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.

In long-memory tasks, real-world and industrial time-series data, such as sunspot sequences, typically exhibit complex intertemporal dependencies. Traditional time-delay reservoir (TDR) computing models perform well on short-term sequences but struggle with long-term dependencies, resulting in degraded prediction performance, particularly with isomorphic models and shallow connections. Inspired by the node construction approach of TDR based on the Mackey–Glass equation, a deep decoupled heterogeneous delayed reservoir computing model based on 2-D discrete memristor hyperchaotic maps (DMHM-DHDDR) is proposed. This model replaces time-delay differential equations in TDR with discrete memristor (DM) nonlinear dynamics and maps three types of 2-D discrete memristor systems [sine-coupled absolute value DM (sA-DM), sine-coupled sinusoidal value DM (sS-DM), and sine-coupled exponential value DM (sE-DM)] to different layers. By integrating the masked input and cross-layer state transition mechanisms, the reservoir exhibits significantly enhanced capability in extracting temporal features and improving prediction accuracy, while the model demonstrates relatively low parameter sensitivity without substantially increasing memory overhead. Numerical experiments demonstrate that the DMHM-DHDDR model achieves a notable reduction in normalized root-mean-square error compared with traditional reservoir computing models on both chaotic sequence and real-world prediction tasks. Furthermore, this work, for the first time, employs fractal dimension analysis and phase-space reconstruction to evaluate reservoir states. The results confirm that reservoirs driven by hyperchaotic mappings exhibit predictive behaviors comparable to those of conventional reservoirs. This provides theoretical support for applying discrete memristor-based mappings in reservoir computing.

Reservoir computing is a machine learning paradigm with lower training costs that replaces traditional recurrent neural networks in some time series processing areas to simplify complexity. The compact network structure and low-complexity training method of this approach make it more suitable for hardware implementation, and reservoir computing exhibits unique advantages over other deep learning models. Memristor is a single device that can change its resistance state by memorizing the applied voltage or history current. The non-linear and time-memory characteristics of memristors are highly compatible with the dynamic properties required for reservoir computing. Consequently, memristors can be harnessed to construct nonlinear nodes within reservoirs, forming intricate dynamical units. This study introduces a novel type of reservoir building unit, termed as a memristor array in a random state, and proposes a reservoir computing hardware system based on memristor arrays in random states (MARS-RC). The randomness and nonlinear properties of this memristor array give the MARS-RC system the unique ability to more effectively capture the dynamic characteristics of the data. Simultaneously, we’ve designed an array random initialization circuit unit (ARI) to facilitate control over the memristor’s state, thus enhancing the system’s controllability. The MARS-RC system exhibits comparable predictive performance to conventional software reservoirs in predictive experiments involving chaotic time series. This is supported by comparisons with five distinct reservoir computing platforms. Furthermore, we’ve applied the MARS-RC system to the task of multi-classifying ECG signals. In these experiments, by employing multiple MARS-RC arrays in parallel, the system exhibits substantial robustness when dealing with varying input data sizes, attaining a remarkable classification accuracy of 99.375%. This study proposes a novel construction approach to advance reservoir computing hardware systems and provides new insights.

Aiming at the problem that the existing one-dimensional chaotic system has small chaotic interval, Lyapunov exponent is small and the generated chaotic sequence is unevenly distributed, and the correlation is high, a new image encryption algorithm is proposed by this paper. The logistic chaotic mapping and tent chaotic mapping are cascaded by iteration based on Arnold transform, logistic and tent mapping. Experiments show that the algorithm effectively extends the key space of chaotic systems, has good encryption effect and security, and can resist several common attacks.