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• W2057635365 startingPage "3234" @default.
• W2057635365 abstract "A ring neural network is a closed chain in which each unit is connected unidirectionally to the next one. Numerical investigations indicate that continuous-time excitatory ring networks composed of graded-response units can generate oscillations when interunit transmission is delayed. These oscillations appear for a wide range of initial conditions. The mechanisms underlying the generation of such patterns of activity are studied. The analysis of the asymptotic behavior of the system shows that (i) trajectories of most initial conditions tend to stable equilibria, (ii) undamped oscillations are unstable, and can only exist in a narrow region forming the boundary between the basins of attraction of the stable equilibria. Therefore the analysis of the asymptotic behavior of the system is not sufficient to explain the oscillations observed numerically when interunit transmission is delayed. This analysis corroborates the hypothesis that the oscillations are transient. In fact, it is shown that the transient behavior of the system with delay follows that of the corresponding discrete-time excitatory ring network. The latter displays infinitely many nonconstant periodic oscillations that transiently attract the trajectories of the network with delay, leading to long-lasting transient oscillations. The duration of these oscillations increases exponentially with the inverse of the characteristic charge-discharge time of the neurons, indicating that they can outlast observation windows in numerical investigations. Therefore, for practical applications, these transients cannot be distinguished from stationary oscillations. It is argued that understanding the transient behavior of neural network models is an important complement to the analysis of their asymptotic behavior, since both living nervous systems and artificial neural networks may operate in changing environments where long-lasting transients are functionally indistinguishable from asymptotic regimes." @default.
• W2057635365 created "2016-06-24" @default.
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• W2057635365 date "1997-03-01" @default.
• W2057635365 modified "2023-09-26" @default.
• W2057635365 title "Transient oscillations in continuous-time excitatory ring neural networks with delay" @default.
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• W2057635365 doi "https://doi.org/10.1103/physreve.55.3234" @default.
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