title: Synchronization of nearly identical dynamical systems: Size instability.
abstract: We study the generalized synchronization and its stability using the master stability function (MSF) in a network of coupled nearly identical dynamical systems. We extend the MSF approach for the case of degenerate eigenvalues of the coupling matrix. Using the MSF we study the size instability in star and ring networks for coupled nearly identical dynamical systems. In the star network of coupled Rössler systems we show that the critical size beyond which synchronization is unstable can be increased by having a larger frequency for the central node of the star. For the ring network we show that the critical size is not significantly affected by parameter variations. The results are verified by explicit numerical calculations.
authors.affiliation: Physical Research Laboratory, Navrangpura, Ahmedabad 380009, India.
authors.forename: Suman
authors.initials: S
authors.lastname: Acharyya
authors.affiliation: Physical Research Laboratory, Navrangpura, Ahmedabad 380009, India.|Institute of Infrastructure, Technology, Research and Management, Khokhra Circle, Maninagar, Ahmedabad 380026, India.
authors.forename: R E
authors.initials: RE
authors.lastname: Amritkar