Spatiotemporal periodic pattern and propagated spatiotemporal on-off intermittency in the one-way coupled map lattice system

One-way coupled map lattice system is investigated. An antiphase spatiotemporal period-2 state (a running wave), and an alternative type of propagated spatiotemporal on-off intermittency are found. The stability of the wave is discussed in both stationary frame and comoving frame. They are characterized by conventional Lyapunov exponent and comoving Lyapunov exponent, respectively. The stability boundaries of this state are also obtained in the parameter plane. Numerical calculation shows that the propagated spatiotemporal on-off intermittency has negative Lyapunov exponent. The distribution of the laminar phases for various sites is calculated numerically. Those sites far from the boundary site obey a power law with power exponent -3/2. This interesting phenomenon seems to be independent of the choices of local function map.