Geodesic
The Effect of Domain Deformation on the Behavior of a Distributed Kinetic System
Modelirovanie i analiz informacionnyh sistem, Tome 20 (2013) no. 1, pp. 99-106.

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The behavior of a distributed kinetic system, which is in homogeneous equilibrium within a flat circular reactor, under circular domain deformation is studied. We show that the deformation of domain may lead to appearance of stable spatially inhomogeneous oscillatory solutions, including chaotic oscillations (strange attractors), in the neighborhood of homogeneous equilibrium. We also speak about mechanisms of initiation of chaotic attractors and calculate Lyapunov exponents and Lyapunov dimension for these regimes. We call this mechanism of appearance of spatially inhomogeneous nonlinear oscillations in distributed kinetic system the domain effect.
Keywords: distributed kinetic system, nonlinear oscillations of a distributed system, strange attractor.
Mots-clés : domain deformation, chaotic oscillations 
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E. P. Kubyshkin. The Effect of Domain Deformation on the Behavior of a Distributed Kinetic System. Modelirovanie i analiz informacionnyh sistem, Tome 20 (2013) no. 1, pp. 99-106. http://geodesic.mathdoc.fr/item/MAIS_2013_20_1_a4/

[1] Yu. M. Romanovsky, N. V. Stepanova, D. S. Chernavsky, Matematicheskoye modelirovaniye v biofizike, Institut komp'yuternykh issledovaniy, Moskva–Izhevsk, 2003, 402 pp. (in Russian)

[2] D. Henry, Geometric theory of semilinear parabolic equations, Springer-Verlag, 1981, 348 pp. | MR

[3] M. A. Lavrent'yev, B. V. Shabat, Metody teorii funktsiy kompleksnogo peremennogo, Nauka, M., 1973, 736 pp. (in Russian) | MR

[4] A. Yu. Kolesov, A. N. Kulikov, Invariantnye tory nelineinykh evolyutsionnykh uravnenii, Uchebnoe posobie, Yaroslavl, 2003, 108 pp.

[5] J. E. Marsden, M. McCracken, The Hopf Bifurcation and Its Applications, Springer-Verlag, New York, 1976, 409 pp. | MR

[6] D. S. Glyzin, Paket programm dlya analiza dinamicheskikh sistem “Tracer”. Versiya 3.70 (RU), Svidetel'stvo o gosudarstvennoy registratsii programmy dlya EVM 2008611464 (in Russian)

[7] D. S. Glyzin, S. D. Glyzin, A. Yu. Kolesov, N. Kh. Rozov, “The Dynamic Renormalization Method for Finding the Maximum Lyapunov Exponent of a Chaotic Attractor”, Differential Equations, 41:2 (2005), 284–289 | DOI | MR | Zbl