基于储库计算的光学时间延迟混乱系统的非线性复杂性的量化
Huan Wang1, Wei Ren1, Yijun Zeng1
1School of Computer Science, China University of Geosciences (Wuhan), Wuhan, China.
Chaos (Woodbury, N.Y.)
|December 2, 2025
概括
我们开发了一种新的方法,使用储库计算 (RC) 来测量光学时间延迟混乱系统的动态复杂性. 这种复杂度指标对参数变化比现有方法更敏感,有助于安全评估.
科学领域:
- 非线性动力学是一种非线性动力学.
- 光学工程是指光学工程.
- 复杂的系统复杂的系统.
背景情况:
- 光学时间延迟 (TD) 混乱系统对于安全通信至关重要.
- 量化它们的动态复杂性对于性能和安全分析至关重要.
- 现有的复杂度指标,如变量,可能无法完全捕捉系统动态.
研究的目的:
- 提出一种用于测量光学DT混乱系统的动态复杂性的新方法.
- 引入基于储库计算 (RC) 网络学习性能的复杂度指标.
- 为了将拟议的指标与光学混乱时间序列的既定指标进行比较.
主要方法:
- 利用储库计算 (RC) 网络来学习系统输出与其时间延迟变体之间的映射.
- 量化了RC网络的学习性能作为一个复杂度指标.
- 通过使用两个光学TD混沌发生器,评估了指标对变的响应能力,碎形维度和最大Liapunov指数.
- 研究了复杂度指标和时间延迟签名之间的关系.
主要成果:
- 提出的基于RC的复杂度指标有效量化了重建系统动态的难度.
- 与传统方法相比,新指标在光学TD混乱系统中对参数变化的响应性更高.
- 在广泛的参数范围内观察到复杂度指标和时间延迟特征之间的反向关系.
结论:
- 开发的复杂度指标为分析光学DT混乱系统提供了一个敏感的工具.
- 这种方法为基于动态重建的光学混乱发生器的安全评估提供了一个新的视角.
- 这些发现有助于更深入地了解光学混乱系统中的复杂性-动态关系.
相关概念视频
01:26Linear Approximation in Frequency Domain
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Linear systems are characterized by two main properties: superposition and homogeneity. Superposition allows the response to multiple inputs to be the sum of the responses to each individual input. Homogeneity ensures that scaling an input by a scalar results in the response being scaled by the same scalar.
In contrast, nonlinear systems do not inherently possess these properties. However, for small deviations around an operating point, a nonlinear system can often be approximated as linear....
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01:31Classification of Systems-II
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Continuous-time systems have continuous input and output signals, with time measured continuously. These systems are generally defined by differential or algebraic equations. For instance, in an RC circuit, the relationship between input and output voltage is expressed through a differential equation derived from Ohm's law and the capacitor relation,
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01:23Linear time-invariant Systems
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A system is linear if it displays the characteristics of homogeneity and additivity, together termed the superposition property. This principle is fundamental in all linear systems. Linear time-invariant (LTI) systems include systems with linear elements and constant parameters.
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01:27State Space Representation
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The frequency-domain technique, commonly used in analyzing and designing feedback control systems, is effective for linear, time-invariant systems. However, it falls short when dealing with nonlinear, time-varying, and multiple-input multiple-output systems. The time-domain or state-space approach addresses these limitations by utilizing state variables to construct simultaneous, first-order differential equations, known as state equations, for an nth-order system.
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01:21First Order Systems
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First-order systems, such as RC circuits, are foundational in understanding dynamic systems due to their straightforward input-output relationship. Analyzing their responses to different input functions under zero initial conditions reveals significant insights into system behavior.
When a first-order system is subjected to a unit-step input, its response is characterized by its transfer function. By applying the Laplace transform of the unit-step input to the transfer function, expanding the...
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01:10Entropy Change in Reversible Processes
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