Effective synchronization of a class of Chua's chaotic systems using an exponential feedback coupling

In this work a robust exponential function based controller is designed to synchronize effectively a given class of Chua's chaotic systems. The stability of the drive-response systems framework is proved through the Lyapunov stability theory. Computer simulations are given to illustrate and verify the method.Comment: 12 pages, 18 figure

Chaotic Observer-based Synchronization Under Information Constraints

Limit possibilities of observer-based synchronization systems under information constraints (limited information capacity of the coupling channel) are evaluated. We give theoretical analysis for multi-dimensional drive-response systems represented in the Lurie form (linear part plus nonlinearity depending only on measurable outputs). It is shown that the upper bound of the limit synchronization error (LSE) is proportional to the upper bound of the transmission error. As a consequence, the upper and lower bounds of LSE are proportional to the maximum rate of the coupling signal and inversely proportional to the information transmission rate (channel capacity). Optimality of the binary coding for coders with one-step memory is established. The results are applied to synchronization of two chaotic Chua systems coupled via a channel with limited capacity.Comment: 7 pages, 6 figures, 27 reference

Use of synchronization and adaptive control in parameter estimation from a time series

A technique is introduced for estimating unknown parameters when time series of only one variable from a multivariate nonlinear dynamical system is given. The technique employs a combination of two different control methods, a linear feedback for synchronizing system variables and an adaptive control. The technique is shown to work even when the unknown parameter appears in the evolution equations of the variables other than the one for which the time series is given. The technique not only esablishes that explicit detailed information about all system variables and parameters is contained in a scalar time series, but also gives a way to exract it out under suitable conditions. Illustrations are presented and effect of noise is studied.Comment: Revised for simultaneous estimation of many parameters. 24 pages of RevTex, 12 figures in postscript files. To appear in PR(E