Abstract
We formally derive a simple normal form for the dynamics of a nonlocally coupled neural field model when the local dynamics is near a saddle-node infinite cycle (SNIC) bifurcation. The derivation produces a nonlocally coupled scalar model which does not satisfy the comparison principle (ordered initial data produces ordered dynamical solutions). We prove the existence of unique traveling waves for the corresponding nonlocal evolution problem with a new tool that does not use the comparison principle. We obtain sharp estimates for the speed of fast and slow waves and compare these to numerical results.
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