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research-article

Bursting, dynamics and circuit implementation of a new fractional-order chaotic system with coexisting hidden attractors

[+] Author and Article Information
Mengjiao Wang

College of Information Engineering, Xiangtan University, Xiangtan 411105, Hunan, China
wangmj@xtu.edu.cn

Xiaohan Liao

College of Information Engineering, Xiangtan University, Xiangtan 411105, Hunan, China
13971259469@163.com

Yong Deng

College of Information Engineering, Xiangtan University, Xiangtan 411105, Hunan, China
13875346353@163.com

Zhijun Li

College of Information Engineering, Xiangtan University, Xiangtan 411105, Hunan, China
lizhijun@xtu.edu.cn

Yicheng Zeng

School of Physics and Opotoelectric Engineering, Xiangtan University, Xiangtan 411105, Hunan, China
yichengz@xtu.edu.cn

Minglin Ma

College of Information Engineering, Xiangtan University, Xiangtan 411105, Hunan, China
minglin_ma@xtu.edu.cn

1Corresponding author.

ASME doi:10.1115/1.4043003 History: Received September 27, 2018; Revised February 15, 2019

Abstract

Systems with hidden attractors have attracted increasing interest because of its striking features in the last few years. Fractional-order systems with hidden attractors are newly introduced and barely investigated. In this paper, a new 4-D fractional-order chaotic system with hidden attractors is proposed. The abundant and complex hidden dynamic behaviors are studied by nonlinear theory, numerical simulation and circuit simulation. As the main mode of electrical behavior in many neuroendocrine cells, bursting oscillations (BOs) exist in this system. This more complicated phenomenon is seldom found in chaotic systems, especially in fractional-order chaotic systems without equilibrium points. With the view of practical application, the spectral entropy (SE) algorithm is chosen to estimate the complexity of the fractional-order system for selecting more appropriate parameters. Importantly, there is a state variable in relation with offset boosting that can adjust amplitude of the system conveniently. The physical existence of hidden chaotic or periodic behaviors found in the proposed system are verified by analog as well as hardware circuit. All the results of electronic circuit are consistent well with those of numerical simulation.

Copyright (c) 2019 by ASME
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