Identifying parameter by identical synchronization between different systems. (English) Zbl 1080.37092

Summary: Here, 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.


37M15 Discretization methods and integrators (symplectic, variational, geometric, etc.) for dynamical systems
37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior
93B30 System identification
Full Text: DOI


[1] DOI: 10.1143/PTP.69.32 · Zbl 1171.70306
[2] DOI: 10.1103/PhysRevLett.64.821 · Zbl 0938.37019
[3] DOI: 10.1016/S0375-9601(99)00667-2 · Zbl 0936.37010
[4] DOI: 10.1063/1.166500 · Zbl 0973.34041
[5] DOI: 10.1103/PhysRevE.63.066219
[6] DOI: 10.1016/0375-9601(92)90745-8
[7] DOI: 10.1103/PhysRevLett.71.65
[8] DOI: 10.1142/S0218127494000691 · Zbl 0875.93445
[9] DOI: 10.1103/PhysRevE.49.3784
[10] DOI: 10.1103/PhysRevLett.74.5028
[11] DOI: 10.1103/PhysRevE.48.R1624
[12] DOI: 10.1103/PhysRevLett.70.3031
[13] DOI: 10.1016/0375-9601(84)90009-4
[14] DOI: 10.1103/PhysRevE.53.4351
[15] DOI: 10.1063/1.1489115
[16] DOI: 10.1016/S0370-1573(02)00137-0 · Zbl 0995.37022
[17] DOI: 10.1103/PhysRevLett.76.1232
[18] DOI: 10.1103/PhysRevE.54.6253
[19] DOI: 10.1103/PhysRevE.59.284
[20] DOI: 10.1006/jdeq.2000.3902 · Zbl 0974.34056
[21] DOI: 10.1103/PhysRevE.56.2272
[22] DOI: 10.1016/S0167-2789(99)00127-X · Zbl 0997.37060
[23] DOI: 10.1142/S0218127499001024 · Zbl 0962.37013
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.