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Delayed self-feedback echo state network for long-term dynamics of hyperchaotic systems

作     者:Xu Xu Jianming Liu Eric Li 

作者机构:College of Mathematics School of Computing Engineering & Digital Technologies 

出 版 物:《Physical Review E》 (Phys. Rev. E)

年 卷 期:2024年第109卷第6期

页      面:064210-064210页

核心收录:

基  金:National Major Science and Technology Projects of China, (2021ZD0112500) National Major Science and Technology Projects of China National Natural Science Foundation of China, NSFC, (12072128) National Natural Science Foundation of China, NSFC Nanjing University of Aeronautics and Astronautics, NUAA, (MCAS-E-0224K01) Nanjing University of Aeronautics and Astronautics, NUAA 

主  题:Bifurcations Control & applications of chaos Chaotic systems Dynamical systems Machine learning 

摘      要:Analyzing the long-term behavior of hyperchaotic systems poses formidable challenges in the field of nonlinear science. This paper proposes a data-driven model called the delayed self-feedback echo state network (self-ESN) specifically designed for the evolution behavior of hyperchaotic systems. Self-ESN incorporates a delayed self-feedback term into the dynamic equation of a reservoir to reflect the finite transmission speed of neuron signals. Delayed self-feedback establishes a connection between the current and previous m time steps of the reservoir state and provides an effective means to capture the dynamic characteristics of the system, thereby significantly improving memory performance. In addition, the concept of local echo state property (ESP) is introduced to relax the conventional ESP condition, and theoretical analysis is conducted on guiding the selection of feedback delay and gain to ensure the local ESP. The judicious selection of feedback gain and delay in self-ESN improves prediction accuracy and overcomes the challenges associated with obtaining optimal parameters of the reservoir in conventional ESN models. Numerical experiments are conducted to assess the long-term prediction capabilities of the self-ESN across various scenarios, including a 4D hyperchaotic system, a hyperchaotic network, and an infinite-dimensional delayed chaotic system. The experiments involve reconstructing bifurcation diagrams, predicting the chaotic synchronization, examining spatiotemporal evolution patterns, and uncovering the hidden attractors. The results underscore the capability of the proposed self-ESN as a strategy for long-term prediction and analysis of the complex systems.

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