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Updated: Jun 4, 2025

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探索非线性混乱系统的应用在随机过程中.

H G Abdelwahed1,2, Islam M Elbaz3,4, M A Sohaly5

  • 1Department of Physics, College of Science and Humanities, Prince Sattam bin Abdulaziz University, Al-Kharj, 11942, Saudi Arabia.

Scientific reports
|December 23, 2024
PubMed
概括

这项研究使用利亚普诺夫函数分析了随机系统的稳定性. 它建立了各种稳定性类型的标准,并将其应用于艾滋病毒/艾滋病的动态和财务模型.

关键词:
金融市场模型 金融市场模型全球平均平方稳定性 (GMSS)艾滋病毒/艾滋病随机模型 随机模型坚持不 坚持不随机和随机系统是随机和随机系统.

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Linear Approximation in Frequency Domain01:26

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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.
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Linear time-invariant Systems

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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Classification of Systems-I01:26

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Linearity is a system property characterized by a direct input-output relationship, combining homogeneity and additivity.
Homogeneity dictates that if an input x(t) is multiplied by a constant c, the output y(t) is multiplied by the same constant. Mathematically, this is expressed as:
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Feedback control systems

Feedback control systems are categorized in various ways based on their design, analysis, and signal types.
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Nonlinear systems often require sophisticated approaches for accurate modeling and analysis, with state-space representation being particularly effective. This method is especially useful for systems where variables and parameters vary with time or operating conditions, such as in a simple pendulum or a translational mechanical system with nonlinear springs.
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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.
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