Spatio-Temporal Chaotic Synchronization for Modes Coupled Two Ginzburg-Landau Equations

HU Man-feng; XU Zhen-yuan

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HU Man-feng, XU Zhen-yuan. Spatio-Temporal Chaotic Synchronization for Modes Coupled Two Ginzburg-Landau Equations[J]. Applied Mathematics and Mechanics, 2006, 27(8): 1001-1008.

Citation:

HU Man-feng, XU Zhen-yuan. Spatio-Temporal Chaotic Synchronization for Modes Coupled Two Ginzburg-Landau Equations[J]. Applied Mathematics and Mechanics, 2006, 27(8): 1001-1008.

Citation:

HU Man-feng, XU Zhen-yuan. Spatio-Temporal Chaotic Synchronization for Modes Coupled Two Ginzburg-Landau Equations[J]. Applied Mathematics and Mechanics, 2006, 27(8): 1001-1008.

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Spatio-Temporal Chaotic Synchronization for Modes Coupled Two Ginzburg-Landau Equations

School of Science, Southern Yangtze University, Wuxi, Jiangsu 214122, P. R. China

Received Date: 2004-08-17
Rev Recd Date: 2006-02-24
Publish Date: 2006-08-15

Abstract

Abstract

On the basis of numerical computation,the conditions of the modes coupling were proposed.The high-frequency modes are coupled,but the low frequency modes are uncoupled.It was proved that the existence of an absorbing set and a global finite dimensional attractor which is compact,connected in the function space for the high-frequency modes coupled two Ginzburg-Landau equations(MGLE).The trajectory of driver equation may be spatio-temporal chaotic.One associats with MGLE,a truncated form of the equations.The prepared equations will persist in long time dynamical behavior of MGLE.MGLE possess the squeezing properties under some conditions.It was proved that the complete spatio-temporal chaotic synchronization for MGLE can occur.Synchronization phenomenon of infinite dimensional dynamical system(IFDDS) was illustrated on the mathematical theory qualitatively.The method is different from Liapunov function methods and approximate linear methods.
- complete synchronization,
- Ginzburg-Landau equations,
- attractor,
- spatio-temporal chaos

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References(10)

References

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