Titlebook: Chaos Detection and Predictability; Charalampos (Haris) Skokos,Georg A. Gottwald,Jacqu Book 2016 Springer-Verlag Berlin Heidelberg 2016 Ch

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https://doi.org/10.1007/978-3-662-48410-4Chaos Detection and Phase Space Reconstruction; Covariant and Finite Site Lyapunov Vectors; Determinis

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Book 2016e expected to occur is of utmost importance in as disparate areas as astronomy, particle physics and climate dynamics... ..To address these issues there exists a plethora of methods for chaos detection and predictability. The most commonly employed technique for investigating chaotic dynamics, i.e.

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Theory and Applications of the Mean Exponential Growth Factor of Nearby Orbits (MEGNO) Method, with that given by the maximum Lyapunov characteristic exponent but in a shorter evolution time. Applications of the MEGNO to simple discrete and continuous dynamical systems are discussed and an overview of the stability studies present in the literature encompassing quite different dynamical systems is provided.

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Der Polyneuropathie auf der Spur,s, but also with the analysis of periodic orbits and regular regions, and with the efficient computation of the solution of the variational equations by means of Taylor series methods. Finally, the methods are shown in several Hamiltonian problems, as well as in several classical dissipative systems, as the Lorenz and Rössler models.

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https://doi.org/10.1007/978-3-662-67144-3 standard map exhibiting weak chaos. We also consider examples of continuous time dynamics such as the Lorenz-96 system and a driven and damped nonlinear Schrödinger equation. Finally, we show the applicability of the 0-1 test for time series contaminated with noise as found in real world applications.

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Theory and Applications of the Orthogonal Fast Lyapunov Indicator (OFLI and OFLI2) Methods,s, but also with the analysis of periodic orbits and regular regions, and with the efficient computation of the solution of the variational equations by means of Taylor series methods. Finally, the methods are shown in several Hamiltonian problems, as well as in several classical dissipative systems, as the Lorenz and Rössler models.

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