Abstract
This paper deals with the dynamics of diffusively coupled strange attractors. Such interaction tends to equalize their instantaneous states and, for large coupling constant, results in a homogeneous state that is chaotic in time. The stability of this state depends on the relation between the Lyapunov exponent and the coupling constant. Statistical properties are determined for weakly inhomogeneous disturbances near a stable homogeneous regime. The inhomogeneous state beyond the stability threshold is treated by using the mean-field approximation. We show that both cases of soft (supercritical) and hard (subcritical) excitation of the inhomogeneous state may occur.
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Rabinovich, M.I.: Sov. Phys. Usp.21, 443 (1978)
Eckmann, J.-P.: Rev. Mod. Phys.53, 643 (1981)
Ott, E.: Rev. Mod. Phys.53, 655 (1981)
Bennett, D., Bishop, A.R., Trullinger, S.E.: Z. Phys. B.-Condensed Matter47, 265 (1982)
Fife, P.C.: Mathematical aspects of reacting and diffusio systems. Lecture Notes in Biomathematics. Vol. 29. Berlin, Heidelberg, New York: Springer 1979
Gollub, J.P., Brunner, T.V., Danley, B.G.: Science200, 48 (1978)
Ruelle, D.: Ann. N.Y. Acad. Sci.316, 408 (1979)
Haken, H.: Synergetics. Berlin, Heidelberg, New York: Springer 1981
Hudson, J.L., Hart, M., Marinko, D.: J. Chem. Phys.71, 1601 (1979)
Turner, J.S., Roux, J.-C., McCormick, W.D., Swinney, H.L.: Phys. Lett. A85, 9 (1981)
Simoyi, R.H., Wolf, A., Swinney, H.L.: Phys. Rev. Lett.49, 245 (1982)
Trikomi, F.: Lectures on partial differential equations. Torino: Editrice Gheroni 1954
Kiyashko, S.V., Pikovsky, A.S., Rabinovich, M.I.: Radiotekhn. Electron.25, 336 (1980)
Stratonovich, R.L.: Topics in the Theory of Random Noise. Vol. 1. New York: Gordon and Breach 1963
Haken, H., Wunderlin, A.: Z. Phys. B-Condensed Matter46, 181 (1982)
Fujisaka, H., Yamada, T.: Prog. Theor. Phys.69, 32 (1983)
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Pikovsky, A.S. On the interaction of strange attractors. Z. Physik B - Condensed Matter 55, 149–154 (1984). https://doi.org/10.1007/BF01420567
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DOI: https://doi.org/10.1007/BF01420567