A network model with auto-oscillating output and dynamic connections

A major problem that researchers attempting to elaborate mathematical models of neurophysiological and/or psychophysiological processes are confronted with is the identification of the mechanisms that give rise, in a neural network, to oscillatory behavior, either spontaneous or induced by external stimuli. The present work starts by considering a network model of a central pattern generator (CPG), introduced by Sompolinsky and co-authors. The present authors try to generalize this model to a wider range of biological situations, by introducing into it dynamic adjustments of connections among the processing units. Although the study performed so far is quite preliminary, some analytical considerations can be presented, supported by the results of numerical simulations, which show always a relaxation of the network toward specific stable states.

[1]  S Dehaene,et al.  Neural networks that learn temporal sequences by selection. , 1987, Proceedings of the National Academy of Sciences of the United States of America.

[2]  Kanter,et al.  Temporal association in asymmetric neural networks. , 1986, Physical review letters.

[3]  Allen I. Selverston,et al.  Model Neural Networks and Behavior , 1985, Springer US.

[4]  A. Aertsen,et al.  Neuronal assemblies , 1989, IEEE Transactions on Biomedical Engineering.

[5]  D. Hartline,et al.  Pattern generation in the lobster (Panulirus) stomatogastric ganglion , 1979, Biological Cybernetics.

[6]  Adam N. Mamelak,et al.  Network Model of State-Dependent Sequencing , 1991, NIPS.

[7]  Horn,et al.  Neural networks with dynamical thresholds. , 1989, Physical review. A, General physics.

[8]  John J. Hopfield,et al.  Neural networks and physical systems with emergent collective computational abilities , 1999 .

[9]  Marius Usher,et al.  Chaotic Behavior of A Neural Network with Dynamical Thresholds , 1991, Int. J. Neural Syst..

[10]  A. Selverston,et al.  The Crustacean Stomatogastric System , 1987, Springer Berlin Heidelberg.

[11]  Haim Sompolinsky,et al.  Associative network models for central pattern generators , 1989 .

[12]  H Sompolinsky,et al.  Associative neural network model for the generation of temporal patterns. Theory and application to central pattern generators. , 1988, Biophysical journal.

[13]  Daniel K. Hartline,et al.  Pattern generation in the lobster (Panulirus) stomatogastric ganglion , 1979, Biological Cybernetics.