标题： FCOC：一种用于金融波动预测的分形混沌协同框架 显示英文标题

标题： FCOC: A Fractal-Chaotic Co-driven Framework for Financial Volatility Forecasting

摘要： 本文介绍了分形-混沌振荡协同（FCOC）框架，这是一种用于金融波动预测的新范式，系统地解决了特征保真度和模型响应性的双重挑战。 FCOC结合了两项核心创新：我们设计的新型分形特征校正器（FFC），用于提取高保真分形信号，以及受生物启发的混沌振荡组件（COC），用动态处理系统取代静态激活。 在标普500和道琼斯工业指数上经过实证验证，FCOC框架表现出深远且可推广的影响。 该框架从根本上提升了之前表现不佳的架构（如Transformer）的性能，同时在Mamba等先进模型的关键风险敏感指标上实现了显著提升。 这些结果确立了一种强大的协同方法，其中模型由优越的理论特征引导，并由动态内部处理器驱动，为风险感知预测设定了新基准。 显示英文摘要

摘要： This paper introduces the Fractal-Chaotic Oscillation Co-driven (FCOC) framework, a novel paradigm for financial volatility forecasting that systematically resolves the dual challenges of feature fidelity and model responsiveness. FCOC synergizes two core innovations: our novel Fractal Feature Corrector (FFC), engineered to extract high-fidelity fractal signals, and a bio-inspired Chaotic Oscillation Component (COC) that replaces static activations with a dynamic processing system. Empirically validated on the S\&P 500 and DJI, the FCOC framework demonstrates profound and generalizable impact. The framework fundamentally transforms the performance of previously underperforming architectures, such as the Transformer, while achieving substantial improvements in key risk-sensitive metrics for state-of-the-art models like Mamba. These results establish a powerful co-driven approach, where models are guided by superior theoretical features and powered by dynamic internal processors, setting a new benchmark for risk-aware forecasting.