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We investigate the existence of cantori for a dissipative version of the sawtooth map. Making use of an explicit parametric representation of the solution, we prove that cantori exist for any irrational value of the frequency. We also perform a numerical study aimed to determine some dynamical properties of the dissipative sawtooth map. [ABSTRACT FROM AUTHOR]

In this paper, parameters of a given (chaotic) dynamical system are estimated from time series by using identical synchronization between two different systems. This technique is based on the invariance principle of differential equations, i.e., a dynamical Lyapunov function involving synchronization error and the estimation error of parameters. The control used in this synchronization consists of feedback and adaptive control loop associated with the update law of estimation parameters. Our estimation process indicates that one may identify dynamically all unknown parameters of a given (chaotic) system as long as time series of the system are available. Lorenz and Rössler systems are used to illustrate the validity of this technique. The corresponding numerical results and analysis on the effect of noise are also given. © 2004 American Institute of Physics. [ABSTRACT FROM AUTHOR]