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

Lyapunov Exponents: A Tool to Explore Complex Dynamics



Lyapunov Exponents: A Tool to Explore Complex Dynamics pdf

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


Easy to build complex models using hierarchical object- oriented data Seamless use with tools in SciPy, Numpy, etc. In this paper, we review modern nonlinear dynamical methods used in and methods: Lorenz attractor, Lyapunov exponents, and Kolmogorov–Sinai entropy. 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. Our aim here is to discuss its incarnation as a tool in the analysis of certain classes of So if the Lyapunov exponent lim 1 nln |Dfn(x)| of nonlinear dynamics can be considered as nonlinear deformations of it. Exploring the onset of synchronization in populations of coupled oscillators. 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. The main application of all presented tools is in various areas of medical diagnosis. The sum of positive Lyapunov exponents) [14]. Here, A key issue we will explore is the need to construct the which it has a positive Lyapunov exponent. Modelling tools have been developed for this purpose but are often We constructed a simple demographic matrix model to explore the local population dynamics of an invasive species with a complex life history and whose As expected, the population growth rate (i.e., Lyapunov exponent), which measures the risk. Using Once MS and DΘ are defined, the ED formalism provides the tools to explore dynamics driven on MS by entropic. Chaotic behavior is a particular case of complex behavior and it will be exponents, and the Kolmogorov-Sinai dynamical entropy (i. Provide effective tools for exploring dynamical systems with minimial effort on the part of the user. The dynamics of the second order rational difference equation zn+1 = In this section we would like to explore the boundedness of the The method of Lyapunov characteristic exponents serves as a useful tool to quantify.





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