Plenary Talks

Guanrong Chen
City University of Hong Kong

A hidden bifurcation route to multi-scroll chaotic attractors

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.


James A. Yorke

University of Maryland, USA

Large and small chaos models

Abstract: I will discuss one large model, a whole-Earth model for predicting the weather, and how to initialize such a model and what aspects of chaos are essential. Then I will discuss a couple related “very simple” maps that tell us a great deal about very complex models. The results on simple models are new. I will discuss the logistic map mx(1-x). Its dynamics can make us rethink climate models. Also, we have created a piecewise linear map on a 3D cube that is unstable in 2 dimensions in some places and unstable in 1 in others. It has a dense set of periodic points that are 1 D unstable and another dense set of periodic points that are all 2 D unstable.


A.B., Columbia University 1963;

James Yorke has been at the University of Maryland since 1963.

Ph.D. in Mathematics: University of Maryland at College Park 1966.

Currently: Distinguished University Research Professor of Mathematics and Physics, Univ. of Maryland, College Park, MD, USA.

James Yorke is perhaps best known for coining the mathematical term chaos in his 1975 paper with Tien-Yien Li “Period Three Implies Chaos”. He came to the University of Maryland as a math graduate student in 1963 hoping to explore interdisciplinary mathematics. Those hopes were fully realized after he received his Ph.D. and joined the faculty of the University of Maryland. He feels that a Ph.D. in mathematics is a license to investigate the universe. His current research interests include simple models for covid-19, for ecosystems, for ergodic chaotic systems with multiple instabilities. In 2003 he was awarded the Japan Prize jointly with Benoit Mandelbrot for their work in chaos and fractals in a ceremony presided over by the Emperor of Japan.

Jan Awrejcewicz

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 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


 Jian-Qiao Sun
University of Delaware

Identification of Nonlinear Mechanical Systems with Time Delay


Abstract: In this talk, we present some recent studies on identification of nonlinear mechanical systems with time delay.  With the available measured response of the system and a rough knowledge about the nature of the mechanical system, we propose to use a general polynomial to describe the nonlinearity of the damping and restoring forces.  To this end, the number of terms in the polynomial is minimized with the sparse optimization algorithm.  The proposed method of this study combines cross-validation techniques from machine learning for automatic model selection and an algebraic operation for preprocessing signals to filter the noise and for removing the dependence on initial conditions. We also apply the bootstrapping resampling technique with the sparse regression to obtain the statistical properties of estimation.  The Taylor expansion of the
time delay term is used to make the time delay explicit for estimation.  A nonlinear Duffing oscillator is simulated to demonstrate the efficiency and accuracy of the proposed technique. An experimental example of a nonlinear rotary flexible joint is presented to further validate the proposed method.


Dr. Jian-Qiao Sun earned a BS degree in Solid Mechanics from Huazhong University of Science and Technology in Wuhan, China in 1982, a MS and a PhD in Mechanical Engineering from University of California at Berkeley in 1984 and 1988.  He worked for Lord Corporation at their Corporate R&D Center in Cary, North Carolina.  In 1994, Dr. Sun joined the faculty in the department of Mechanical Engineering at the University of Delaware as an Assistant Professor, was promoted to Associate Professor in 1998 and to Professor in 2003. He joined University of California at Merced in 2007, and is currently a professor and chair of the Department of Mechanical Engineering in School of Engineering.  Besides many other editorial experiences, he is the Editor-in-Chief of International Journal of Dynamics and Control published by Springer.

Juan J. Nieto
University of Santiago de Compostela, Spain

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.


Prof. Knuth is an Associate Professor in the Department of Physics at the University at Albany (SUNY), and is the Editor-in-Chief of the journal Entropy (MDPI). He is a former NASA research scientist having worked for four years at NASA Ames Research Center in the Intelligent Systems Division designing artificial intelligence algorithms for astrophysical data analysis. He has over 20 years of experience in applying Bayesian and maximum entropy methods to the design of machine learning algorithms for data analysis applied to the physical sciences. His current research interests include the foundations of physics, quantum information, inference and inquiry, autonomous robotics, and the search for and characterization of extrasolar planets. He has published over 90 peer-reviewed publications and has been invited to give over 80 presentations in 14 countries.

