Wiener noise-contained two-dimensional chaotic system

A chaotic system and noise technology, applied in the fields of engineering technology and biology, can solve the problems of little consideration of the influence of chaotic motion, and achieve the effect of wide application value

Inactive Publication Date: 2013-06-12
王少夫
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Problems solved by technology

[0002]At present, people pay more and more attention to the chaotic motion of nonlinear systems under the action of period or noise. The three common oscillators are Duffing oscillator, Van-der-Pol oscillator and Rayleigh oscillator; in recent years, many scholars have done a lot of work on the above-mentioned related oscillators using the Melnikov method, and most of their research work is based on the excitation amplitude of bounded noise However, the impact of other factors, such as noise and other factors, on the chaotic motion of the system is rarely considered, and the related research is rarely reported.

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  • Wiener noise-contained two-dimensional chaotic system
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  • Wiener noise-contained two-dimensional chaotic system

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Embodiment Construction

[0021] (1)

[0022] In the formula is the nonlinear damping parameter, represent the coefficients of the linear and nonlinear restoring forces, respectively; are the amplitudes of the harmonic excitation and the bounded noise, respectively, is bounded noise, that is,

[0023] (2)

[0024] (3)

[0025] In the formula Expressed as the average frequency of the excitation, is a standard Wiener process whose response is as figure 1 shown; for A uniform random variable on , is the noise intensity. By adjusting the parameters of the system, the system can generate two scroll chaotic attractors such as figure 2 shown.

[0026] make The system equation (1) can be transformed into

[0027] (4)

[0028] when When , the corresponding motion equation of the undisturbed system is

[0029] (5)

[0030] The corresponding Hamilton quantity and potential function are respectively . System (5) has three fixed points: and ; It can be known from...

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Abstract

The invention relates to a Wiener noise-contained two-dimensional chaotic system. Researches in the past are mostly based on the influence of the excitation amplitude of bounded noise on the system, but the influences of noise and other factors on the chaotic motion of the system are little considered. Aiming at the problem, the invention provides the Wiener noise-contained two-dimensional chaotic system. Through analyzing the dynamic characteristic of the Wiener noise-contained two-dimensional chaotic system, the condition that chaos is generated under the mean square meaning during a random Melnikov process is given. The simple two-dimensional chaotic system has a wide application prospect and important application value in the field of engineering technology, physics, chemistry, biology and the like.

Description

technical field [0001] The invention relates to a two-dimensional chaotic system containing Wiener noise, which belongs to the fields of engineering technology, biology and the like. Background technique [0002] At present, people pay more and more attention to the chaotic motion of nonlinear systems under the action of period or noise. The three common oscillators are Duffing oscillator, Van-der-Pol oscillator and Rayleigh oscillator; in recent years, many scholars have done a lot of work on the above-mentioned related oscillators using the Melnikov method, and most of their research work is based on the excitation amplitude of bounded noise However, the influence of other factors, such as noise and other factors, on the chaotic motion of the system is rarely considered, and the related research is rarely reported. [0003] The invention proposes a two-dimensional chaotic system containing Wiener noise, and provides the conditions for random Melnikov process to appear cha...

Claims

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Application Information

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Patent Type & AuthorityApplications(China)
IPC IPC(8): G06F19/00
Inventor不公告发明人
Owner王少夫