An Echo State Network Based on Enhanced Intersecting Cortical Model for Discrete Chaotic System Prediction

Xubin Wang¹Pei Ma¹Jing Lian²Jizhao Liu¹Yide Ma^1*

• ¹Lanzhou University, Lanzhou, China
• ²Lanzhou Jiaotong University, Lanzhou, China

Chaotic time series prediction presents significant challenges due to its inherent sensitivity to initial conditions and complex, nonlinear dynamics. While deep learning models offer powerful representational capabilities, they often suffer from high computational costs, black-box characteristics, and extensive data requirements. Reservoir Computing (RC), particularly Echo State Networks (ESNs), provides an efficient alternative by training only the output weights, but traditional ESNs often rely on overly simple neuron models and require hyperparameter tuning, limiting their adaptability and performance on complex chaotic systems. This work introduces an Echo State Network Based on EnhancedIntersecting Cortical Model (ESN-EICM). This design enhances the network's dynamic richness, operationally defined as its capacity to generate a wide variety of complex temporal patterns and maintain high-dimensional state representations. Furthermore, a Bayesian Optimization strategy is employed for systematic and efficient hyperparameter tuning. Comprehensive experiments on three discrete chaotic systems (Logistic, Sine, and Ricker) demonstrate that ESN-EICM significantly outperforms standard ESN and Long Short-Term Memory (LSTM) networks in both one-step and multi-step prediction tasks, achieving lower error metrics (MSE, RMSE, MAE) and greater stability. Notably, ESN-EICM exhibits superior computational efficiency compared to LSTM and often surpasses standard ESN in training time for complex multi-step predictions due to its enhanced stability facilitating faster convergence during optimization. These findings establish ESN-EICM as a robust, accurate, and efficient approach for discrete chaotic system prediction.