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ISSN 2542-1905 (Online)

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Nikiforov A. I., Ryabov D. S., Chechin G. M. Dynamical chaos in three-dimensional dissipative system with D_2-symmetry group. Izvestiya VUZ. Applied Nonlinear Dynamics, 2004, vol. 12, iss. 6, pp. 28-43. DOI: 10.18500/0869-6632-2004-12-6-28-43

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512.54; 517.925.42

Dynamical chaos in three-dimensional dissipative system with D_2-symmetry group

Nikiforov Anton Igorevich, Brigham Young University
Ryabov Denis Sergeevich, Southern Federal University
Chechin Georgij Mihajlovich, Southern Federal University

Earlier, we found all three-dimensional dissipative systems with quadratic nonlinearities which are invariant with respect to any of 32 point symmetry groups of crystallographic symmetry and which can demonstrate chaotic behavior for appropriate values оf their pertinent parameters. Among these systems, there is one with е D_2-symmetry group. This system seems to be more simple and more elegant than those by Lorenz and Rossler which also belong to the above mentioned class of dissipative systems. In the present paper, we investigate regular and chaotic dynamics оf the Dy-symmetry system emphasizing the usefulness of the general theory of the nonlinear dynamical systems with discrete symmetries.

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We express our sincere gratitude to V.P. Sakhnenko for support of the research direction developed by the authors and to N.A. Kolodin for carrying out a number of calculations at the initial stage of preparation of this article.
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