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The distinct timescales of synaptic plasticity and neural activity dynamicsplay an important role in the brain's learning and memory systems.Activity-dependent plasticity reshapes neural circuit architecture, determiningspontaneous and stimulus-encoding spatiotemporal patterns of neural activity.Neural activity bumps maintain short term memories of continuous parametervalues, emerging in spatially-organized models with short term excitation andlong-range inhibition. Previously, we demonstrated nonlinear Langevin equationsderived using an interface method accurately describe the dynamics of bumps incontinuum neural fields with separate excitatory/inhibitory populations. Herewe extend this analysis to incorporate effects of slow short term plasticitythat modifies connectivity described by an integral kernel. Linear stabilityanalysis adapted to these piecewise smooth models with Heaviside firing ratesfurther indicate how plasticity shapes bumps' local dynamics. Facilitation(depression), which strengthens (weakens) synaptic connectivity originatingfrom active neurons, tends to increase (decrease) stability of bumps whenacting on excitatory synapses. The relationship is inverted when plasticityacts on inhibitory synapses. Multiscale approximations of the stochasticdynamics of bumps perturbed by weak noise reveal the plasticity variablesevolve to slowly diffusing and blurred versions of that arising in thestationary solution. Nonlinear Langevin equations associated with bumppositions or interfaces coupled to slowly evolving projections of plasticityvariables accurately describe the wandering of bumps underpinned by thesesmoothed synaptic efficacy profiles.

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