Networks of Mobile Elements for Biological Systems

Abstract

In this paper we present a network model to study the impact of spatial distribution of constituents, coupling between them and diffusive processes in the context of biological situations. The model is in terms of network of mobile elements whose internal dynamics is given by differential equations exhibiting switching and/or oscillatory behaviour. To make the model more consistent with the underlying biological phenomena we incorporate properties like growth and decay into the network. We characterise this network by calculating the usual network measures like network efficiency, entropy growth, vertex degree distribution, geodesic lengths, centrality as well as fractal dimensions and generalised entropy. It is seen that the model can demonstrate the features of both scale free networks as well as small worlds network in different parameter domains. The formation of spatio-temporal patterns is another feature of such networks which makes them appealing for understanding broad qualitative aspects of problems like cell differentiation and synchronization. The response of the network to various attack strategies(isolated and multiple) is also studied.