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Master Stability Function (MSF) is one the most important tools for analyzing stability of synchronization. MSF was first introduced by Pecora and Carroll for analyzing stability of complete synchronization of identical oscillators. We extended the master stability formalism to analyze stability of generalized synchronization for coupled nearly identical oscillators which have similar dynamics with different parameter values. In this talk, I will discuss our approach to obtain MSF for nearly identical oscillators. I will then demonstrate two applications of the MSF. The MSF can be used to manipulate the maximum size of a star network showing stable synchronization, by tuning some parameter of the coupled oscillators. As a second application, we used the stability criteria provided by the MSF to design optimized networks with better synchronizability from a fixed set of nearly identical oscillators and edges. In the optimized networks the nodes with parameter values at one extreme of distribution are chosen as hubs and also pair of nodes with relatively larger parameter differences are chosen to create links.
References
[1] L. M. Pecora and T. L. Carroll, Phys. Rev. Lett. 80, 2109 (1998).
[2] Suman Acharyya and R. E. Amritkar, EPL 99, 40005 (2012). |