Astrocytic Resource Diffusion Stabilizes Persistent Activity in Neural Fields

Abstract. Persistent neural activity underlying working memory requires sustained synaptic transmission, yet the metabolic and neurotransmitter support provided by astrocyte networks is largely absent from spatially extended neural circuit models. We introduce a coupled astrocyte–neural field model in which synaptic efficacy is regulated by depletion and recovery of a conserved resource pool recycled and spatially redistributed through diffusively coupled astrocytes. We obtain explicit stationary bump profiles and self-consistency conditions for bump width and amplitude on a canonical ring architecture. Linearizing about these solutions while carefully accounting for perturbations at bump boundaries, we analyze the resulting spectral problem governing stability. Our analysis, supported by numerical simulations and low-dimensional Fourier truncations, reveals a two-stage stabilization mechanism: astrocytic diffusion smooths resource asymmetries created by small bump displacements, and synaptic replenishment transfers this smoothing back to the synaptic pool. Together, sufficiently strong diffusion and replenishment suppress drift instabilities and enlarge the parameter regime in which stationary bumps persist. Relevance to Life Sciences. Astrocytes recycle neurotransmitters and redistribute ions and metabolic substrates through diffusively coupled networks, yet existing spatially extended neural circuit models rarely account for this resource cycling. As a result, there are few frameworks for studying how the interplay between local synaptic depletion and nonlocal astrocytic transport shapes spatiotemporal neural dynamics. We address this gap with a model whose conserved resource structure ensures that sustained firing in one region draws resources from neighboring tissue through the astrocyte network, mirroring observed metabolic support patterns. Our results suggest that both diffusive coupling strength and neurotransmitter recycling rates are critical for maintaining stable persistent activity, offering testable predictions linking glial network features to working memory robustness. Mathematical Content. We derive explicit stationary bump solutions to the coupled astrocyte–neural field system on a periodic domain with cosine connectivity and Heaviside firing rate. Self-consistency conditions yield bump half-width and amplitude through a nonlinear relation for the resource depletion level. Linearization produces a piecewise-smooth spectral problem whose coefficients, determined by the interaction of the Heaviside nonlinearity with the resource coupling, depend on the sign of the perturbation at each bump boundary, generating four distinct cases. For each case, we construct an Evans function whose real zeros determine linear stability. The astrocyte diffusion equation is solved explicitly, yielding constant-coefficient ordinary differential equations on three subdomains. We analyze the limiting regimes of zero and infinite diffusion, obtaining closed-form expressions for the linearized resource perturbations. Analytic predictions are validated against numerical simulations and a low-dimensional Fourier truncation of the perturbed system.