(7) Chaotic Dynamics and Applications: Hai Yu, Northeastern University, China (Chair)

7.1. Speaker: Prof. Chunbiao Li,  Nanjing University of Information Science and Technology, China

Talk Title: Amplitude Control and Offset Boosting of Chaotic Signal

Abstract: Chaotic signal is considered with great potential in radar and communication engineering for its inherent property of broadband frequency spectrum. However, there are two stumbling blocks in the way to chaos application: how to obtain the suitable amplitude or offset of chaotic signal? Because of the broadband property and the sensitivity to initial condition, it is a great challenge to design an amplifier or a polarity converter. Fortunately, differential-equation-based continuous chaotic system may share a structure-friendly mathematical form, which could be equipped with an independent knob to control the amplitude or offset directly without losing the fundamental property of chaos. This brings great convenience for chaos application, enabling us possible to ignore the chaotic signal conditioning before signal transmission and processing. In this talk, firstly various regimes of chaotic system with an independent amplitude controller are discussed combined with circuit realization. Secondly, chaotic systems with one or two independent offset controllers are introduced, after which infinitely many attractors are constructed when the offset boosting is based on the initial condition by a periodic function. Finally, the potential application of the proposed systems with easy amplitude/offset control will be briefly discussed.

Biography: Prof. Chunbiao Li is a professor in the School of Electronic & Information Engineering at Nanjing University of Information Science & Technology. He received his Master degree and Ph.D. degree from Nanjing University of Science and Technology in succession in 2004 and 2009. From 2010 to 2014 he was a postdoctoral fellow in school of information science and engineering at Southeast University. He was a visiting scholar in the department of physics at the University of Wisconsin-Madison in 2012 and 2013. His research interests are in the areas of nonlinear dynamics and chaos including nonlinear circuits, memristive systems and corresponding applications. He has been devoted to finding the multistability mechanism in dynamical system and the methodology for constructing chaotic systems with amplitude control and offset boosting. He has received several awards for his teaching and research in Jiangsu Province.

7.2. Speaker: Prof. Yuncai Wang,  Tai Yuan University of Technology, China

Talk Title: Chaotic Applications: From Random Number Generator to Noise Generator

Abstract: “Philosophers only interpret the world in different ways, but the problem is to change the world”, Chaos will be more attractive only it had more applications. In this presentation, the speaker introduce two important chaotic applications in his group: How to build the fast random number generator and wideband millimeter wave noise generator utilizing chaotic laser diode.

Biography: Prof. Yuncai Wang received the B.Sc. in electronics from the Nankai University of Tianjin, China, in 1982, the M.Sc degree in Electronics, particles & vacuum physics in 1994, and the Ph.D degree in Optics from Xi’an Institute of Optics & Fine Mechanics, CAS, respectively. In 1986, he joined the Department of Physics & Optoelectronics Engineering, Taiyuan University of Technology as an Assistant Lecture, then a Lecture(1994), an Associate Professor(1998), and a Professor(2003). From 2000 to 2001, he was a visiting staff member at the Institute of Solid State Physics, Technology University of Berlin. In 2009, he was the visiting professor in Technology University, Darmstadt. Since 2019, he has been a professor with the School of Information Engineering, Guangdong University of Technology.

He is currently working on the applications of chaotic laser & chaotic chip, such as fast random number and millimeter wave noise generation, physical secure communications, sensor and detection using chaotic laser.

Dr. Wang is a senior member of Optical Society of China, the Vice Chairman of the Professional Committee of Optical-Mechanical-electronic Technology & System Integration,Instrument and Control Society, China, and the vice President of the Chaotic Secure communications Committee, Association for Cryptologic Research, China.

