Method for rapidly determining Lyapunov index spectrum of discontinuous system

A continuous system and exponential spectrum technology, applied in the fields of electrical digital data processing, special data processing applications, instruments, etc., can solve problems such as complex calculation process and weak algorithm versatility

Pending Publication Date: 2021-11-12
WUHAN UNIV OF TECH
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Problems solved by technology

In recent years, some scholars have proposed mapping methods, compensation matrix methods, complete synchronization methods, clone dynamics methods, etc. These methods have high accuracy for some types of discontinuous systems, but the algorithms are not universal and computationally The process is more complicated

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  • Method for rapidly determining Lyapunov index spectrum of discontinuous system
  • Method for rapidly determining Lyapunov index spectrum of discontinuous system
  • Method for rapidly determining Lyapunov index spectrum of discontinuous system

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Embodiment Construction

[0019] Below in conjunction with accompanying drawing and specific embodiment the present invention is described in further detail:

[0020] A two-degree-of-freedom dry friction shock oscillator system consists of a 1 The mass M of the spring and the damping coefficient c 1 The viscous damper composition, such as figure 2 As shown, another mass m is located on the mass M, its position relative to M is limited by the buffers A and B, and there is friction F between the masses T and a damping coefficient of c 2 the viscous damping force. The two-degree-of-freedom shock oscillator is a mass-spring-damper system, in which two masses can collide with each other and have dry friction during relative motion.

[0021] A two-degree-of-freedom shock oscillator can be described by the following equations:

[0022]

[0023] In the formula, means x 1 The first derivative of , means x 1 The second derivative of , means x 2 The first derivative of , means x 2 The second ...

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Abstract

The invention discloses a method for rapidly determining a Lyapunov index spectrum of a discontinuous system, and the method comprises the steps of taking a state parameter initial value of the discontinuous system and a disturbance quantity of each basic vector along a phase space as initial conditions, and determining a phase trajectory; secondly, adopting a difference quotient approximate derivative method to obtain an approximate matrix of the Jacobi matrix; then, performing feature value extraction on the Jacobi matrix, and obtaining a Lyapunov index spectrum of a discontinuous system; finally, applying the new algorithm to a two-degree-of-freedom dry friction impact oscillator system example, comparing a calculation result with a calculation result of the synchronization method, and verifying the effectiveness of the new method. The method is not only suitable for a discrete system and a continuous time system, but also can quickly determine the Lyapunov index of the complex discontinuous system, and provides a new thought for determining the dynamic behavior of the complex discontinuous system.

Description

technical field [0001] The invention relates to the technical field of chaotic system identification, in particular to a method for quickly determining the Lyapunov exponent spectrum of a discontinuous system. Background technique [0002] The Lyapunov exponent is a numerical value to determine the stability of the system under the local and global stability criteria, which characterizes the average exponential rate of the convergence or divergence of the system between adjacent orbitals in the phase space. From a mathematical point of view, the Lyapunov exponent is the eigenvalue of the state transition matrix, which determines the evolution process of the infinitesimal disturbance on the trajectory of the system attractor. Therefore, the Lyapunov exponent is considered to be an important index to measure the sensitivity of the system to the initial conditions. The sum of all Lyapunov exponents determines the divergence of the volume of the system in phase space, and the n...

Claims

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Application Information

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IPC IPC(8): G06F30/17G06F119/14
CPCG06F30/17G06F2119/14
Inventor 周瑞平马召召杨庆超
Owner WUHAN UNIV OF TECH
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