Abstract
Cellular automata (CA) are a remarkably efficient tool for exploring general properties of complex systems and spatiotemporal patterns arising from local rules. Totalistic cellular automata, where the update rules depend only on the density of neighboring states, are at the same time a versatile tool for exploring dynamical processes on graphs. Here we briefly review our previous results on cellular automata on graphs, emphasizing some systematic relationships between network architecture and dynamics identified in this way. We then extend the investigation towards graphs obtained in a simulated-evolution procedure, starting from Erdő s–Renyi (ER) graphs and selecting for low entropies of the CA dynamics. Our key result is a strong association of low Shannon entropies with a broadening of the graph’s degree distribution.
Highlights
Understanding the shaping of biological networks by function is a major challenge in current research on complex systems
The results presented here show that the degree distribution can be related to the dynamic properties of the network: In the following we will show that a dynamic requirement selected for via simulated evolution can have a direct impact on the degree distribution
One striking example is Turing’s concept of reaction-diffusion processes [56], which has a vast range of applications—from biology to social systems
Summary
Understanding the shaping of biological networks by function is a major challenge in current research on complex systems. For biological networks, this large-scale, system-wide perspective of the network architecture (the “topology” of such graphs) has yielded some unexpected universal features (e.g., the ubiquity of heavy-tail degree distributions [1,2], the presence and possible functions of modules [3,4] and a similarity in motif content of functionally similar networks [5,6]). On this basis, network analysis provides a unifying framework to investigate the dynamics of numerous complex systems, ranging from social and technical systems to regulatory functions of living organisms (see, e.g., [7]). The intuition that some properties of dynamics on graphs are determined (or at least systematically shaped) by graph topology stems from a range of case studies, of random walk (or diffusion processes) on graphs [9] and of synchronization of oscillatory nodes in a graph (see, e.g., [10])
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