Transverse Modes of Coupled Nonlinear Oscillator Arrays
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.
KeywordsDiffusive Coupling Semiconductor Laser Transverse Mode Couple Oscillator Coupling Matrix
N.N. would like to thank Alejandro Aceves of Southern Methodist University, Department of Mathematics for valuable discussions were important for the outcome of this work. This research was supported in part by the Office of Naval Research and the Laboratory Directed Research and Development Program of Oak Ridge National Laboratory. Oak Ridge National Laboratory is managed by UT-Battelle, LLC for the U.S. Department of Energy under Contract DE-AC05-00OR22725. Opinions, interpretations, and conclusions, and recommendations are those of the authors and are not necessarily endorsed by the U.S. government.
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