AI 中文总结
研究噪声诱导有序中的周期性，发现其由退火转移算子的吕埃勒 - 波利科特共振控制，与动力学稳定性无关。通过可解析求解模型和数值结果验证，基于共振预测与经验功率谱一致，还指出稳定性和统计周期性转变产生三种不同类型的NIO。
AI 中文摘要
噪声诱导有序（NIO）是非平凡噪声诱导现象的典型例子，其特征在于明显的光谱峰值和准周期动力学。我们表明这种周期性由退火转移算子的吕埃勒 - 波利科特共振控制，与动力学稳定性无关。一个可解析求解模型的精确结果以及一个修改后的拉萨托 - 麦基映射的数值结果表明，基于共振的预测与广泛噪声幅度下的经验功率谱之间具有出色的一致性。由李雅普诺夫指数诊断的稳定性独立转变以及由吕埃勒 - 波利科特共振诊断的统计周期性产生了三种不同类型的NIO。
英文摘要
Noise-induced order (NIO) is a paradigmatic example of nontrivial noise-induced phenomena, characterized by pronounced spectral peaks and pseudoperiodic dynamics. We show that this periodicity is governed by the Ruelle-Pollicott resonances of the annealed transfer operator, independently of dynamical stability. Exact results for an analytically solvable model and numerical results for a modified Lasota--Mackey map show excellent agreement between resonance-based predictions and empirical power spectra across a broad range of noise amplitudes. Independent transitions in stability, diagnosed by the Lyapunov exponent, and statistical periodicity, diagnosed by the Ruelle-Pollicott resonances, give rise to three distinct types of NIO.
