Stability of synchronisation manifold in coupled fractional order nonlinear oscillators: a master stability function approach

Abstract

Master stability function (MSF) plays a substantial role in understanding the synchronisation behaviour of coupled nonlinear oscillators. Recent attention in the fractional calculus and its applications in nonlinear dynamics has expanded to investigate the network dynamics of them. Hence, we derive the MSF for couped fractional order nonlinear oscillators and investigate their relation with coupling strength and fractional order. To make the comparison between integer and fractional order MSF, we have used well known nonlinear oscillators for investigation. Similar to the integer order, the fractional order coupled nonlinear oscillators too exhibit MSFs which are analysed for existence of negative with in the finite interval of normalized coupling parameter value. We have used the same classifications of integer order MSFs to define different classes for fractional order MSF’s. By using numerical simulations, we could show that majority of fractional order coupled oscillators exhibit higher classes of MSF confirming better synchronisation compared to their integer order counterparts.