​A ​MINIMAL MEMRISTIVE NEURON MODEL OF DYNAMICAL MEMORY

Dynamical memory allows neural systems to retain useful internal states over short and intermediate timescales, supporting computations relevant to navigation, motor control, and working memory. Conventional models typically rely on recurrent networks with separate excitatory and inhibitory populations. However, recent observations of localized excitatory activity in the Drosophila head-direction system suggest that such dynamics may in fact be implemented by a handful of neurons. This raises a timely and fundamental question: what is the minimal neural substrate required to generate persistent activity?

Here, we show, contrary to common intuition, that a single leaky integrate-and-fire (LIF) neuron with recurrent slow self-excitation is sufficient to produce a persistent firing state that is stable and robust to distractors. Alongside numerical solutions, we provide an empirical demonstration using a minimal hardware implementation. We further show that this finding extends to the widely used Izhikevich and AdEx models, in which robust persistent activity can be obtained simply by reversing the sign of the slow adaptation variable. Together, these results identify a minimal substrate for memory-like dynamics and suggest a compact building block for future neuromorphic cognitive architectures.