Time Delay Reservoir Computing Under Edge-of-Chaos Mapping and Its Application in Nonlinear Time Series Forecasting

This work proposes a novel time delay reservoir computing (TDRC) system based on a two-dimensional discrete memristor edge-of-chaos mapping (ECM-TDR). By integrating edge-of-chaos dynamics into the reservoir architecture, the proposed system fundamentally reconstructs the virtual node structure of traditional TDR. It leverages the inherent non-monotonic edge effects and fractal boundary characteristics of locally active memristor to enhance the nonlinear projection capability of the reservoir. Comparative prediction experiments on chaotic sequences generated by the Mackey–Glass equation and real-world time series demonstrate that the proposed model outperforms traditional reservoir computing approaches in prediction accuracy, particularly in long-term forecasting tasks with pronounced memory dependencies. Meanwhile, practical evaluations further confirm that ECM-TDR offers favorable resource controllability and high compatibility with hardware implementation. Furthermore, a critical finding is the establishment of the principle of dynamical consistency between the discrete memristive chaotic map and the reservoir output. Through Lyapunov exponent (LE) spectrum analysis, we demonstrate that the nonlinear dynamics of the ECM-TDR are not stochastically generated but are precisely governed by the edge-of-chaos map. This discovery provides novel physical interpretability for RC based on discrete memristor (DM) chaotic maps.