R E Amritkar
Articles written in Pramana – Journal of Physics
Volume 64 Issue 3 March 2005 pp 455-464
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.
Volume 71 Issue 2 August 2008 pp 195-201
We study the synchronization of coupled dynamical systems on networks. The dynamics is governed by a local nonlinear oscillator for each node of the network and interactions connecting different nodes via the links of the network. We consider existence and stability conditions for both single- and multi-cluster synchronization. For networks with time-varying topology we compare the synchronization properties of these networks with the corresponding time-average network. We find that if the different coupling matrices corresponding to the time-varying networks commute with each other then the stability of the synchronized state for both the time-varying and the time-average topologies are approximately the same. On the other hand, for non-commuting coupling matrices the stability of the synchronized state for the time-varying topology is in general better than the time-average topology.
Volume 77 Issue 5 November 2011 pp 891-904 Synchronization, Coupled Systems and Networks
We present a mechanism for the synchronization of one-way coupled nonlinear systems in which the coupling uses a variable delay, that is reset at ﬁnite intervals. Here the delay varies in the same way as the system in time and so the coupling function remains constant for the reset interval at the end of which it is reset to the value at that time. This leads to a novel and discrete error dynamics and the resulting general stability analysis is applicable to chaotic or hyperchaotic systems. We apply this method to standard chaotic systems and hyperchaotic time delay systems. The results of the detailed numerical analysis agree with the results from stability analysis in both cases. This method has the advantage that it is cost-effective since information from the driving system is needed only at intervals of reset. Further, in the context of time delay systems, optimization among the different time-scales depending upon the application is possible due to the ﬂexibility among the four different time-scales in our method, viz. delay in the driving system, anticipation in the response system, system delay time and reset time. We suggest a bi-channel scheme for implementing this method in communication ﬁeld with enhanced security
Volume 83 Issue 6 December 2014 pp 945-953 Research Articles
Kuramoto oscillators have been proposed earlier as a model for interacting systems that exhibit synchronization. In this article, we study the difference between networks with symmetric and asymmetric distribution of natural frequencies. We first indicate that synchronization frequency of oscillators in a completely connected network is always equal to the mean of the natural frequency distribution. In particular, shape of the natural frequency distribution does not affect the synchronization frequency in this case. Then, we analyse the case of oscillators in a directed ring network, where asymmetry in the natural frequency distribution is seen to shift the synchronization frequency of the network. We also present an estimate of the shift in the frequencies for slightly asymmetric distributions.
Volume 84 Issue 2 February 2015 pp 173-182
The extension of the master stability function (MSF) to analyse stability of generalized synchronization for coupled nearly identical oscillators is discussed. The nearly identical nature of the coupled oscillators is due to some parameter mismatch while the dynamical equations are the same for all the oscillators. From the stability criteria of the MSF, we construct optimal networks with better synchronization property, i.e., the synchronization is stable for widest possible range of coupling parameters. In the optimized networks the nodes with parameter value at one extreme are selected as hubs. The pair of nodes with larger parameter difference are preferred to create links in the optimized networks, and the optimized networks are found to be disassortative in nature, i.e., the nodes with high degree tend to connect with nodes with low degree.
Volume 96, 2022
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