Transient Periodic Rotating Waves and Fast Propagation of Synchronization in Linear Arrays of Chaotic Systems

Abstract

We study the behavior of arrays of unidirectionally coupled Lorenz systems in the chaotic regime. In the case of rings an instability in the uniform synchronized state leads to the appearance of a periodic rotating wave through a symmetric Hopf bifurcation. From theoretical grounds it is argued that this behavior must also manifest in the behavior of linear arrays. Numerically it is shown that this happens in a transient way, leading to unexpected consequences in the velocity of synchronization, that becomes larger.