The effect of quenched disorder on dynamical transitions in systems of coupled cells

Non-equilibrium systems are characterized by a rich variety of dynamical behaviors, which may sensitively depend on control parameters. Here, we investigate and provide a quantitative analysis of the role of disorder on the transitions between different dynamical regimes in extended heterogeneous systems of excitable and passive cells, induced by varying the strength of the coupling between cells. The random distribution of passive cells provides a quenched disorder in important biological contexts, such as the appearance of contractions in the pregnant uterus. We observe a large variability between different realizations of the disorder (replicas) in a lattice of excitable cells, each cell being coupled to a random number of passive cells. The statistics of these large disorder-induced fluctuations are related to the properties of the coarse-grained distribution of passive cells, in particular, to its extreme values. We show that these fluctuations can be characterized by a simple scaling relation, involving the strength of the coupling between excitable cells, the mean passive cell density and the logarithm of the system size. Our results provide a quantitative understanding of the important effect of a quenched disorder in the transition between dynamical regimes in extended dynamical systems.