Titlebook: Stochastic and Chaotic Oscillations; Yu. I. Neimark,P. S. Landa Book 1992 Springer Science+Business Media Dordrecht 1992 Generator.Mathema

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Brain-Imaging

https://doi.org/10.1007/978-94-011-2596-3Generator; Mathematica; Trend; dynamical systems

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Mathematical Models of Deterministic Discrete and Continuous Dynamical Systems, phase space, thus specifying its variation with time. In the course of treating motions of dynamical systems and oscillatory phenomena phasewise, chaotic motions of deterministic dynamical systems crop up for the first time.

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Order and Chaos as Two General Basic Trends in the Evolution of Dynamical Systems, viz., equilibrium states, self-excited and forced oscillations, various types of wave motions, diffusion processes and chaotic motions. All this unusual variety of motions can be separated into two basic types: order and chaos, or regularity and irregularity.

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Stochasticity Transformers, Amplifiers and Generators,while, irregular chaotic motions were represented as the joint effect of regular and random components, or as the perturbation of some regular component by a certain random component. Here, we discuss the nature of the random components of irregular chaotic motions.

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Brief Survey of Studies Related to the Appearance of the Problem of Chaotic and Stochastic Motions ics, classical mechanics, and electro-dynamics studied the former; probability theory, the theory of random processes, statistical physics, and quantum mechanics, the latter. This sharp borderline seemed unquestionable, and raised no doubts, though certain discrepancies did arise: The probabilistic

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Bifurcations and Routes to Chaos and Stochasticity,n, these sets are attracting, then they are also strange attractors with the local instability property, but are stable as a whole. It is of interest together with the “static” study of J to clarify how such sets arise in dynamics with varying parameters. The “static” and “dynamical” approaches make

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Brief Survey of Studies Related to the Appearance of the Problem of Chaotic and Stochastic Motions m mechanics, the latter. This sharp borderline seemed unquestionable, and raised no doubts, though certain discrepancies did arise: The probabilistic nature of classical statistical physics laws was not justified accurately, and was accounted for by the very large number of particles and degrees of freedom.