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Method for constructing grid multi-wing chaotic attractor generator by fractional order differential system

A technology of chaotic attractor and fractional differentiation, which is applied in the direction of chaos model, nonlinear system model, complex mathematical operation, etc.

Active Publication Date: 2020-08-25
HUNAN INSTITUTE OF ENGINEERING
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  • Abstract
  • Description
  • Claims
  • Application Information

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Problems solved by technology

However, the design of mesh multi-wing chaotic attractors in fractional order systems is still a very challenging problem

Method used

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  • Method for constructing grid multi-wing chaotic attractor generator by fractional order differential system
  • Method for constructing grid multi-wing chaotic attractor generator by fractional order differential system
  • Method for constructing grid multi-wing chaotic attractor generator by fractional order differential system

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Embodiment Construction

[0068] The present invention will be further described below in conjunction with the accompanying drawings and embodiments.

[0069] Such as figure 1 As shown, a method for constructing a grid multi-wing chaotic attractor generator for a fractional order differential system includes the following steps:

[0070] Step 1: Determine the fractional form of the fractional-order Rucklidge system, and linearize the fractional-order Rucklidge system at its two symmetrical equilibrium points to obtain two basic fractional-order linear systems.

[0071] The process of determining the fractional form of a fractional Rucklidge system is:

[0072] The fractional differential equation is:

[0073]

[0074] Among them, D t Indicates partial derivative for t; x(t), y(t), z(t) are state variables; t is time variable; f 1 , f 2 , f 3 Respectively represent the partial derivative functions of x(t), y(t), z(t) to t; T is the maximum time value; α i is the order; initial value x(0)=x 0 ...

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Abstract

The invention discloses a method for constructing a grid multi-wing chaotic attractor generator by a fractional order differential system. The method comprises the following steps of 1, determining afractional order form of a fractional order Rucklige system, and linearizing the fractional order Rucklige system at two symmetrical balance points of the fractional order Rucklige system to obtain two basic fractional order linear systems; and 2, constructing an extraordinary loop, and connecting all balance points of the two basic fractional order linear systems through saturation function switching control to realize the grid multi-wing chaotic attractor generator. A construction system represented by three fractional order differential equations without multipliers can capture basic characteristics of generalized Lorenz attractors and generate a butterfly effect, so that a hardware circuit is simpler to implement, and the invention has potential engineering application.

Description

technical field [0001] The invention relates to the field of chaotic signals, in particular to a method for constructing a grid multi-wing chaotic attractor generator for a fractional order differential system. Background technique [0002] Fractional calculus is a classic mathematical concept for over 300 years. But its use in physics and engineering applications is only the subject of recent attention. Recently, many researchers have found surprisingly that many fractional nonlinear differential systems can also display complex bifurcation and chaos phenomena. For example, fractional Chua's circuits also have a double-scroll chaotic attractor. Ahmad introduced a step function method to create n chaotic attractors from fractional order systems, and designed a multi-directional multi-swirl chaotic attractor based on fractional order differential systems controlled by switching. A four-winged chaotic attractor was generated in a fractional system obtained by coupling two f...

Claims

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Application Information

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Patent Type & Authority Applications(China)
IPC IPC(8): G06N7/08G06F17/13G06F17/16
CPCG06N7/08G06F17/13G06F17/16
Inventor 林愿谢庆华
Owner HUNAN INSTITUTE OF ENGINEERING
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