7.3. Speaker: Prof. Chengqing Li,  Hunan University, China

Talk Title: Dynamic analysis of digital chaotic maps via state-mapping networks

Abstract: Complex dynamics of chaotic maps under an infinite-precision mathematical framework have been well known. The case in a finite-precision computer remains to be further explored. Previous work treated a digital chaotic map as a black box and gave different explanations according to the test results of the output. Using the Logistic map, Tent map, Cat map as typical examples, we disclose some dynamical properties of chaotic maps in fixed-point arithmetic by studying its corresponding state-mapping network, where every possible value is considered as a node and every possible mapping relation between a pair of nodes works as a directed edge. The scale-free property of the state network will be quantitatively proven. The obtained results can be extended to the scenario of floating-point arithmetic and to other chaotic maps. Understanding the real network structure of the state space of a chaotic map in the digital domain will help evaluate and improve the randomness of pseudo-random number sequences generated by chaotic maps.

Biography: Prof. Chengqing Li received his M.Sc. degree in applied mathematics from Zhejiang University, China in 2005 and his Ph.D. degree in electronic engineering from City University of Hong Kong in 2008. Thereafter, he worked as a Postdoctoral Fellow at The Hong Kong Polytechnic University till September 2010. Then, he worked at the College of Information Engineering, Xiangtan University, China. From April 2013 to July 2014, he worked at the University of Konstanz, Germany, under the support of the Alexander von Humboldt Foundation. Since April 2018, he has been working with the School of Computer Science and Electronic Engineering, Hunan University, China as a full professor. Prof. Li focuses on dynamics analysis of digital chaotic systems and their applications in multimedia security. He has published more than fifty papers on the focal subject in the past 15 years, receiving more than 2800 citations with h-index 29.

7.4. Speaker: Prof. Qigui Yang,  South China University of Technology, China

Talk Title: Homoclinic/heteroclinic cycles and chaos in 3D three-zone piecewise affine systems

Abstract: It is a great challenge to detect homoclinic/heteroclinic cycles and chaos in dynamical systems with multiple discontinuous boundaries. This paper takes the challenge to investigate the coexistence of homoclinic, heteroclinic and homoclinic/ heteroclinic cycles in a new class of three-dimensional three-zone piecewise affine systems. It develops a method to accurately predict the coexisting homoclinic, heteroclinic and homoclinic/heteroclinic cycles in such a system. Furthermore, this paper establishes some conditions for chaos to exist in the system, with rigorous mathematical proof of chaos emerged from the coexistence of these homoclinic, heteroclinic and homoclinic/heteroclinic cycles. Finally, it presents numerical simulations to verify the theoretical results. Moreover, it is hoped that the investigation of the paper will shed some lights to more systematic studies of 3D Lorenz-type chaotic systems.

Biography: Prof. Qigui Yang is a professor of the second grade, Doctor of Science, Doctoral supervisor, teaching masters at South China University of Technology. He received his Master from Chongqing University, Ph.D. from Sun Yat-sen University, and the Postdoctoral from Tsinghua University. He has engaged in teaching and reaching the geometric theory of differential equations, the chaotic dynamical systems and stochastic dynamical systems and their applications. He is interested in studying the existence condition of chaotic complexity with simply systems and revealing the chaos mechanism and complex dynamical characteristics of chaotic systems. Also, he was awarded the first prize for ‘’Guangxi Scientific and Technological Progress Award’’ (rank: 1/4), the second prize for ‘’Guangdong Higher Education Provincial Teaching Achievement Prize’’ (rank: 2/5), and the excellent supervisor award in “Excellent Doctoral Dissertation of Guangdong Province” for three times consecutively. Up to now, he has published 119 papers in domestic and international professional journals including J. Differential Equations, Chaos, Int. J. Bifur. Chaos, Proc. Royal Soc. Edinburgh (A), of which 101 papers have been indexed in the SCI and positively cited over 1500. Moreover, he has hosted 4 projects from National Natural Science Foundation of China (NSFC) and 5 projects from provincial Natural Science Foundation on the topic of Chaos, and he also participated in the Major Research Instrumentation Program of NSFC, 3 other projects from NSFC and the Provincial Innovation Team Project. Besides, he has hosted 7 provincial teaching and research projects. In addition, he was engaged as an evaluation express for NSFC with both meeting and communication deciding.Until now, he has guided 4 postdoctoral, 18 graduated Ph.D. students (including 2 international students) and 33 graduated master students and is supervising 1 postdoctoral, 5 Ph.D. and 6 master candidates.