City University of Hong Kong
Abstract: In this talk, the phenomenon of a hidden bifurcation route (HBR) to multi-scroll chaotic attractors is presented using the model of a 3D autonomous Chua-like system with saturated function series, which has two bifurcation parameters. These HBR is characterized by the appearing order of the multiple scrolls and the maximal ranges of the chaotic attractors under the control of the two bifurcation parameters. It is shown that such HBR has some interesting symmetry with respect to the two parameters, revealing a new generating mechanism of multi-scroll chaotic attractors.
Prof. Guanrong Chen received the M.Sc. degree in Computer Science from Sun Yat-sen (Zhongshan) University, Guangzhou, China in 1981 and the Ph.D. degree in Applied Mathematics from Texas A&M University, College Station, USA in 1987. He did not receive a BS degree due to the “Cultural Revolution” in China during 1996-1976. Since year 2000, he has been a Chair Professor and the Founding Director of the Centre for Chaos and Complex Networks at the City University of Hong Kong, prior to which he was a tenured Full Professor in the University of Houston, Texas, USA.
Prof. Chen is a Fellow of the IEEE, awarded in January 1997, for his fundamental contributions to the theory and applications of chaos control and bifurcation analysis. He is a Highly Cited Researcher in Engineering as well as in Physics ranked by Thomson Reuters, with more than 30,000 non-self citations and H_index 81 as of Spring 2014 according to Scopus. He served and is serving as Chief Editor for the IEEE Circuits and Systems Magazine and the International Journal of Bifurcation and Chaos, and as Deputy Chief Editor, Advisory Editor, and Associate Editors for several IEEE Transactions and other international journals. He received 5 best journal paper awards in the past, and the 2008 and 2012 State Natural Science Awards of China and the 2010 Ho-Leung-Ho-Lee Science and Technology Award, China, as well as the 2011 Euler Gold Medal awarded by the Euler Foundation, Russia. He was conferred Honorary Doctorate (Doctores Honoris Causa) by the Saint Petersburg State University, Russia in 2011 and by the University of Le Havre, Normandie, France in 2014. He is also an Honorary Professor at different ranks in some thirty universities worldwide.
Lodz University of Technology
Dynamics of mechanical oscillators under magnetic field
Abstract: The last two decades have shown a significant increase in research towards various applications of mechatronic systems matching two different branches of sciences, which are mechanics and electromagnetism. Along with technological progress, more and more vibrating objects embedded into magnetic and electric fields are fabricated based on the earlier derived mathematical models and their analyticval, numerical and experimental investigations. Examples of such devices include electric motors, magnetorheological vibration dampers, MEMS magnetic actuators and magnetic levitation systems. Three oscillating mechanical systems that are subjected to a magnetic field are presented. The first system consists of a single pendulum at the end of which a magnet is mounted. The coil located under the pendulum is powered by an alternating current, which forces the system to move. One-sided oscillating pendulum motion was investigated theoretically and experimentally. The origin of this type of motion and the ranges of current parameters for which it occurs have been determined numerically. Moreover, bifurcation analysis showed the existence of multi-period solutions as well as chaotic behaviours. The second system consists of the guide endowed with mass suspended in the air by the linear aerostatic bearing. Linear mechanical spring is attached to one side of the guide whereas the neodymium magnet is fixed to the other side. Magnet-magnet and magnet-coil interactions have been investigated. The magnet-magnet interaction plays the role of the nonlinear magnetic spring while the magnet-coil interaction plays the role of the electromagnetic spring or electromagnetic damper in terms of the coil current signal. Static and dynamic characteristics of mechanical, magnetic and electromagnetic springs have been analysed. A new physical model of the magnet-magnet interaction has been proposed, the validity of which is confirmed experimentally. The reliable results of the entire system and its springs are obtained by conducting tests on a specially constructed laboratory setup. The main benefit of the fabricated prototype concerns elimination of dry friction effects thought the frictions is viscous with identifiable movement resistance. The third studied mechanical system is a universal multi-degree-of-freedom system equipped with linear rolling bearings. It has been adapted to the study of oscillations of a two-degrees-of-freedom system with magnetic interactions. A mathematical model of the harmonically forced system was developed taking into account the non-linear magnetic elasticity generated by coaxially arranged cylindrical neodymium magnets. Numerical bifurcation analysis of the system was conducted, and experimental validation was performed obtaining a good agreement of both results. Period doubling cascades, chaotic attractors, hysteresis behaviour, amplitude jumps, quasi-periodic oscillations and wide multi-period windows were observed during the experiments, which will be illustrated and discussed during the talk.
Professor Jan AWREJCEWICZ is a Head of the Department of Automation, Biomechanics and Mechatronics at Lodz University of Technology and Head of Ph.D. School on ‘Mechanics’. He is also recipient of Doctor Honoris Causa (Honorary Professor) of Academy of Arts and Technology (Poland, Bielsko-Biala, 2014) and of Czestochowa University of Technology (Poland, Czestochowa, 2014), Kielce University of Technology (2019), National Technical University “Kharkiv Polytechnic Institute” (2019), and Gdańsk University of Technology (2019). His papers and research cover various disciplines of mechanics, material science, biomechanics, applied mathematics, automation, physics and computer oriented sciences, with main focus on nonlinear processes.
