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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
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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 parameter synchronization method, etc., most of these synchronization methods are suitable for integer order Synchronization between chaotic systems, but there are few reports on heterostructure projection synchronization of fractional hyperchaotic systems

Method used

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  • 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

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Embodiment Construction

[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] ...

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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

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Application Information

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IPC IPC(8): H04L9/00
Inventor 不公告发明人
Owner 王少夫
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