Luis Vázquez
Complutense University at Madrid

About the simulations of  Maxwell equations

Abstract: A panoramic view of certain large and massive simulations related to the propagation of the electromagnetic waves carried out by our team at
Universidad Complutense of Madrid (Spain).

•The Solar Radiation and the Atmospheric Dust. Martian Planetary
Boundary Layer. Fractional Calculus Modeling
• Main Radiation Transportation Codes
• Electromagnetic Waves and Fractals
• Metamaterials.


Professor Luis Vázquez is  currently Professor Emeritus of Applied Mathematics at Departamento de Analisis Matemático y Matemática Aplicada, Facultad de Informática, UCM. He was Professor of Applied Mathematics (PROPIO program of MEC) 1/2/1196-31/8/2019, at Facultad de Informática, UCM, Assistant Professor, Universidad de Zaragoza, 1/10/1972-30/09/1975,  Assistant Professor and Temporary Associate Professor, Facultad de Ciencias Físicas, UCM 1/10/1977-19/6/1978,  Tenured Associate Professor-University Professor, Facultad de Ciencias Físicas, UCM 20/6/1978-31/1/1986.

– Founding member of the Centre of Astrobiology (INTA-CSIC) associated to the NASA Astrobiology Institute (1999), where I founded and managed the Advance Computer Laboratory.
– Coordinator for the Calibration of Ultravioleta (UV) Sensors of Module Beagle 2 coupled to Mars Express Mission from the European Space Agency (ESA, 2002-2003).
– Principal Investigator for the Rover Environmental Monitoring Station (REMS) in the rover Curiosity of Mars Science Laboratory (MSL) NASA Mission to Mars. I was the first Spanish who played the role as a Principal Investigator associated with an instrument sent to Mars as well as with the NASA. Specially, I was in charge of the definition and design of the ultraviolet radiation along with the temperature of the soil (GTS: Ground Temperature Sensor).
– Team Leader of the Research Group from the Universidad Complutense of Madrid: “Modelling and Simulation on Fractional Calculus and the Atmosphere of Mars” (910711). From 2005.
– Spanish Scientific Director of Mars MetNet Mision Precursor of Russia, Finland and Spain (2007-2014);
– Spanish Scientific Director of the Instrument SIS-DREAMS for the Mission to Mars from ESA: EXOMARS 2016 (2013-2016).
– Co-researcher (from 2014) in the Russian Instrument ACS (Atmospheric Chemistry Suite) of the Orbital Module Trace Gas Orbiter for the Mission to Mars from ESA: EXOMARS 2016.


Marat Akhmet
Middle East Technical University

Domain structured  dynamics and chaos

Abstract: A new modeling tool, the abstract similarity dynamics, has been invented in our research as a simple way to understand mathematical chaos as well as to open a gate to a deep perception of the world in motion.  The product of the application of the tool is called the domain structured dynamics. Accordingly, a labeling for state space points is suggested and the result is called the abstract similarity set. The abstract similarity map is another novelty, coupled with the labeling to complete the toolkit for the research. We strongly believe that the domain structuring and the abstract similarity map are effective instruments to investigate many problems of modern dynamics, chaos first of all.  

     The abstract similarity dynamics follows the Pythagorean doctrine, considering finite number of indices for the labeling.   A result of the present research activity is the conviction that the labeling is more picturesque than any equations and methods considered for the same goals. Thus, the structuring will help researchers to understand chaos more easily and the power of domain structured dynamics is guaranteed by the theoretical depth of our research. Practically, it is determined by the existing and potential algorithms of labeling. The most familiar one is the Fatou–Julia iteration, which is applied for self-similarity structures, fractals, and chaos in discrete and differential equations and neural networks in our study.

     The abstract similarity dynamics can be exemplified by the symbolic dynamics, but most formally, as it relates to symbolic dynamics as integration to summation, in calculus. That is, the symbolic dynamics is a special case of the abstract similarity dynamics, when the labeling for the set of symbol sequences is maximally simple.  

     We are confident that the new method can be utilized as a universal one for the study of the most sophisticated dynamics as well as for chaos initiation in many applications. The immediate power of the approach can be seen for fractals as domains of chaos, revisited famous deterministic and stochastic models, new types of differential equations and neural networks.


