DESIGN OF A FOUR-WING HETEROGENEOUS FRACTIONAL-ORDER CHAOTIC SYSTEM AND ITS CIRCUIT SIMULATION

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International Journal on Smart Sensing and Intelligent Systems

Professor Subhas Chandra Mukhopadhyay

Exeley Inc. (New York)

Subject: Computational Science & Engineering , Engineering, Electrical & Electronic

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VOLUME 7 , ISSUE 4 (December 2014) > List of articles

DESIGN OF A FOUR-WING HETEROGENEOUS FRACTIONAL-ORDER CHAOTIC SYSTEM AND ITS CIRCUIT SIMULATION

Xiaohong ZHANG * / Qiang SUN / Peng CHENG

Keywords : Fractional-order differential system, chaotic system, heterogeneous fractional-order, circuit simulation, feedback control.

Citation Information : International Journal on Smart Sensing and Intelligent Systems. Volume 7, Issue 4, Pages 0-0, DOI: https://doi.org/10.21307/ijssis-2017-725

License : (CC BY-NC-ND 4.0)

Received Date : 10-April-2014 / Accepted: 12-November-2014 / Published Online: 01-December-2014

ARTICLE

ABSTRACT

Integer orders differential system is a special case of fractional-order differential system.
Integer orders chaotic system that we usually study is ideally approximate to realistic chaotic system.
Fractional-order chaotic system has broader and changeable values of order and more complex
dynamical behavior than integer order chaotic system. Thus, fractional-order differential equation
can describe the nonlinear characteristics of actual chaotic system more exactly, which has more
prominent research meanings and application value. This paper designs a new four-wing
four-dimensional heterogeneous fractional-order chaotic system, when the values of
fractional-order q (i = 1,2,3,4) i are not identical( 0.9, 0.8 1 2 3 4 q = q = q = q = , in step size of 0.1),
the attractors of this chaotic system will all show four-wing shapes in any direction. After analysis
this chaotic system's stability and existence, this paper also introduces a nonlinear state feedback
controller, and adopts the chain shape circuit to conduct experiment simulation through Multisim
software 10.0. The results of circuit simulation and Matlab numerical operation have the same
chaotic attractor phase diagram. This demonstrates the effectiveness of this four-wing
four-dimensional heterogeneous fractional-order chaotic system's design and the feasibility of the
feedback controller in the circuit; meanwhile, it provides referable bases for the application in
actual circuits.

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