The modification of Lyapunov exponents spectrum calculation approach for coupled self-oscillating systems, simulated within the framework of PIC-method (the most efficient approach for numerical simulation of beam-plasma systems with intensive electron flows), is suggested in this work. The analysis of Lyapunov exponents spectrum allows to study the nonlinear progressing in chains and networks of coupled spatially-extended self-oscillating systems and estimate the exact bound of generalized synchronization of interacting generators appearance.
05.45.Jn High-dimensional chaos
05.45.Pq Numerical simulations of chaotic systems
05.45.Xt Synchronization; coupled oscillators
$^1$Department of Electronic, Oscillations and Waves, Faculty of Nonlinear Processes, Saratov State University. Saratov 410012, Russia
$^2$Department of Physics of Open Systems, Faculty of Nonlinear Processes, Saratov State University. Saratov 410012, Russia
$^3$Scientific Educational Centre «Nonlinear Dynamics of Complex Systems», Saratov State Technical University. Saratov 410054, Russia
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