Persistence of supertransients of spatiotemporal chaotic dynamical systems in noisy environment

Superlong chaotic transients have been discovered in numerical simulations of model spatiotemporal chaotic dynamical systems. The presence of such transients poses a fundamental difficulty for observing the asymptotic state of the system. In this paper, we investigate the effect of small random noise on the lifetime of the chaotic transient. It is found that the averaged transient lifetime scales algebraically with the amplitude of the noise, with a near-zero exponent. This indicates that the transient lifetime is almost independent of the noise amplitude and, consequently, the presence of noise is not advantageous in attempts to reduce the transient lifetime. Therefore, we expect supertransients to be common in spatially-extended chaotic systems.