Stability of synchronization in a shift-invariant ring of mutually coupled oscillators
Starting with a shift-invariant ring of \(N\) mutually coupled self-sustained electrical units, the authors come to consideration of the system of \(N\) nearest neighbour coupled identical Rayleigh-Duffing oscillators \[ \ddot{x}_n - \mu (1 - \dot{x}_n^2) \dot{x}_n + x_n + \beta x_n^3 = K (x_{n+1}-2 x_n + x_ {n-1}),\quad n=1,\dots,N, \] where \(\mu\), \(\beta\) and \(K\) are system parameters. For this system, they perform linear stability analysis of completely synchronized \(T\)-periodic solutions. Exploiting the translation symmetry of the system, they develop a qualitative theory for the Lyapunov exponents which relates to some extent to the Master stability function approach. Theoretical predictions about the stability of synchronous regime are compared with the results of numerics on the corresponding dynamical systems.
scientific article; zbMATH DE number 5359472