Moving bumps in theta neuron networks

Abstract

We consider large networks of theta neurons on a ring, synaptically coupled with an asymmetric kernel. Such networks support stable "bumps" of activity, which move along the ring if the coupling kernel is asymmetric. We investigate the effects of the kernel asymmetry on the existence, stability and speed of these moving bumps using continuum equations formally describing infinite networks. Depending on the level of heterogeneity within the network we find complex sequences of bifurcations as the amount of asymmetry is varied, in strong contrast to the behaviour of a classical neural field model.

To appear in Chaos

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• Patched patterns and emergence of chaotic interfaces in arrays of nonlocally coupled excitable systems
• Data assimilation for networks of coupled oscillators: Inferring unknown model parameters from partial observations
• Bumps, chimera states, and Turing patterns in systems of coupled active rotators