  1. Akhmet, Domain structured dynamics: unpredictability, chaos, randomness, fractals,  differential equations and  neural networks,  IOP Publishing,  2021.
  2. Akhmet and E. Alejaily, Abstract similarity, fractals and chaos, Discrete and Continuous Dynamical  Systems -Series B,  Open  Access, 26(5),  2021, 2479-2497.
  3. Akhmet and E. Alejaily, Abstract fractals,  Discontinuity,  Nonlinearity,  and Complexity,  10(1), 2021, 135-142.
  4. Akhmet and E. Alejaily, Domain structured chaos in a Hopfield neural network, International Journal of Bifurcation and Chaos,  29(1430), 2019,  1950205.



Dr.  Marat Akhmet is a professor of mathematics at Middle East Technical University (Ankara, Turkey) known for his research on the chaos and bifurcation theory in differential equations and hybrid systems with applications in physics, neural networks, biology, medicine and economics. Born in Kazakhstan, he studied at Aktobe State University. He received his doctorate in 1984 at Kiev University . He has been awarded a Science Prize of TUBITAK (Turkey, 2015), for best achievments in scientific research.

     Akhmet is an author of eight  books: “Principles of Discontinuous Dynamical Systems”, Springer, 2010, “Nonlinear Hybrid Continuous Discrete-Time Models”, Atlantis Press (Springer), 2011, “Neural networks with Discontinuous Impact Activations,” Springer, 2014,  “Replication of Chaos in Neural Networks, Economics and Physics”, Springer&HEP, 2015, “Bifurcation in autonomous and nonautonomous differential equations with discontinuities”, Springer,  2017, “Dynamics with chaos and fractals”,  Springer,  2020, “Almost periodicity,  chaos and asymptotic equivalence”,  Springer,  2020, and  “Domain structured dynamics”,  IOP Publishing,  2021.  

     Akhmet  has solved the Second Peskin conjecture for Integrate-and-fire biological oscillators, has introduced and developed theory of differential equations with piecewise constant argument of generalized type, many aspects of discontinuous dynamical systems. The last decade his main subject of research is input-output analysis of chaos and irregular behavior of hybrid neural networks. The concept of the Poisson  stability  has been  specified such  that  the unpredictability  implies chaos.  Finally,  the method  of domain  structured dynamics has been invented and   developed,  which  follows  the Pythagorean  doctrine, with potential  to become universal in  future.   

Marty Golubitsky
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.

Nikolay V. Kuznetzov
Saint-Petersburg State University, Russia

The theory of  hidden oscillations and stability of dynamical systems

Abstract: The development of the theory of global stability, the theory of bifurcations, the theory of chaos, and new computing technologies made it possible to take a fresh look at a number of well-known theoretical and practical problems in the analysis of multidimensional dynamical systems and led to the emergence of the theory of hidden oscillations which represents the genesis of the modern era of Andronov’s theory of oscillations. The theory of hidden oscillations is based on a new classification of attractors as self-excited or hidden. While trivial attractors (equilibrium points) can be easily found analytically or numerically, the search of periodic or chaotic attractors may turn out to be a challenging problem (see, e.g. famous 16th Hilbert problem on the number and disposition of limit periodic oscillations in two-dimensional polynomial systems which is still unsolved). Self-excited attractors can be easily discovered when observing numerically the dynamics with initial data from the vicinity of the equilibria. While hidden attractors have the basins of attraction, which are not connected with equilibria, and their search requires the development of special analytical and numerical methods.

For various applications, the transition of system’s state to a hidden attractor, caused by external disturbances, may results in undesirable behavior and is often the cause of accidents and catastrophes. For various engineering applications the importance of identifying hidden attractors is related with the classical problems of determining the boundaries of global stability in the space of parameters and in the phase space. Outer estimations of the global stability boundary in the space of parameters and the birth of self-exited oscillations in the phase space can be obtained by the linearization around equilibria and the analysis of local bifurcations and are related with various well-known conjectures on global stability by the first approximation (see, e.g. Andronov’s proof of the conjecture on the Watt regulator global stability by the first approximation). Inner estimations of the global stability boundary can be obtained by classical sufficient criteria of global stability. In the gap between outer and inner estimations there is exact boundary of global stability which study requires the analysis of nonlocal bifurcations and hidden oscillations.

