Correlated Brownian motion and diffusion of defects in spatially extended chaotic systems

One of the spatiotemporal patterns exhibited by coupled map lattices with nearest-neighbor coupling is the appearance of chaotic defects, which are spatially localized regions of chaotic dynamics with a particlelike behavior. Chaotic defects display random behavior and diffuse along the lattice with a Gaussian signature. In this note, we investigate some dynamical properties of chaotic defects in a lattice of coupled chaotic quadratic maps. Using a recurrence-based diagnostic, we found that the motion of chaotic defects is well-represented by a stochastic time series with a power-law spectrum 1/f^σ with 2.3≤σ≤2.4, i.e., a correlated Brownian motion. The correlation exponent corresponds to a memory effect in the Brownian motion and increases with a system parameter as the diffusion coefficient of chaotic defects.