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

Synchronization of coupled nonidentical dynamical systems

We analyze the stability of synchronized state for coupled nearly identical dynamical systems on networks by deriving an approximate Master Stability Function (MSF). Using this MSF we treat the problem of designing a network having the best synchronizability properties. We find that the edges which connect nodes with a larger relative parameter mismatch are preferred and the nodes having values at one extreme of the parameter mismatch are preferred as hubs.Comment: 11 pages, 4 figure

Synchronization of Coupled Chaotic Dynamics on Networks

We review some recent work on the synchronization of coupled dynamical systems on a variety of networks. When nodes show synchronized behaviour, two interesting phenomena can be observed. First, there are some nodes of the floating type that show intermittent behaviour between getting attached to some clusters and evolving independently. Secondly, two different ways of cluster formation can be identified, namely self-organized clusters which have mostly intra-cluster couplings and driven clusters which have mostly inter-cluster couplings.Comment: 15 pages, 3 figure