Multiscale motion and deformation of bumps in stochastic neural fields with dynamic connectivity.

The distinct timescales of synaptic plasticity and neural activity dynamics play an important role in the brain's learning and memory systems. Activity-dependent plasticity reshapes neural circuit architecture, determining spontaneous and stimulus-encoding spatiotemporal patterns of neural activity. Neural activity bumps maintain short term memories of continuous parameter values, emerging in spatially-organized models with short term excitation and long-range inhibition. Previously, we demonstrated nonlinear Langevin equations derived using an interface method accurately describe the dynamics of bumps in continuum neural fields with separate excitatory/inhibitory populations. Here we extend this analysis to incorporate effects of slow short term plasticity that modifies connectivity described by an integral kernel. Linear stability analysis adapted to these piecewise smooth models with Heaviside firing rates further indicate how plasticity shapes bumps' local dynamics. Facilitation (depression), which strengthens (weakens) synaptic connectivity originating from active neurons, tends to increase (decrease) stability of bumps when acting on excitatory synapses. The relationship is inverted when plasticity acts on inhibitory synapses. Multiscale approximations of the stochastic dynamics of bumps perturbed by weak noise reveal the plasticity variables evolve to slowly diffusing and blurred versions of that arising in the stationary solution. Nonlinear Langevin equations associated with bump positions or interfaces coupled to slowly evolving projections of plasticity variables accurately describe the wandering of bumps underpinned by these smoothed synaptic efficacy profiles.