Continuous Data Assimilation for Memristive FitzHugh--Nagumo Neural Networks

In this study, we investigate continuous data assimilation for a class of partly diffusive FitzHugh–Nagumo neural networks with memristive feedback and linear synaptic coupling. The nudging algorithm implemented here only adds a feedback term to the membrane-potential equations, while the recovery and memductance variables remain unobserved. We obtain weighted energy estimates that give sufficient conditions for exponential convergence of the data-assimilated solution to the reference solution under full or coarse membrane potential observations. Moreover, we prove energy-class uniqueness in dimensions one and two. In dimension three, the uniqueness criterion is an $L^4$ membrane-potential initial data. We also establish an observational-noise estimate for locally square-integrable forcing, yielding an asymptotic error bound when the noise energy is eventually bounded.