Fractional order hyper chaotic system and projection synchronization method thereof

A chaotic system, fractional-order technology, applied in digital transmission systems, transmission systems, electrical components, etc., to achieve the effect of simple controller, wide application value, and overcoming the problem of projection synchronization

Inactive Publication Date: 2013-06-12
王少夫
View PDF0 Cites 17 Cited by
  • Summary
  • Abstract
  • Description
  • Claims
  • Application Information

AI Technical Summary

Problems solved by technology

A variety of chaos control and synchronization methods have been proposed, such as drive response chaos synchronization method, linear and nonlinear feedback synchronization method, coupling synchronization method, adaptive synchronization method, driving

Method used

the structure of the environmentally friendly knitted fabric provided by the present invention; figure 2 Flow chart of the yarn wrapping machine for environmentally friendly knitted fabrics and storage devices; image 3 Is the parameter map of the yarn covering machine
View more

Image

Smart Image Click on the blue labels to locate them in the text.
Viewing Examples
Smart Image
  • Fractional order hyper chaotic system and projection synchronization method thereof
  • Fractional order hyper chaotic system and projection synchronization method thereof
  • Fractional order hyper chaotic system and projection synchronization method thereof

Examples

Experimental program
Comparison scheme
Effect test

Example Embodiment

[0033] By constructing a fractional four-dimensional hyperchaotic system, the corresponding partial differential equation is:

[0034]

[0035] (1)

[0036]

[0037]

[0038] in, is the state variable, the parameter is a positive real number, is a fractional value. when a=10; b=40; c=2.5; d=10.6; h=4 ;k=1, the initial condition is [1 1 50 1 ] T hour, figure 1 are the two-dimensional and three-dimensional phase diagrams of the trajectory of system (1). from figure 1 It can be seen that this fractional hyperchaotic system has complex dynamical behavior.

[0039] 1 Basic dynamic characteristics

[0040] 1.1 Balance point, dissipation

[0041] Let the right side of the system (1) equation be 0, that is, the equilibrium point can be obtained by solving the following algebraic equation

[0042] ...

the structure of the environmentally friendly knitted fabric provided by the present invention; figure 2 Flow chart of the yarn wrapping machine for environmentally friendly knitted fabrics and storage devices; image 3 Is the parameter map of the yarn covering machine
Login to view more

PUM

No PUM Login to view more

Abstract

The invention relates to a fractional order hyper chaotic system and a projection synchronization method thereof. By introducing a feedback function, a fractional order four-dimensional hyper chaotic system is provided, the system is provided with one balance point only and has a complex dynamical behavior, and a two-wing type is shown by a chaotic attractor of the system. Through nonlinear feedback control, a nonlinear chaotic synchronous error system is changed into a linear system; according to a fractional order linear system Lyapuvov stability theory, a synchronous controller is designed; and different scaling factors are selected, isomer projection synchronization between fractional order hyper chaotic systems is realized, and the validity of the method is confirmed through numerical simulation.

Description

technical field [0001] The invention relates to a fractional hyperchaotic system and a projection synchronization method thereof, belonging to the field of electronic communication and nonlinear control. Background technique [0002] In recent years, fractional-order hyperchaotic systems and their applications have aroused widespread interest and in-depth research. Integer-order calculus is a special case of fractional-order calculus theory, and integer-order hyperchaotic systems are idealized treatments of actual chaotic systems. Fractional calculus is an extension of integer-order calculus theory, and the use of fractional-order calculus operators can more accurately describe the dynamics of the actual hyperchaotic system. When the order of various systems is fractional, the hyperchaotic state still appears and can better reflect the engineering physical phenomena presented by the system, which greatly promotes the use of fractional calculus theory to study chaos, a ubiqui...

Claims

the structure of the environmentally friendly knitted fabric provided by the present invention; figure 2 Flow chart of the yarn wrapping machine for environmentally friendly knitted fabrics and storage devices; image 3 Is the parameter map of the yarn covering machine
Login to view more

Application Information

Patent Timeline
no application Login to view more
IPC IPC(8): H04L9/00
Inventor 不公告发明人
Owner 王少夫
Who we serve
  • R&D Engineer
  • R&D Manager
  • IP Professional
Why Eureka
  • Industry Leading Data Capabilities
  • Powerful AI technology
  • Patent DNA Extraction
Social media
Try Eureka
PatSnap group products

Browse by: Latest US Patents, China's latest patents, Technical Efficacy Thesaurus, Application Domain, Technology Topic.

© 2024 PatSnap. All rights reserved.Legal|Privacy policy|Modern Slavery Act Transparency Statement|Sitemap