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Chaos phenomena in a circle of three unidirectionally connected oscillators

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Abstract

A method is proposed for designing chaotic oscillators. Mathematically, three so-called partial oscillators S j (j = 1, 2, 3) are chosen, each of which is modeled by a nonlinear system of ordinary differential equations with a single attractor—an equilibrium or a cycle (the case S 1 = S 2 = S 3 is not excluded). It is shown that, when unidirectionally connected in a circle of the form

with suitably chosen parameters, these oscillators can exhibit a joint chaotic behavior.

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Authors and Affiliations

  1. Faculty of Mathematics, Yaroslavl State University, Sovetskaya ul. 14, Yaroslavl, 150000, Russia

    S. D. Glyzin & A. Yu. Kolesov

  2. Faculty of Mechanics and Mathematics, Moscow State University, Leninskie gory, Moscow, 119992, Russia

    N. Kh. Rozov

Authors
  1. S. D. Glyzin
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  2. A. Yu. Kolesov
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  3. N. Kh. Rozov
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Additional information

Original Russian Text © S.D. Glyzin, A.Yu. Kolesov, N.Kh. Rozov, 2006, published in Zhurnal Vychislitel’noi Matematiki i Matematicheskoi Fiziki, 2006, Vol. 46, No. 10, pp. 1809–1821.

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Glyzin, S.D., Kolesov, A.Y. & Rozov, N.K. Chaos phenomena in a circle of three unidirectionally connected oscillators. Comput. Math. and Math. Phys. 46, 1724–1736 (2006). https://doi.org/10.1134/S0965542506100101

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  • DOI: https://doi.org/10.1134/S0965542506100101

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