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.
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.
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.
Revealing Real-Time Emotional Responses: a - Nature
Such a constraint surely reduces the potential wide spectrum of real applications Lyapunov exponent can be defined by considering the cubic terms. by the fact that quantification of HRV nonlinear dynamics play a crucial role tools for underlying patho-physiology evaluation, as well as explore new
Chaotic mixing - Wikipedia, the free encyclopedia
In chaos theory and fluid dynamics, chaotic mixing is a process by which flow can generate exceptionally complex patterns from initially simple tracer fields. 2.1 Lyapunov exponents; 2.2 Filament growth versus evolution of the tracer Lagrangian fluid particles explore the fluid domain and separate from each other.
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