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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.
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On perturbations of generators of analytic semigroups Martin Adler University of Tübingen, Germany Miriam Bombieri University of Tübingen, Germany,Prof Tim Benton BA, Oxford, PhD 1990, Cambridge, FSB, FLS Professor of Population Ecology; UK Champion for Global Food Security and Professor of Population Ecology ,WSEAS Transactions on Systems and Control. Print ISSN: 1991-8763 E-ISSN: 2224-2856. Volume 10, 2015. Notice: As of 2014 and for the forthcoming years, the publication ,Chaos theory is a mathematical field of study which states that non-linear dynamical systems that are seemingly random are actually deterministic from much ,Applied Mathematics Department at Brown University Courses . UNDERGRADUATE COURSES . APMA 0090. Introduction to Modeling Topics of Applied Mathematics, introduced ,Any system (needing a lot more precise definition) with the following two attributes is by definition mathematically chaotic. But that statement ,Mathematica » The #1 tool for creating Demonstrations and anything technical. Wolfram|Alpha » Explore anything with the first computational knowledge engine.,Highlights The paper focuses on turning points and complex structure of tourism demand. Overnights time series are transformed into networks and examined.,The main structures of the flow, which are essentially filaments, become finer as resolution is increased, behaving much like the geometrical persistence of a fractal ,Chaos: Classical and Quantum Chapter 31 - Noise About noise: how it affects classical dynamics, and the ways it mimicks quantum dynamics.
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