Size instabilities in the ring and linear arrays of chaotic systems

We investigate the dynamical stabilities of ring and linear arrays of chaotic oscillators with asymmetric nearest-neighbor and long-range couplings. It is shown that the instabilities of complete chaotic synchronization occur as the numbers of oscillators are increased beyond critical values which depend on the coupling schemes and coupling parameters of the systems. Based on the master stability function and eigenvalue analysis methods, we give the semi-analytical relations between the critical values and the coupling parameters. Results are demonstrated with numerical simulations in a set of coupled Lorenz oscillators.