
Modeling nonlinear dynamical systems with long-horizon temporal dependencies remains a central challenge in data-driven analysis and time-series prediction. Conventional reservoir computing approaches, such as Echo State Networks (ESNs), provide efficient temporal modeling but often exhibit limited memory depth, sensitivity to parameter settings, and reduced stability when applied to delayed nonlinear processes. This work introduces a K–R controlled reservoir computing framework that restructures internal state dynamics to enhance nonlinear representation, temporal memory, and prediction stability without increasing reservoir size or architectural complexity.The proposed formulation integrates controlled nonlinear excitation, delay-embedded state construction, and stabilized readout learning to improve the separability and persistence of temporal features. The framework is evaluated on established nonlinear benchmarks, including the NARMA-30 process and the Mackey–Glass chaotic time series (τ = 30), which require modeling of delayed nonlinear interactions and long-range dependencies. Experimental results demonstrate substantial reductions in prediction error compared to a baseline ESN, along with increased memory capacity and improved robustness under noise and parameter variations.Analysis of reservoir state-space dynamics indicates that the K–R transformation enhances the geometric structure of temporal representations, enabling compact reservoirs to capture complex nonlinear behavior more effectively. The approach maintains computational efficiency while improving modeling reliability, making it suitable for data-driven analysis of nonlinear dynamical systems. These findings highlight the role of state-space restructuring in reservoir computing and provide a compact framework for modeling delayed nonlinear temporal processes in complex systems.
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