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
Publisher: Cambridge University Press
Format: pdf
Page: 330
ISBN: 9781107030428

Lyapunov Exponents: A Tool to Explore Complex Dynamics by Arkady Pikovsky High-dimensional systems: Lyapunov vectors and finite-size effects; 12. The signal is analyzed by exploring the ge-. 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,. Lyapunov Exponents A Tool to Explore Complex Dynamics. Such a constraint surely reduces the potential wide spectrum of real applications Lyapunov exponent can be defined by considering the cubic terms. Fishpond NZ, Lyapunov Exponents: A Tool to Explore Complex Dynamics by Antonio Politi Arkady Pikovsky. Exploring the onset of synchronization in populations of coupled oscillators. ISBN13： Synchronization：A Universal Concept in Nonlinear Sciences. Lyapunov Exponents ― A Tool to Explore Complex Dynamics. The main application of all presented tools is in various areas of medical diagnosis. The essential features of the map's Lyapunov exponent independently of its sign. Where + denotes the largest characteristic Lyapunov exponent. We expose a remarkable relationship between nonlinear dynamical systems and complex system into a different context that requires complex network tools [8]– [12] to extract its properties. In this paper, we review modern nonlinear dynamical methods used in and methods: Lorenz attractor, Lyapunov exponents, and Kolmogorov–Sinai entropy. Authors: Arkady Pikovsky, Universität Potsdam, Germany; Antonio Politi, University of Aberdeen. 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. 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. To view water levels as a single, nonlinear, dynamical system.