This lecture is devoted to well-known theoretical and practical problems in which hidden attractors (their absence or presence and disposition) play an important role.



  1. Wang X., Kuznetsov N.V., Chen G., Chaotic Systems with Multistability and Hidden Attractors, Springer, 2021
  1. Kuznetsov N.V., Theory of hidden oscillations and stability of control systems, Journal of Computer and Systems Sciences International, 59(5), 2020, 647-668.
  2. Kuznetsov N.V., Lobachev M.Y., Yuldashev M.V., Yuldashev R.V., Kudryashova E.V., Kuznetsova O.A., Rosenwasser E.N., Abramovich S.M., The birth of the global stability theory and the theory of hidden oscillations, of European Control Conf. (ECC-2020), St. Petersburg, 2020, 769–774.
  3. Dudkowski D., Jafari S., Kapitaniak T., Kuznetsov N.V., Leonov G.A., Prasad A., Hidden attractors in dynamical systems, Physics Reports, 637, 2016, 1-50
  4. Kuznetsov N.V., Hidden attractors in fundamental problems and engineering models. A short survey, Lecture Notes in Electrical Engineering, vol. 371, 2016, pp. 13-25
  5. Leonov G.A., Kuznetsov N.V., Hidden attractors in dynamical systems. From hidden oscillations in Hilbert-Kolmogorov, Aizerman, and Kalman problems to hidden chaotic attractor in Chua circuits, International Journal of Bifurcation and Chaos in Applied Sciences and Engineering, 23(1), 2013, art. no. 1330002


Nikolay V. Kuznetsov graduated from the St. Petersburg University, Russia in 2001. In 2004 he received the Candidate of Science degree and in 2016 the Doctor of Science degree from St. Petersburg University, where he is currently a Professor and the Head of the Department of Applied Cybernetics. From 2018, the research group chaired by Prof. Kuznetsov has the status of the Leading Scientific School (Center of Excellence) of Russia in the field of mathematics and mechanics. In 2020 he was named Professor of the Year in the field of mathematics and physics in Russia. In 2008, he defended his Ph.D. degree at the University of Jyväskylä (Finland), where now he is a Visiting Professor and co-chair of the Finnish-Russian Educational & Research program organized together with St. Petersburg University. In 2020 he was elected as foreign member of the Finnish Academy of Science and Letters. Since 2018, he is the Head of the Laboratory of information and control systems at the Institute for Problems in Mechanical Engineering of the Russian Academy of Science. Prof. Kuznetsov’s research interests are in nonlinear dynamics and applied mathematics. In his works, a combination of rigorous analytical and reliable numerical methods allowed for both the advancement in solving previously known fundamental open problems as well as the development of modern engineering technologies.

Ruy Ribeiro
Los Alamos National Laboratory

Viral Dynamics: mathematical modeling to study virus biology

Abstract: Modeling of the non-linear dynamics of virus in vivo, for example during primary infection or following drug treatment, has been used in the last two decades to study the biology of diverse virus. I will discuss, with examples from HIV and hepatitis C virus (HCV) infection, the principles and approach of this methodology. I will also present recent examples of insights into the biology of these viruses and SARS-CoV-2 gained with viral dynamics


Ruy M. Ribeiro got his Ph.D. in Mathematical Biology at the University of Oxford, UK. He then joined Los Alamos National Laboratory (LANL) in 2000, as a Postdoctoral Researcher, later becoming a staff scientist working on viral and immune system dynamics. His main research interests are the pathogenesis of infections, and the use of quantitative modeling tools to gain insight into viral and immune system dynamics. His work has always entailed close collaborations with experimental researchers to develop proper statistical and dynamic models to analyze experimental data. His modeling work spans multiple scales from the intracellular (eg. a model of the molecular details of HCV infection) to the epidemiological (including HIV and influenza epidemics). He was Professor of Statistics at the Medical School of the University of Lisbon, while on leave from LANL, between 2017 and 2020. Ruy Ribeiro has over 140 peer-reviewed papers in this area, and he is/was the PI of several research projects funded by the National Institutes of Health, the European Union, and the Department of Energy.