Identifying parameter by identical synchronization between different systems
- 1 March 2004
- journal article
- research article
- Published by AIP Publishing in Chaos: An Interdisciplinary Journal of Nonlinear Science
- Vol. 14 (1), 152-159
- https://doi.org/10.1063/1.1635095
Abstract
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.Keywords
This publication has 23 references indexed in Scilit:
- Unifying framework for synchronization of coupled dynamical systemsPhysical Review E, 2001
- A unifying definition of synchronization for dynamical systemsChaos: An Interdisciplinary Journal of Nonlinear Science, 2000
- On the chaos synchronization phenomenaPhysics Letters A, 1999
- General Approach for Chaotic Synchronization with Applications to CommunicationPhysical Review Letters, 1995
- A UNIFIED FRAMEWORK FOR SYNCHRONIZATION AND CONTROL OF DYNAMICAL SYSTEMSInternational Journal of Bifurcation and Chaos, 1994
- Modeling and synchronizing chaotic systems from time-series dataPhysical Review E, 1994
- Circuit implementation of synchronized chaos with applications to communicationsPhysical Review Letters, 1993
- Continuous control of chaos by self-controlling feedbackPhysics Letters A, 1992
- Synchronization in chaotic systemsPhysical Review Letters, 1990
- Stability Theory of Synchronized Motion in Coupled-Oscillator SystemsProgress of Theoretical Physics, 1983