Realization of the Bienenstock-Cooper-Munro rule in a single memristor

Neuromorphic computing aims to build electronic systems that mimic the brain's remarkable efficiency and adaptability. A key feature of brain is homeostatic plasticity, which stabilizes neural activity; the Bienenstock-Cooper-Munro (BCM) rule accurately describes this by adjusting a neuron's sensitivity threshold based on past activity. However, implementing the homeostatic rule in synaptic device remains challenging. Here we show that a CuInP₂S₆ memristor naturally realizes the complete BCM rule. We reveal that the device's intrinsic junction capacitance generates reverse spikes that cause spike-rate-dependent conductance depression, combining with second-order ionic dynamics to replicate key BCM features. Through simulations, we demonstrate that adding a similar capacitance can universally enable this behavior in conventional memristors. Finally, we build a physical reservoir computing system based on this strategy that exhibits robust, noise-tolerant spatiotemporal processing. This work provides a viable path for deploying adaptive homeostatic plasticity in hardware, enhancing the reliability of neuromorphic systems.