For citation:
Anishchenko V. S., Akopov A. A., Vadivasova T. E., Strelkova G. I. Cluster synchronization destruction and chaos in an inhomoceneous active medium. Izvestiya of Saratov University. Physics , 2006, vol. 6, iss. 1, pp. 73-81. DOI: 10.18500/1817-3020-2006-6-1-2-73-81
Cluster synchronization destruction and chaos in an inhomoceneous active medium
We show that in an inhomogeneous self-sustained oscillatory medium the destruction of perfect clusters of partial synchronization, that is induced both by varying the control parameter and by noise, leads to the onset of chaotic behavior. We study the mechanisms of chaos formation in both cases. It is demonstrated that as parameters change, the transition to chaos in the deterministic medium can result from a hard (subcritical) period-doubling bifurcation and can be accompanied by intermittency. The noise-induced initiation of chaotic dynamics can be related with the existence of non-attracting chaotic motions in the vicinity of a regular regime.
- Shraiman B.I., Pumir A., Saarlos W. van etal. Spatiotemporal chaos in the one-dimensional complex Ginzburg -Landau equation//Physica D. 1992. V. 57. P. 241 -248.
- Cross M.C., Hohenberg P.С Pattern formation outside it equilibrium//Rev. Mod. Phys. 1993. V. 65. P. 851 -1112.
- Chate H. Spatiotemporal intermittency regimes of the onedimensional complex Ginzburg-Landau equation//Nonlinearity. 1994. V. 7. P. 185-204.
- Aranson I.S., Kramer L. The word of the complex Ginzburg Landau equation//Rev. Mod. Phys. 2002. V. 74. P. 99-143.
- Sakaguchi //., Shinomoto S., Kuramoto Y. Local and global self-entrainments in oscillator lattices // Progr. Theor. Phys. 1978. V. 77. P. 1005.
- Strogatz S.H., Mirollo R.E. Phase-locking and critical phenomena in lattices of coupled nonlinear oscillators with random intrinsic frequencies//Physica D. 1988. V. 31. P. 143-168.
- Ermentrout G.B., Kopell N. Frequency plateaus in a chain of weakly coupled nonlinear oscillators//Physica D. 1990. V. 41. P. 219-231.
- Osipov G.V., Sushchik MM. Synchronized clusters and multistability in arrays of oscillators with different natural frequencies//Phys. Rev. E. 1998. V. 58, № 6. P. 7198.
- Ermentrout G.B., Troy W.C. Phase locking in a reactiondiffusion system with a linear frequency gradient//SIAM J. Math. Ann. 1986. V. 46, № 3. p. 359.
- Diamant N.E., Bortoff A. Nature of the intestinal slowwave frequency//Amer. J. Physiol. 1969. V. 216, № 2. P.301-307.
- Winfree AT. The geometry of biological time. N. Y.: Springer, 1980.
- Anishchenko V.S., Vadivasova Т.Е., Okrokvertskhov G.A. et ail Chaotic dynamics of a spatio-inhomogeneous medium//Intern. J. of Bifurcation and Chaos. 2005. V. 15, №11. P. 3661 -3673.
- Vadivasova Т.Е., Strelkova G.J., Anishchenko V.S. Phasefrequency synchronization in a chain of periodic oscillators in the presence of noise and harmonic forcings//Phys. Rev. E. 2001. V. 63. P. 036225.
- Garcia-Ojalvo J., SanchoJ.M. Noise in Spatially Extended Systems. N. Y.: Springer, 1999.
- Berge P., Pomeau }'., Vidal Ch. Order within chaos. N. Y.: Wiley, 1984.
- Schuster H.G. Deterministic Chaos. Wienhiem: Physik-Verlag, 1984.
- Dubois M, Rubio M.A., Berge P. Experimental Evidence of Intermittencies Associated with a Subharmonic Bifurcation//Phys. Rev. Lett. 1983. V. 51. P. 1446 -1449.
- Anishchenko VS., Herzel H. Noise induced chaos in a system with homoclinic points//ZAMM. 1988. V. 68, № 7. P. 317.
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