Simplest element circuit with synchronous integral orders and fractional orders

A fractional-order and integer-order technology, applied in the field of the simplest element circuit, can solve the problems that the synchronization research of fractional-order chaotic system and integer-order chaotic system is rarely involved, etc.

Inactive Publication Date: 2014-03-12
NORTHWEST A & F UNIV
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Problems solved by technology

[0003] However, many existing chaotic synchronization results only focus on the synchronization between integer-order chaotic systems or only on the synchronizati...

Method used

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  • Simplest element circuit with synchronous integral orders and fractional orders
  • Simplest element circuit with synchronous integral orders and fractional orders
  • Simplest element circuit with synchronous integral orders and fractional orders

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Experimental program
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Embodiment Construction

[0021] Mathematical model 1 is an equation of the simplest element circuit that synchronizes integer order and fractional order:

[0022] d β y i dt β = d β x i dt β - χe i = d β x i dt β - χ ( y i - x i )

[0023] Where χ> 0,β=[β 1 ,β 2 ,..., β i ,..., β n ] T ,(0i ≤1fori=1,2,...,n),x i ∈R n , Y i ∈R n

[0024] The specific circuit mathematical expression is:

[0025] d β y i dt β = R 5 R 7 R 6 R 9 d β x i dt β + R 2 R 5 R 7 R 3 R 4 R 6 R 8 C 0 y i - R 2 R 5 R 7 R 1 R 3 R 4 R 6 C 0 x i

[0026] Here C 0 = 1uF, R 1 =R 8 , R 4 =R 5 =R 6 =R 7 =R 8 =10KΩ, the linear equation can be rewritten as:

[0027] d β y i dt β = d β x i dt β + ...

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Abstract

The invention discloses a simplest element circuit of which an integral order system and a fractional order system are synchronous. A corresponding simulation circuit consists of a first channel, a second channel, a third channel and a fourth channel; and by four whole circuits, an integral order chaotic system and a fractional order chaotic system can be synchronous. By using the simplest element circuit, the integral order chaotic system and the fractional order chaotic system are synchronous; and the simplest element circuit is a bridge for the integral order chaotic system and the fractional order chaotic system, and can be finally applied to fields such as electronic engineering. The circuit is simple in structure and convenient to understand and integrate, and greatly facilitates technological development on secrete communication and radar application.

Description

Technical field: [0001] The present invention belongs to the simplest element circuit, and particularly relates to a circuit that synchronizes an integer order system and a fractional order system. technical background: [0002] Chaotic system is a complex motion form unique to nonlinear dynamic system, and it is a complex phenomenon that exists universally in nature. Since the 1990s, nonlinear chaos research has been one of the hot issues in the field of nonlinear science. The synchronization of integer-order and fractional-order chaotic systems has great potential and development prospects in the fields of physics, communications, and information science. Has attracted widespread attention. From different angles, people have proposed many control methods to realize the synchronization of chaotic systems, and successively proposed complete synchronization of chaotic systems, anti-phase synchronization of chaotic systems, generalized synchronization of chaotic systems, and proje...

Claims

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Application Information

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IPC IPC(8): H04L9/00
Inventor 陈帝伊薛运田张振铎张阳
Owner NORTHWEST A & F UNIV
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