Phase diagram matrix method for nonlinear dynamic behavior analysis

A technology of nonlinear dynamics and behavior analysis, applied in the field of data recognition, can solve problems such as ergodicity cannot be quantitatively analyzed, and achieve the effect of improving the speed of discrimination and fast calculation process

Active Publication Date: 2015-04-15
SHIJIAZHUANG TIEDAO UNIV
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  • Abstract
  • Description
  • Claims
  • Application Information

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Problems solved by technology

[0007] The technical problem to be solved by the present invention is to provide a phase diagram matrix method for nonlinear dynamic behavior analysis, which can overcome the shortcomings of the ergodicity of nonlinear dynamic behavior that cannot be qu

Method used

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  • Phase diagram matrix method for nonlinear dynamic behavior analysis
  • Phase diagram matrix method for nonlinear dynamic behavior analysis
  • Phase diagram matrix method for nonlinear dynamic behavior analysis

Examples

Experimental program
Comparison scheme
Effect test

Embodiment 1

[0047] The equation of the Duffing system is:

[0048] x · · + δ x · - x + x 3 = γ cos ( ωt )

[0049] Where δ≥0 is the damping coefficient, and γ is the amplitude of the built-in periodic driving force. The equation behaves as a chaotic state under some parameter values. The existing methods of judging the state of the system by using the change of the phase trajectory mainly determine the state of the system by observing the phase trajectory of the system. This method is very dependent on people's subjective cognition, there is no quantitative standard, the generality is not good, and the operability is not high.

[0050] The specific operation steps of using this method to judge the system status are as fol...

Embodiment 2

[0066] The difference from Example 1 is that γ in the Duffing equation is set to 0.98, and the phase space of the system is as follows image 3 shown. The graphical display of the phase diagram matrix obtained by this method is as follows Figure 4 As shown, the ergodic parameter s=0.0824 of the system in this state is obtained through calculation. Compared with the threshold of chaos discrimination thresh=0.35, it can be seen that the system is not in a chaotic state. The result of the fact is that the system is in a large-scale state at this time. The graphical display of graph matrix confirms this conclusion at the same time, which also shows the effectiveness and correctness of this method.

Embodiment 3

[0068] The difference from Embodiment 1 is that the size of the phase diagram matrix is ​​set to 100×100. The graphical display of the phase diagram matrix obtained by this method is as follows Figure 5 As shown, the ergodic parameter s=0.5462 of the system in this state is obtained through calculation. Compared with the threshold value of thresh=0.35, it can be seen that the system is in a chaotic state. The result of the fact is that the system is in a chaotic state at this time. The graphical display of graph matrix confirms this conclusion at the same time, which also shows the effectiveness and correctness of this method.

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Abstract

The invention discloses a phase diagram matrix method for nonlinear dynamic behavior analysis and belongs to the technical field of data recognition. The invention provides a novel phase diagram matrix method for nonlinear dynamic behavior analysis. The method can be used for analyzing nonlinear dynamic behaviors from the perspective of ergodicity and further identifying a chaos state of a system. According to the method, ergodicity parameters are creatively provided and can be used for quantitatively describing the ergodicity characteristics of chaos dynamic behaviors, and the calculation process is quick, simple and convenient, so that the identification speed of the chaos state can be greatly improved; according to the method, a phase diagram matrix is also provided, the size of the phase diagram matrix can be automatically set, and the ergodicity of a system phase space is investigated from different scales. The invention has an important application value in nonlinear system dynamics analysis, in particular to chaotic behavior recognition.

Description

technical field [0001] The invention belongs to the technical field of data identification. Background technique [0002] Nonlinear science is known as the "third revolution" of natural science in the 20th century, and the research on nonlinear science has developed rapidly in recent years. The study of nonlinear science not only has great scientific significance, but also has broad application prospects. It involves almost every field of natural science and social science, and is changing people's traditional view of the real world. [0003] Chaos is a field that is very active and has broad application prospects in nonlinear science. Over the past 20 years, chaos has developed rapidly at an unprecedented speed into a modern subject with rich nonlinear physics background and profound mathematical connotation. [0004] Chaos is a quasi-random phenomenon in deterministic systems, which has the following main characteristics: (1) extreme sensitivity to initial conditions; (2...

Claims

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Application Information

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IPC IPC(8): G06F17/16
Inventor 赵志宏杨绍普王扬
Owner SHIJIAZHUANG TIEDAO UNIV
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