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NJIT Applied Mathematics Colloquium

Friday, September 3rd 2010, 11:30am
Cullimore Lecture Hall II
New Jersey Institute of Technology

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Relating dynamics to structure on random graphs

Amit Bose

NJIT

Rhythmic activity in complex systems is generated and sustained through interactions among the constituent units. In this talk we discuss the interplay between topology and dynamics of excitable nodes on random networks. We address the question of whether a particular network design pattern confers dynamical advantage for the generation and sustainment of rhythmic activity. We find that structural features of the graph, in conjunction with the intrinsic properties of a node and the rules for interaction between them determine when sustained activity is permissible. When the rules for interaction are relatively simple, the level of periodic activity in the graph increases monotonically with the probability of connections between nodes. Alternatively, when the interaction rules become more complicated, the level of activity is nonmonotonic. The results are illustrated through a combination of simulations and analysis.