Novel transition to fully absorbing state without long-range spatial order in directed percolation class

•We observe directed percolation (DP) transition to the absorbing state in a coupled Gaussian maps.•It reaches a coarse-grained period-2 state in time. It has no long-range spatial order even in a coarse-grained sense.•We propose flip rate F(t) (fraction of sites which don't return to the same band after two time-steps) as an order parameter.•Estimates of decay exponent of F(t), persistence exponent as well as of z and v‖ put the transition firmly in DP class. [Display omitted] We study coupled Gauss maps in one dimension and observe a transition to band periodic state with 2 bands. This is a periodic state with period-2 in a coarse-grained sense. This state does not show any long-range order in space. We compute two different order parameters to quantify the transition a) Flipping rate F(t) which measures departures from period-2 and b) Persistence P(t) which quantifies the loss of memory of initial conditions. At the critical point, F(t) shows a power-law decay with exponent 0.158 which is close to 1-D directed percolation (DP) transition. The persistence exponent at the critical point is found to be 1.51 which matches with several models in 1-D DP class. We also study the finite-size scaling and off-critical scaling to estimate other exponents z and ν∥. We observe excellent scaling for both F(t) as well as P(t) and the exponents obtained are clearly in DP class. We believe that DP transition could be observed in systems where activity goes to zero even if the spatial profile could be inhomogeneous and lacking any long-range order.