From coupled map lattices to the stochastic Kardar-Parisi-Zhang equation

We discuss the space and time dependence of the continuum limit of an ensemble of coupled logistic maps on a one-dimensional lattice. We show that the resulting partial differential equation has elements of the stochastic Kardar–Parisi–Zhang growth equation and of the Fisher–Kolmogorov–Petrovskii–Piscounov equation describing front propagation. A similar study of the Lyapunov vector confirms that its space–time behaviour is of KPZ type.