ISSN 0869-6632 (Print)
ISSN 2542-1905 (Online)

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Izmailov I. V., Ljachin A. V., Poizner B. N., Shergin D. A. Spatial deterministic chaos: the model and demonstration of phenomenon in computing experiment. Izvestiya VUZ. Applied Nonlinear Dynamics, 2005, vol. 13, iss. 1, pp. 123-136. DOI: 10.18500/0869-6632-2005-13-1-123-136

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535:530.182 + 519.713

Spatial deterministic chaos: the model and demonstration of phenomenon in computing experiment

Izmailov Igor Valerevich, National Research Tomsk State University
Ljachin Aleksandr Vladimirovich, National Research Tomsk State University
Poizner Boris Nikolaevich, National Research Tomsk State University
Shergin Denis Aleksandrovich, National Research Tomsk State University

The concept of spatial deterministic chaos is justified. An attempt to give its settheoretic definition is undertaken. Transition from the ordinary differential equations to discrete maps without use of an approximation of the instantaneous response is realized for mathematical description of spatial deterministic chaos. The developed theoretical theses are applied for deriving a dynamics model in terms of discrete maps of nonlinear phase shift in a ring interferometer. In case of the model discrete realizations, phase portraits Fourier’s spectrums illustrating peculiarities of spatial deterministic chaos in the ring interferometer are constructed. A concept of discrete maps undergoing an evolution is introduced. 

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