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Construction method of unequal-order fractional order chaotic system

A chaotic system and construction method technology, applied in the field of fractional order, can solve the problems of lack of calculation tools and application scenarios, slow development of fractional calculus, etc., and achieve the effect of fast calculation speed, high chaotic characteristics and high precision

Inactive Publication Date: 2020-04-10
海特运通(浙江)科技产业发展有限公司 +1
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Problems solved by technology

However, due to the lack of effective calculation tools and application scenarios, the development of fractional calculus is very slow

Method used

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  • Construction method of unequal-order fractional order chaotic system
  • Construction method of unequal-order fractional order chaotic system
  • Construction method of unequal-order fractional order chaotic system

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[0045] The invention provides a method for constructing a fractional chaotic system with unequal orders, comprising the following steps:

[0046] Step 1: Based on Caputo calculus, determine the mathematical model of the unequal order fractional order chaotic system;

[0047] The Caputo differential is defined as:

[0048]

[0049] in, is the Caputo calculus equation, Γ is the gamma function, m is the integral constant, τ time constant, d m is a differential operator;

[0050] Based on Caputo calculus, the mathematical model of the unequal fractional order chaotic system is determined, and the mathematical model of the unequal order fractional order chaotic system is expressed by the following formula:

[0051]

[0052] in, The differential operator defined for Caputo, x 1 (t), x 2 (t), x 3 (t) and x 4 (t) for x 1 , x 2 , x 3 and x 4 time series of x 1 , x 2 , x 3 and x 4 is the state variable, and a, b, c, and d are the parameters of the unequal order f...

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Abstract

The invention relates to a construction method of an unequal-order fractional order chaotic system. According to the invention, a new unequal-order fractional order chaotic system is defined based onCaputo, and a digital circuit is designed as a chaotic sequence generator by using a digital signal processing technology. The new four-dimensional unequal-order fractional order chaotic system has very complex dynamic characteristics, including complex phenomena of multi-attractor coexistence, attractor hiding and the like. Four variable orders are added to the unequal-order fractional order chaotic system to serve as bifurcation control parameters, the secret key space of the system is increased, and the chaotic performance of the system is improved. And based on the TMS320F28335, the fractional order chaotic system is high in implementation flexibility and high in usability, and any fractional order chaotic system can be implemented.

Description

technical field [0001] The invention relates to the technical field of unequal fractional order, and relates to a construction method of unequal fractional order chaotic system. Background technique [0002] While the rapid development of 5G technology, big data, blockchain and other technical fields has brought great convenience to the public, it has also triggered people's thinking about cyberspace security issues. How to ensure data privacy is the top priority. How to ensure cyberspace security is imminent. Secure communication based on chaos theory has become a research hotspot. The chaotic system has the advantages of initial value sensitivity, noise-like property, high bandwidth and ergodicity, so it has unique advantages in the field of secure communication. In addition, researchers can easily obtain chaotic sequences through simple iterations, which can meet the requirements of real-time encryption. [0003] Integer-order chaotic systems are widely used in the fi...

Claims

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Application Information

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Patent Type & Authority Applications(China)
IPC IPC(8): H04L9/00
CPCH04L9/001
Inventor 陈啸
Owner 海特运通(浙江)科技产业发展有限公司
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