Geodesic
Chaos phenomena in a circle of three unidirectionally connected oscillators
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 46 (2006) no. 10, pp. 1809-1821 Cet article a éte moissonné depuis la source Math-Net.Ru

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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 однонаправленно связанными в кольцо вида $$ \xymatrix{ &S_1\ar[rd]& \\ S_3\ar[ru]&&S_2\ar[ll] } $$ with suitably chosen parameters, these oscillators can exhibit a joint chaotic behavior. 
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S. D. Glyzin; A. Yu. Kolesov; N. Kh. Rozov. Chaos phenomena in a circle of three unidirectionally connected oscillators. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 46 (2006) no. 10, pp. 1809-1821. http://geodesic.mathdoc.fr/item/ZVMMF_2006_46_10_a9/

[1] Khessard B., Kazarinov N., Ven I., Teoriya i prilozheniya bifurkatsii rozhdeniya tsikla, Mir, M., 1985 | MR

[2] Migulin V. V., Medvedev V. I., Mustel E. R., Parygin V. N., Osnovy teorii kolebanii, Nauka, M., 1988

[3] Kolesov A. Yu., Rozov N. Kh., Invariantnye tory nelineinykh volnovykh uravnenii, Fizmatlit, M., 2004

[4] Bibikov Yu. N., Mnogochastotnye nelineinye kolebaniya i ikh bifurkatsii, Izd-vo LGU, L., 1991 | MR

[5] http://tracer3.narod.ru

[6] Kuznetsov S. P., Dinamicheskii khaos. Kurs lektsii, Fizmatlit, M., 2001

[7] Dmitriev A. C., Panas A. I., Dinamicheskii khaos: novye nositeli informatsii dlya sistem svyazi, Fizmatlit, M., 2002