非线性变量阶小数超混乱陈系统的混沌分析,利用辐射基函数神经网络神经网络
Sadam Hussain1, Zia Bashir1, M G Abbas Malik2
1Department of Mathematics, Quaid-i-Azam University, Islamabad, 45320 Pakistan.
Cognitive neurodynamics
|December 16, 2024
概括
这项研究研究了超混沌的陈系统中的混乱动态,使用变量顺序的微积分计算和辐射基础函数神经网络 (RBFNN). 该RBFNN准确地模拟混乱的行为,推进分数动力学研究.
科学领域:
- 非线性动力学是一种非线性动力学.
- 分数微积分的计算.
- 计算智能是一种计算智能.
背景情况:
- 超混沌的陈系统表现出复杂的动态.
- 分数微积分为建模动态系统提供了一个更普遍的框架.
- 辐射基函数神经网络 (RBFNN) 是用于近似复杂函数的强大工具.
研究的目的:
- 探索超混沌的陈系统的混沌特征,在一个变量顺序分数 (VOF) 微积分计算框架内.
- 开发和验证一种非线性和适应性的RBFNN,用于模拟VOF混乱系统.
- 调查系统的混乱吸引子,并评估RBFNN的准确性.
主要方法:
- 使用卡普托-法布里齐奥导数,对VOF微分方程进行数值计算.
- 为超混沌的陈系统制定一个参数RBFNN模型.
- 使用统计方法,相位空间重建和利亚普诺夫指数分析混乱吸引子.
- 使用根平均平方误差 (RMSE) 验证RBFNN模型.
主要成果:
- 该研究成功计算了VOF超混乱陈系统的数值解.
- 一个全面的参数RBFNN模型被开发和验证.
- 混乱的吸引力被系统地研究,揭示了复杂的动态.
- 该RBFNN证明了高精度和可靠性,结果与数值算法密切匹配.
结论:
- 拟议的RBFNN方法对于研究VOF系统中的混乱是有效的.
- 这项研究促进了变量级分数动态学的理解和应用.
- 这些发现对涉及混乱系统的各种科学和工程领域有潜在的影响.
相关概念视频
01:26Linear Approximation in Frequency Domain
85
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....
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....
85
01:21First Order Systems
83
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...
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...
83
01:21Linear Approximation in Time Domain
62
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.
For a simple pendulum with a mass evenly distributed along its length and the center of mass located at half the pendulum's length,...
For a simple pendulum with a mass evenly distributed along its length and the center of mass located at half the pendulum's length,...
62
01:20Second Order systems I
135
A servo system exemplifies a second-order system, featuring a proportional controller and load elements that ensure the output position aligns with the input position. The relationship between these components is described by a second-order differential equation. Applying the Laplace transform under zero initial conditions yields the transfer function, showing how inputs are converted to outputs in the system.
By reinterpreting the system, one can derive the closed-loop transfer function, which...
By reinterpreting the system, one can derive the closed-loop transfer function, which...
135
01:27State Space Representation
162
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.
Consider an RLC circuit, a...
Consider an RLC circuit, a...
162
01:24Pole and System Stability
248
The transfer function is a fundamental concept representing the ratio of two polynomials. The numerator and denominator encapsulate the system's dynamics. The zeros and poles of this transfer function are critical in determining the system's behavior and stability.
Simple poles are unique roots of the denominator polynomial. Each simple pole corresponds to a distinct solution to the system's characteristic equation, typically resulting in exponential decay terms in the system's...
Simple poles are unique roots of the denominator polynomial. Each simple pole corresponds to a distinct solution to the system's characteristic equation, typically resulting in exponential decay terms in the system's...
248