Synchronization of coupled nonidentical dynamical systems

Abstract

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. Also, the nodes having values at one extreme of the parameter mismatch are preferred as hubs where the extreme is the one which gives a better stability according to the MSF curve.

Synchronization of nearly identical dynamical systems: Size instability

“…By coupled nearly identical systems we mean systems which have a node dependent parameter (NDP). Preliminary results of this study were earlier reported in [41]. We then extend the MSF formalism to coupled nearly identical systems with degenerate eigenvalues of the coupling matrix.…”

“…[41], we have extended the formalism of MSF to coupled nearly-identical systems and in this subsection, we briefly review the same. This is done for the sake of completeness and also to establish the notation.…”

“…(1) around the solutioñ x of a system with some typical parameterr [46]. In the expansion, we retain terms up-to second order and we get [41],…”

“…The MSF for coupled nearly-identical systems obtained using the above formalism is an approximation to the actual values. The accuracy of MSF and the Lyapunov exponents obtained using this formalism are discussed in Ref [41] with numerical examples. It is found that the errors are small when the systems are synchronized.…”

Synchronization-optimized networks for coupled nearly identical oscillators and their structural analysis

“…Thus, to better understand synchronization processes of natural systems it is important to construct a master stability function for generalized synchronization. Motivated by this problem, we have extended the formalism of the master stability function to the generalized synchronization of coupled nearly identical oscillators [8][9][10].…”