Transverse Modes of Coupled Nonlinear Oscillator Arrays

Abstract

We derive and apply an extension of Master Stability Function (MSF) theory to learn how transverse modes arise in arrays of coupled nonlinear oscillators. The MSF theory shows how network topology affects the stability of perfect synchrony between the oscillators. In particular it shows how the dynamics of the single oscillator and the eigenvalue spectrum of the coupling matrix determine the degree of synchronization of a coupled nonlinear system. In our description, the synchronous state actually corresponds to the first transverse mode of the system. We show that the MSF theory can also describe whether a non-synchronous transverse mode is stable. We apply this analysis to arrays of semiconductor lasers in order to demonstrate how mode selection occurs.