Existence and stability of standing pulses in neural networks: I. Existence

  • Guo Y
  • Chow C
  • 37

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Abstract

We consider the existence of standing pulse solutions of a neural network integro-differential equa- tion. These pulses are bistable with the zero state and may be an analogue for short term memory in the brain. The network consists of a single layer of neurons synaptically connected by lateral inhibition. Our work extends the classic Amari result by considering a nonsaturating gain function. We consider a specific connectivity function where the existence conditions for single pulses can be reduced to the solution of an algebraic system. In addition to the two localized pulse solutions found by Amari, we find that three or more pulses can coexist. We also show the existence of nonconvex “dimpled” pulses and double pulses. We map out the pulse shapes and maximum firing rates for different connection weights and gain functions. Key

Author-supplied keywords

  • 040609471
  • 1
  • 10
  • 1137
  • 34a36
  • 37n25
  • 45g10
  • 92b20
  • ams subject classifications
  • doi
  • existence
  • for short periods of
  • information in the brain
  • integral equations
  • integro-differential equations
  • introduction
  • neural networks
  • standing pulses
  • the temporary storage of

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Authors

  • Yixin Guo

  • CC Chow

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