Nonlinear Phenomena in Complex Systems, 2006, Vol.9, No.1, pp.32-42

NONLINEAR PHENOMENA IN COMPLEX SYSTEMS
An Interdisciplinary Journal

2006, Vol.9, No.1, pp.32-42

Discrete Maps as a Model of Spatial Deterministic Chaos.
I. V. Izmailov, A. V. Lyachin, B. N. Poizner, and D. A. Shergin

Concept of spatial deterministic chaos (SDC) was justified. An attempt to give a set-theoretic definition of SDC was undertaken. In order to provide a mathematical description of SDC the transition from ordinary differential equations (ODEs) to discrete maps (DMs) without use of instantaneous response approximation was justified. Developed theoretical theses were used to derive a model of nonlinear phase shift dynamics in nonlinear ring interferometer (NRI) in the form of DM. In case of the model discrete realizations, phase portraits and Fourier's spectrums illustrating peculiarities of SDC in ring interferometer were constructed. Concept of DM undergoing an evolution was introduced.
Key words: spatial deterministic chaos, Lyapunov's exponents, discrete map, ordinary differential equation, nonlinear ring interferometer

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