ABSTRACT
The presence of disorder in the structural composition in many natural systems can affect the transitions between the dynamical regimes they exhibit [Binder and Young 1986; Me´zard et al. 1987]. Such disorder is frequently seen in biological systems, including the uterine muscle which has a heterogeneous composition comprising electrically excitable myocytes (smooth muscle cells) that form the bulk of the tissue and a small fraction of electrically passive cells, like fibroblasts and telocytes. The passive cells are much fewer compared to the myocytes and experimental evidence suggests that the (frozen) pattern of their connections to excitable cells is highly irregular [Popescu et al. 2007], and can be treated as a quenched disorder in the system. In this chapter, we will discuss the role of disorder on the transitions between different dynamical regimes, specifically, the emergence of oscillations from a quiescent state, 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.
