Noise Driven Coupled Nonlinear Systems: A “Dynamical Multilayer Perceptron” Demonstrating XOR Functionality

Abstract

Coupled nonlinear dynamical systems are known to display remarkable behavioral similarities to some aspects of neural activity in biology. When considering the computational properties of such a neuromorphic network (or even an electronic biomimetic computation device underpinned by such a network), the question of whether (and how) such a network realizes fundamental logic operations must be examined. In this work, a dynamical system of coupled noisy overdamped nonlinear bistable elements is considered. The background noise floor is used to drive information flow by helping each element switch randomly between its stable states, with the system response quantified via a long-time probability density function. A theoretical representation of such a system is developed and a simple five-element realization is used to demonstrate a continuous version of an XOR gate, through the proper choice of coupling coefficients and controllable external biases. This is a first step towards synthesizing more general functions, a prerequisite for advanced computing and learning applications. Finally, a silicon implementation is proposed and simulated using a verified process model that could be fabricated to generate a working analog computing system.

Keywords

• Dynamical nonlinear oscillator
• network
• noise-floor
• stochastic differential equation
• XOR gate