On the application of adaptive control and phase synchronization in non-linear fluid dynamics. (English) Zbl 1225.76137

Banerjee, Santo; Saha, Papri; Roy Chowdhury, A.

Int. J. Non-Linear Mech. 39, No. 1, 25-31 (2004).

Summary: In this paper we study certain aspects of nonlinear dynamical systems arising in atmospheric physics from the viewpoint of their synchronization. Apart from phase synchronization, a new method using an adaptive controller is formulated. The model under investigation was originally obtained by L. Stenflo [Phys. Scr. 53, 83–84 (1996)] in case of acoustic gravity waves and its chaotic properties were studied by Z. Liu [Phys. Scr. 61, 526 (2000)], C. Zhou et al. [J. Math. Phys. 38, No. 10, 5225–5239 (1997; Zbl 0897.76038)] and S. Banerjee et al. [Phys. Scr. 63, 177 (2001)]. Here, we have shown how an adaptive controller can be constructed for the synchronization of two such systems by analysing the error equation and utilizing the properties of the corresponding Hurwitz matrix

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. As a result, suitable criteria are obtained for synchronization. On the other hand, the phase of such a chaotic time series is defined from the view of Hilbert transform

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and is shown that the technique of phase synchronization can be equally applied to such systems.

MSC:

76E30	Nonlinear effects in hydrodynamic stability
37N10	Dynamical systems in fluid mechanics, oceanography and meteorology
93C40	Adaptive control/observation systems
65P20	Numerical chaos
37M10	Time series analysis of dynamical systems
86A10	Meteorology and atmospheric physics

Keywords:

synchronization; chaos; Hilbert transform; Hurwitz matrix

Citations:

Zbl 0897.76038