Universal exponents at critical line pertaining to second order phase transition in coupled logistic maps

We report results of computations carried out on a coupled map lattice (CML) of real values between 0 and 1. The local dynamics is defined by the logistic map. The CML model we investigate is endowed with time-delayed nearest-neighbor coupling as well as a feedback. Our primary focus is on possible existence of power law dependence of an appropriately defined persistence on time. We coarse grain the system by associating lattice site values below the fixed point of the logistic map with the spin-down state, and those equal to, or above the fixed point with the spin-up state. We define a modulo-2 persistence at a time t as the number of sites, which do not flip their spin up to t. We find that persistence does show power-law dependence on time with different exponents for linear coupling and feed back with odd and even delays. We find that the exponent is∼2/7 for even delays, whereas it is∼3/8 for odd delays irrespective of whether the feedback is zero, or not. In case the feedback and coupling are nonlinear, we find that the exponent is always ∼ 3/8 for even delays.