Computing Attractor Fields in Coupled Dynamical Discrete Networks
The processes of stabilization and synchronization in networks of dynamic interacting entities are almost ubiquitous in nature and play a very important role in many different contexts, from biology to sociology. Coupled Discrete Dynamic Networks (CDDN) are a class of models for interagent dynamic entity networks, which include coupled Boolean networks, and which present a wide range of potential applications, especially in Systems Biology. Despite their importance, there are relatively few studies focused on stability involving this particular class of models, in particular studies based on computational approaches. Attractor fields in CDDNs consist of a restricted class of globally stable system states, in which the dynamics of every interacting entity remains ``locally confined '' - for every time - in the same local attractor. The goal of this project is to develop a computationally efficient method that, given a CDDN as input, is able to respond whether or not it contains attractor fields, as well as to identify them. Experimental results show that our method is capable of recovering all attractor fields in a feasible time (in the order of minutes or at most a couple of hours in a single desktop), even for CDDNs containing several thousands of attractor fields,
suggesting that the proposed method is suitable to capture the dynamics structure of large scale CDDNs.