He authored/co-authored over 850 journal papers and refereed international conference papers and 53 monographs. JA is Editor-in-Chief of 3 international journals and member of the Editorial Boards of 90 international journals (23 with IF) as well as editor of 33 books and 37 journal special issues. He also reviewed 45 monographs and textbooks and over 800 journal papers for about of 140 journals, and he supervised 27 finalized and 6 ongoing PhD theses. He is a recipient of numerous scientific awards including The Alexander von Humboldt Award for research and educational achievements (2010/2011 and 2016). For more information please visit www.abm.p.lodz.pl
Juan J. Nieto
University of Santiago de Compostela
University of Santiago de Compostela
Fractional dynamics and COVID-19 epidemics
Abstract: We discuss some differential equations of fractional order. Some of them are originated on real world problems including epidemiological models. Some classical methods and new techniques and perspectives will be discussed. The possibility of developing a digital twin for the COVID-19 epidemic will be presented.
Juan J. Nieto got his PhD in Mathematics at the USC in Spain after a Fulbright fellowship at the University of Texas (USA). He is currently Full Professor of Mathematical Analysis, Director of the Institute of Mathematics of the USC and Editor-in-Chief of the journal Fixed Point Theory and Algorithms for Sciences and Engineering. His research interests include nonlinear functional analysis and differential equations, fractional dynamics and their biomedical applications.
Kevin H. Knuth
University at Albany
Transfer Entropy and Dynamical Systems
Abstract: Transfer entropy is an information-theoretic quantity that describes the degree to which knowing the value of one variable of a system enables you to predict the future value of another variable of the system. For this reason, transfer entropy is often associated with the concept of information flow, which is an important factor in understanding the behavior of complex systems. We introduce the concepts of transfer entropy and mutual information and discuss the numerical estimation of these information-theoretic quantities from data. We demonstrate that the transfer entropy computed from time-series data derived from the three-dimensional Lorentz system model of an atmospheric convection cell correctly identifies the overall influence of the three physical variables on one another, which is not immediately obvious from the equations alone. This is followed by an examination of the transfer entropy computed from a set of time-series obtained from a time-delay embedding of the Lorentz system. We conclude with an application involving time-series data obtained from a physical system.
Middle East Technical University
Unpredictable oscillations and applications to neural networks dynamics
Abstract: Chaos, scientifically, is considered as a theory. Even not as a part of mathematics, but interdisciplinary. Since it is discussed by dynamical equations, we see the subject on two lines, which are started by Poincare and Lorenz. Our results are extension of the Poincare research, first of all. What we are doing is at an intersection of the two lines. The first line is the comprehension of the world as a collection of oscillators, abstractly. Then, chaos is nothing, but a new type of oscillation. Sophisticated, difficult for analysis, but an oscillation. The line of Lorenz relies on sensitivity, and this is usually understood as unpredictability of weather, publicly. We have introduced the concept of unpredictability, which is a counterpart of the Lorenz sensitivity. More precisely, the property is assigned for a single motion, then sensitivity in global dynamics is valid. Thus, we prolonged the first line to the Lorenz chaos. Next, we consider the notion in functional spaces and a new type of functions, unpredictable, are obtained. In application sense, the functions are powerful instrument of description for oscillations, which occur in modern neuroscience, artificial intelligence, computer sciences, synchronization, electronics, genetics. Summarizing, we are investigating theoretical aspects of unpredictable functions, differential equations with unpredictable solutions, chaos basics and applications for neural networks dynamics. The state of the research is to be delivered in the talk.
The Ohio State University
Homeostasis in Input-Output Networks
Abstract: A prototypical biological example of homeostasis occurs in warm-blooded mammals where internal body temperature is held approximately constant on variation of the external ambient temperature. Our study of homeostasis focuses on biochemical networks and abstracts these networks in three ways. First, we assume that an input node and an output node are designated. Second, an input-output function is defined by how the output varies on change of the input. Third, infinitesimal homeostasis (the derivative of output with respect to input vanishes) replaces homeostasis (output is approximately constant on variation of input). In this talk we use graph theoretic methods to classify infinitesimal homeostasis motifs including feedforward loops, substrate inhibition, and negative feedback loops.
Martin Golubitsky is Distinguished Professor of Natural and Mathematical Sciences at the Ohio State University. Dr. Golubitsky works in the fields of nonlinear dynamics and bifurcation theory studying the role of symmetry in the formation of patterns in physical systems and the role of network architecture in the dynamics of coupled systems. His recent research focuses on some mathematical aspects of biological applications: animal gaits, binocular rivalry, homeostasis, and coupled systems. At Ohio State, Golubitsky served as Director of the Mathematical Biosciences Institute (2008-16). He is a Fellow of the American Academy of Arts and Sciences and has served as President of SIAM.
Theoretical Division, Los Alamos National Laboratory