Fixed Points in Two--Neuron Discrete Time Recurrent Networks: Stability and Bifurcation Considerations

dc.contributor.authorTino, Peteren_US
dc.contributor.authorHorne, Bill G.en_US
dc.contributor.authorGiles, C. Leeen_US
dc.description.abstractThe position, number and stability types of fixed points of a two--neuron recurrent network with nonzero weights are investigated. Using simple geometrical arguments in the space of derivatives of the sigmoid transfer function with respect to the weighted sum of neuron inputs, we partition the network state space into several regions corresponding to stability types of the fixed points. If the neurons have the same mutual interaction pattern, i.e. they either mutually inhibit or mutually excite themselves, a lower bound on the rate of convergence of the attractive fixed points towards the saturation values, as the absolute values of weights on the self--loops grow, is given. The role of weights in location of fixed points is explored through an intuitively appealing characterization of neurons according to their inhibition/excitation performance in the network. In particular, each neuron can be of one of the four types: greedy, enthusiastic, altruistic or depressed. Both with and without the external inhibition/excitation sources, we investigate the position and number of fixed points according to character of the neurons. When both neurons self-excite (or self-inhibit) themselves and have the same mutual interaction pattern, the mechanism of creation of a new attractive fixed point is shown to be that of saddle node bifurcation. (Also cross-referenced as UMIACS-TR-95-51)en_US
dc.format.extent328103 bytes
dc.relation.isAvailableAtDigital Repository at the University of Marylanden_US
dc.relation.isAvailableAtUniversity of Maryland (College Park, Md.)en_US
dc.relation.isAvailableAtTech Reports in Computer Science and Engineeringen_US
dc.relation.isAvailableAtUMIACS Technical Reportsen_US
dc.relation.ispartofseriesUM Computer Science Department; CS-TR-3461en_US
dc.relation.ispartofseriesUMIACS; UMIACS-TR-95-51en_US
dc.titleFixed Points in Two--Neuron Discrete Time Recurrent Networks: Stability and Bifurcation Considerationsen_US
dc.typeTechnical Reporten_US


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