Constructive effects of noise in homoclinic chaotic systems

Many chaotic oscillators have coherent phase dynamics but strong fluctuations in the amplitudes. At variance with such a behavior, homoclinic chaos is characterized by quite regular spikes but strong fluctuation in their time intervals due to the chaotic recurrence to a saddle point. We study influences of noise on homoclinic chaos. We demonstrate both numerically and experimentally on a CO₂ laser various constructive effects of noise, including coherence resonance, noise-induced synchronization in uncoupled systems and noise-enhanced phase synchronization, deterministic resonance with respect to signal frequency, and stochastic resonance versus noise intensity in response to weak signals. The peculiar sensitivity of the system along the weak unstable manifold of the saddle point underlines the unified mechanism of these nontrivial and constructive noise-induced phenomena.