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Titlebook: Nonlinear Dynamics in Complex Systems; Theory and Applicati Armin Fuchs Textbook 2013 Springer-Verlag Berlin Heidelberg 2013 Chaos.Complex

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书目名称Nonlinear Dynamics in Complex Systems
副标题Theory and Applicati
编辑Armin Fuchs
视频video
概述Introduces mathematical tools of complexity and shows how these tools work in important applications useful for engineers, physicists, neuroscientists, psychologists, biologists, etc.Well structured p
图书封面Titlebook: Nonlinear Dynamics in Complex Systems; Theory and Applicati Armin Fuchs Textbook 2013 Springer-Verlag Berlin Heidelberg 2013 Chaos.Complex
描述.With many areas of science reaching across their boundaries and becoming more and more interdisciplinary, students and researchers in these fields are confronted with techniques and tools not covered by their particular education. Especially in the life- and neurosciences quantitative models based on nonlinear dynamics and complex systems are becoming as frequently implemented as traditional statistical analysis. Unfamiliarity with the terminology and rigorous mathematics may discourage many scientists to adopt these methods for their own work, even though such reluctance in most cases is not justified..This book bridges this gap by introducing the procedures and methods used for analyzing nonlinear dynamical systems. In Part I, the concepts of fixed points, phase space, stability and transitions, among others, are discussed in great detail and implemented on the basis of example elementary systems. Part II is devoted to specific, non-trivial applications: coordination of human limb movement (Haken-Kelso-Bunz model), self-organization and pattern formation in complex systems (Synergetics), and models of dynamical properties of neurons (Hodgkin-Huxley, Fitzhugh-Nagumo and Hindmarsh
出版日期Textbook 2013
关键词Chaos; Complex Systems; Complexity; Dynamical Methods; Mathematical Methods of Complexity; Nonlinear Diff
版次1
doihttps://doi.org/10.1007/978-3-642-33552-5
isbn_softcover978-3-642-42781-7
isbn_ebook978-3-642-33552-5
copyrightSpringer-Verlag Berlin Heidelberg 2013
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Two-Dimensional SystemsTwo-dimensional dynamical systems can be represented by either a single differential equation of second order, which contains a second derivative with respect to time, or by two equations of first order.
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Discrete Maps and Iterations in Space understand the complexity that can originate from simple iterative procedures. Maps are much easier to implement numerically than differential equations and exhibit an incredible richness of complex structures.
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Higher-Dimensional Systems and Chaosines, i.e. they are limit cycles. In general, as long as the ratio between .. and .. is a rational number the trajectories are closed after a finite number of turns inside and around the torus: the flow is .. This situation changes when the ratio between the two frequencies is an irrational number l
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Stochastic Systemsain a deterministic part (both feel the gravitational force pulling them downwards) but also the frictional force from the surrounding air. For the paper the air matters substantially and leads to an unpredictable path dominated by the random force. For the stone the stochastic force does not matter
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