An Exponential Chaotic Oscillator Design and Its Dynamic Analysis

Xiaoyuan Wang; Chenxi Jin; Xiaotao Min; Dongsheng Yu; Herbert Ho Ching Iu

doi:10.1109/JAS.2020.1003252

Volume 7 Issue 4

Jun. 2020

IEEE/CAA Journal of Automatica Sinica

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Article Navigation > IEEE/CAA Journal of Automatica Sinica > 2020 > 7(4): 1081-1086

Xiaoyuan Wang, Chenxi Jin, Xiaotao Min, Dongsheng Yu and Herbert Ho Ching Iu, "An Exponential Chaotic Oscillator Design and Its Dynamic Analysis," IEEE/CAA J. Autom. Sinica, vol. 7, no. 4, pp. 1081-1086, July 2020. doi: 10.1109/JAS.2020.1003252

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Xiaoyuan Wang, Chenxi Jin, Xiaotao Min, Dongsheng Yu and Herbert Ho Ching Iu, "An Exponential Chaotic Oscillator Design and Its Dynamic Analysis," IEEE/CAA J. Autom. Sinica, vol. 7, no. 4, pp. 1081-1086, July 2020. doi: 10.1109/JAS.2020.1003252

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An Exponential Chaotic Oscillator Design and Its Dynamic Analysis

doi: 10.1109/JAS.2020.1003252

Funds: This work was supported by the National Natural Science Foundation of China (61871429), and the Natural Science Foundation of Zhejiang Province (LY18F010012)

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Author Bio:
Xiaoyuan Wang (M’19) received the B.S. degree in agricultural electrification and automation from Heilongjiang Bayi Agricultural University in 2003, the M.S. degree in physical electronics from Harbin Institute of Technology in 2008, and the Ph.D. degree in electronical engineering from Harbin Institute of Technology in 2013. From 2010 to 2011, she was a Visiting Student with The University of Western Australia, Australia. In 2017, she was a Visiting Scholar with The University of Western Australia, Australia. She is currently an Associate Professor with the School of Electronics and Information, Hangzhou Dianzi University. Her research interests include nonlinear dynamics, memristive systems, multiple-valued logic technologies, and signal processing. She has published over 40 papers in these areas

Chenxi Jin received the B.Eng. degree in electronic information engineering from School of Electronic Information, Hangzhou Dianzi University, in 2018, where he is currently pursuing the M.S. degree in electronic science and technology. His current research interests include chaotic and hyperchaotic circuit and memristor-based logic circuit design approaches

Xiaotao Min received the B.Eng. degree in communication engineering from School of Physics and Electronic Information, Gannan Normal University, in 2017. He is currently pursuing the M.S. degree in electronics and communication engineering at Hangzhou Dianzi University. His current research interests include chaotic and hyperchaotic circuit and memristor-based logic circuit design approaches

Dongsheng Yu (M’14) received the B.Eng. and Ph.D. degrees from the School of Information and Electrical Engineering, China University of Mining and Technology, in 2005 and 2011, respectively. From 2009 to 2010, he was a Visiting Student with The University of Western Australia, Australia. In 2014, he was an Endeavour Research Fellow with The University of Western Australia, Australia. He is currently an Associate Professor with the School of Electrical and Power Engineering, China University of Mining and Technology. He has owned 5 provincial level awards for outstanding works in the teaching and research. His research interests include power electronics, renewable energy, electric drives, and memristive systems. He has published 2 books and over 40 papers in these areas

Herbert Ho Ching Iu (S’98−M’00−SM’06) received the B.Eng. degree (Hons.) in electrical and electronic engineering from The University of Hong Kong, China, in 1997, and the Ph.D. degree from The Hong Kong Polytechnic University, China, in 2000. In 2002, he joined the School of Electrical, Electronic and Computer Engineering, The University of Western Australia, Australia, as a Lecturer, where he is currently a Professor. His research interests include power electronics, renewable energy, nonlinear dynamics, current sensing techniques, and memristive systems. He has authored over 100 papers in these areas. He was a Recipient of the two IET Premium Awards in 2012 and 2014. He was also a Recipient of the Vice-Chancellor’s Mid-Career Research Award in 2014 and the IEEE PES Chapter Outstanding Engineer in 2015. He currently serves as an Associate Editor of the IEEETransactions On Circuits and Systems II, the IEEE Transactions on Power Electronics, theIEEE Access, the IEEECircuits and Systems Magazine, the IET Power Electronics, and the International Journal of Bifurcation and Chaos, an Editorial Board Member of the IEEEJournal of Emerging and Selected Topics in Circuits and Systems and the International Journal of Circuit Theory and Applications. He is a Co-Editor of the Control of Chaos in Nonlinear Circuits and Systems (Singapore: World Scientific, 2009) and a Co-Author of Development of Memristor Based Circuits (World Scientific, 2013)
Corresponding author: X. Y. Wang, C. X. Jin, and X. T. Min are with the School of Electronics and Information, Hangzhou Dianzi University, Hangzhou 310018, China (e-mail: youyuan-0213@163.com; pjincu@126.com; xiaoring0@163.com)
Received Date: 2020-03-20
Revised Date: 2020-04-14
Accepted Date: 2020-04-18

Available Online: 2020-06-12

Abstract

Abstract

After years of development, chaotic circuits have possessed many different mathematic forms and multiple realization methods. However, in most of the existing chaotic systems, the nonlinear units are composed of the product terms. In this paper, in order to obtain a chaotic oscillator with higher nonlinearity and complexity to meet the needs of utilization, we discuss a novel chaotic system whose nonlinear term is realized by an exponential term. The new exponential chaotic oscillator is constructed by adding an exponential term to the classical Lü system. To further investigate the dynamic characteristics of the oscillator, classical theoretical analyses have been performed, such as phase diagrams, equilibrium points, stabilities of the system, Poincaré mappings, Lyapunov exponent spectrums, and bifurcation diagrams. Then through the National Institute of Standards and Technology (NIST) statistical test, it is proved that the chaotic sequence generated by the exponential chaotic oscillator is more random than that produced by the Lü system. In order to further verify the practicability of this chaotic oscillator, by applying the improved modular design method, the system equivalent circuit has been realized and proved by the Multisim simulation. The theoretical analysis and the Multisim simulation results are in good agreement.
- Chaos,
- exponent,
- multisim,
- nonlinear circuits,
- oscillators,
- simulation

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Highlights

Exponential nonlinear term
The exponential term in this system makes it different from the original chaotic system. This exponentially nonlinear term may make the new chaotic system have better performance. And the effectiveness of this exponential chaotic system has been proved by various theoretical analyses.
NIST test
The exponential chaotic system passed all fifteen tests, but the Lü system passed only fourteen of them. Also the exponential chaotic system has 9 tests with P-values greater than the Lü system in all 15 tests. It shows that the sequence generated by the exponential chaotic system is more random than that produced by the Lü system.
Circuit
This paper has designed a circuit corresponding to the exponential chaotic system. And the simulation results of Multisim are consistent with the theoretical analysis. This proves the effectiveness of the chaotic circuit. The circuit allows the chaotic system to be further applied to future applications.

An Exponential Chaotic Oscillator Design and Its Dynamic Analysis

doi: 10.1109/JAS.2020.1003252

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通讯作者: 陈斌, bchen63@163.com

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