Inducing Periodicity in Lattices of Chaotic Maps with Advection

We investigate a lattice of coupled logistic maps where, in addition to the usual diffusive coupling, an advection term parameterized by an asymmetry in the coupling is introduced. The advection term induces periodic behavior on a significant number of non-periodic solutions of the purely diffusive case. Our results are based on the characteristic exponents for such systems, namely the mean Lyapunov exponent and the co-moving Lyapunov exponent. In addition, we study how to deal with more complex phenomena in which the advective velocity may vary from site to site. In particular, we observe wave-like pulses to appear and disappear intermittently whenever the advection is spatially inhomogeneous