| Abstract: |
| We study a neural field model with both symmetric localized lateral inhibition and asymmetric long distance connections, motivated by the fact that neurons are connected by both short range and long range synapses. We develop a general method to convert the neural field model in the form of integro-differential equation to a delay differential equation. Then we solve the delay differential equation with a piecewise linear firing rate function using a combination of analytical and numerical approach. We show the existence of two coexisting traveling waves and the larger wave of the two is stable with the small one being unstable. |
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