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Multiple bumps in a neuronal model of working memory. (English) Zbl 1017.45006

An integro-partial differential equation defined on a spatially extended domain that arises from the modeling of “working” or short term memory in a neuronal network is studied. The equation is capable of supporting spatially localized regions of high activity which can be switched “on” and “off” by transient external stimuli. The authors also analyzed the effects of coupling between units in the networkg showing that if the connection strengths decay monotonically with the distance, then no more than one region of high activity can persist, whereas if they decay in an oscillatory fashion, then multiple regions can persist.

MSC:

45K05 Integro-partial differential equations
92B20 Neural networks for/in biological studies, artificial life and related topics
34C15 Nonlinear oscillations and coupled oscillators for ordinary differential equations
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