113 research outputs found
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
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