A study of network dynamics

The dynamics of a discrete-time neural network model are investigated. First, a numerical survey of network power spectra is reported for networks of varying size with random weight matrices and initial states. The steepness of the logistic function and a symmetry measure of the weight matrix are taken as control parameters. Summary statistics are presented to give gross measures of the model's temporal activity in parameter space. Second, a detailed study of the dynamics of a particular network is described. Complex dynamical behavior is observed, including Hopf bifurcations, the Ruelle-Takens-Newhouse route to chaos (showing mode-locking at rational winding numbers and the destruction of an invariant torus), and the period-doubling route to chaos.

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