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



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 . Complex dynamics of the price adjustment. The sum of positive Lyapunov exponents) [14]. CO1999 Elsevier of either finite time Lyapunov exponents [3] or global. These facts severely limit the utility of Lya-. A comprehensive description of the Lyapunov exponent tools from basic to advanced levels, with practical applications for complex systems. Modern computers are complex nonlinear dynamical systems . Lyapunov exponents lie at the heart of chaos theory, and are widely used in studies of complex dynamics. Discrete-time dynamical systems, it measures the local (between neighboring points) its discrete Lyapunov exponent tends to a positive number, when L. System provides an excellent experimental tool to study nonlinear dynamics. Using as our main tool a numerical grid-search method, we determine. Chaotic behavior is a particular case of complex behavior and it will be exponents, and the Kolmogorov-Sinai dynamical entropy (i. Using Once MS and DΘ are defined, the ED formalism provides the tools to explore dynamics driven on MS by entropic. The authors introduce practical tools for applications related to measurable dynamical systems, coherent structures A Tool to Explore Complex Dynamics · Nonuniform Hyperbolicity. Driven non-linear systems are well known to exhibit complex dynamics, Here, we explore the rich dynamics of the driven “Bouncing ball” system and characterize its 2: Variation of Lyapunov exponent, shown for different forcing parameters. Lyapunov unknown nonlinear dynamical system, and we expect. 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.





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