ReLU Function-Based Locally Active Memristor and its Application in Generating Spiking Behaviors

Abstract

This brief proposes a systematic method for building multi-lobe locally active memristors (LAMs) via the rectified linear unit (ReLU) function. Theoretical analysis and numerical simulations display that the number of equilibrium states and lobes, and the local active domain range of the ReLU function-based LAM are controllable. All the multi-lobe LAMs possess bootlace-like DC <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$V-I$ </tex-math></inline-formula> curves. Afterward, a ReLU function-based 2-lobe LAM is employed as a paradigm to analyze the DC properties and domains distribution. With the 2-lobe LAM, a third-order circuit is constructed and parameter-dependent dynamics are disclosed, which demonstrates that the circuit can produce periodic/chaotic spiking behaviors. This addresses the effectiveness of the ReLU function-based LAM in developing neuromorphic circuits.