Noise-induced and noise-enhanced complete synchronization of fractional order chaotic systems

Chaos synchronization between identical or non-identical chaotic systems, via either linear or nonlinear feedback control strategy, had been thoroughly studied during these several decades. Most of existed studies were carried out under the conditions where the control signal affects the interacted system´s behavior without noise pollution (or with idea transmitter channel). Unfortunately, the real case always runs as just the other way, which means the noise circumstances universally existed in the real world. In this brief paper, the complete synchronization phenomena of two fractional order chaotic systems under the influence of common noise were investigated, including the case of noise-induced synchronization and the case of noise-enhanced synchronization. By taking the fractional order Liu chaotic system as an illustration, numerical experiments reveal the relationship between noise intensity and the coupled strength for achieving synchronization under traditional linearly coupled scheme. It is found that, both noise intensity D and coupling strength k play positive effects for fractional order chaos synchronization. It is amazingly found that weak coupling can greatly decrease the strength of noise intensity D needed for achieving synchronization in comparison with that of the noise-induced case.