在一类具有同类临床周期的零碎非线性系统中出现混乱
Kai Lu1, Wenjing Xu2
1School of Information and Mathematics, Yangtze University, Jingzhou 434023, People's Republic of China.
Chaos (Woodbury, N.Y.)
|March 21, 2025
概括
在非线性系统中预测同临床周期和混乱是具有挑战性的,特别是对于非光滑系统. 这项研究使用Poincaré返回地图在三维零碎非线性系统中分析证明了复杂的混乱动态.
科学领域:
- 动态系统和混沌理论
- 非线性动力学是一种非线性动力学.
- 数学物理学的数学物理.
背景情况:
- 在平滑的非线性系统中准确预测同临床周期和混乱仍然是一个重大挑战.
- 将这些预测扩展到非光滑系统中会带来更大的困难.
- 对于各种科学和工程领域来说,了解碎片式非线性系统中的混乱动态至关重要.
研究的目的:
- 在特定类型的三维零碎非线性系统中分析研究同临床周期的发生.
- 严格证明这些系统中存在复杂的混乱动态.
- 开发一种可概括的分析方法,用于识别其他零碎非线性系统中的单一循环和混乱.
主要方法:
- 该研究考虑了由非线性子系统和亲系子系统组成的三维零碎非线性系统.
- 使用等效转换来简化系统并获得明确的解决方案.
- 波因卡雷返回图的分析表达式是为了严格分析系统的动态而衍生出来的.
主要成果:
- 在某些条件下,可以将所考虑的零碎非线性系统转换为线性形式,从而允许明确的解决方案.
- 分析的普恩卡雷返回图的导出严格地证明了复杂的混乱动态的存在.
- 开发的分析方法提供了一种方法来识别相似的断片系统中的同临床周期和混乱.
结论:
- 这项研究成功地展示了一种用于分析调查和证明三维零碎非线性系统中的混乱动态的方法.
- 这些发现为理解和预测非平滑动态系统中的复杂行为提供了有价值的理论框架.
- 提出的方法适用于更广泛的表现出非线性的一小部分系统,推进混沌理论领域.
相关概念视频
01:26Classification of Systems-I
164
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:
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:
164
01:21Linear Approximation in Time Domain
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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.
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,...
59
01:26Linear Approximation in Frequency Domain
81
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....
81
01:24BIBO stability of continuous and discrete -time systems
315
System stability is a fundamental concept in signal processing, often assessed using convolution. For a system to be considered bounded-input bounded-output (BIBO) stable, any bounded input signal must produce a bounded output signal. A bounded input signal is one where the modulus does not exceed a certain constant at any point in time.
To determine the BIBO stability, the convolution integral is utilized when a bounded continuous-time input is applied to a Linear Time-Invariant (LTI) system....
To determine the BIBO stability, the convolution integral is utilized when a bounded continuous-time input is applied to a Linear Time-Invariant (LTI) system....
315
01:18Second Order systems II
75
In an underdamped second-order system, where the damping ratio ζ is between 0 and 1, a unit-step input results in a transfer function that, when transformed using the inverse Laplace method, reveals the output response. The output exhibits a damped sinusoidal oscillation, and the difference between the input and output is termed the error signal. This error signal also demonstrates damped oscillatory behavior. Eventually, as the system reaches a steady state, the error diminishes to zero.
75
01:23Linear time-invariant Systems
198
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.
The input-output behavior of an LTI system can be fully defined by its response to an impulsive excitation at its input. Once this impulse response is known, the system's reaction to any other input can be...
The input-output behavior of an LTI system can be fully defined by its response to an impulsive excitation at its input. Once this impulse response is known, the system's reaction to any other input can be...
198