Physics – Condensed Matter – Disordered Systems and Neural Networks
Scientific paper
2006-04-28
Physics
Condensed Matter
Disordered Systems and Neural Networks
16 pages, 5 figures
Scientific paper
We present exact results, as well as some illustrative Monte Carlo simulations, concerning a stochastic network with weighted connections in which the fraction of nodes that are dynamically synchronized is a parameter. This allows one to describe from single-node kinetics to simultaneous updating of all the variables at each time unit. An example of the former limit is the well-known sequential updating of spins in kinetic magnetic models whereas the latter limit is common for updating complex cellular automata. The emergent behavior changes dramatically as the parameter is varied. For small values, we observed relaxation towards one of the attractors and a great sensibility to external stimuli, and for large synchronization, itinerancy as in heteroclinic paths among attractors; tuning the parameter in this regime, the oscillations with time may abruptly change from regular to chaotic and vice versa. We show how these observations, which may be relevant concerning computational strategies, closely resemble some actual situations related to both searching and states of attention in the brain.
Cortes Jesus M.
Marro Joaquin
Torres Javier
Wemmenhove Bastian
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