Plenary talks

Eckehard Schöll

Suzanne Lenhart

Franco Blanchini

Carsten Schneider

Piotr Oprocha 

Azmy S. Ackleh

Gian Italo Bischi

Dorothée Normand-Cyrot

Silviu-Iulian Niculescu 

Hinke Osinga

Erik I. Verriest

JDEA prize talk

Abstract

Chimera states are an intriguing example of partial synchronization patterns emerging in nonlocally coupled networks of identical chaotic time-discrete maps or time-continuous oscillators. They consist of spatially coexisting domains of coherent (synchronized) and incoherent (desynchronized) dynamics. We show that a plethora of partial synchronization scenarios including chimeras arise for various network topologies like one-dimensional ring networks, quasi-fractal connectivities, two-dimensional lattices, or multi-layer structures, and different dynamical maps. In particular, we study the logistic map, the Hénon map and the Lozi map. By analyzing the dependence of the spatiotemporal dynamics on the range and strength of coupling, we uncover dynamical bifurcation scenarios for the transition from coherence to complete incoherence via chimera states, and review numerical and analytial approaches [1-5].
[1] Omelchenko, I., Maistrenko, Y., Hövel, P. and Schöll, E., Loss of coherence in dynamical networks: spatial chaos and chimera states, Phys. Rev. Lett. 106, 234102 (2011).
[2] Hagerstrom, A. M., Murphy, T. E. , Roy, R., Hövel, P., Omelchenko, I. and Schöll, E., Experimental Observation of Chimeras in Coupled-Map Lattices, Nature Phys. 8, 658 (2012).
[3] Semenova, N., Zakharova, A., Schöll, E. and Anishchenko, V. S., Does hyperbolicity impede emergence of chimera states in networks of nonlocally coupled chaotic oscillators?, Europhys. Lett. 112, 40002 (2015).
[4] Winkler, M., Sawicki, J., Omelchenko, I., Zakharova, A., Anishchenko, V. and Schöll, E., Relay synchronization in multiplex networks of discrete maps, Europhys. Lett 126, 50004 (2019).
[5] Shepelev, I. A., Muni, S. S., Schöll, E. and Strelkova, G. I., Repulsive inter-layer coupling induces anti-phase synchronization, Chaos 31, 063116 (2021).

Biography

Eckehard Schöll is a Professor of Theoretical Physics at TU Berlin, a Guest Scientist at the Potsdam Institute for Climate Impact Research, and a Principal Investigator of the Bernstein Center for Computational Neuroscience Berlin. He studied physics at the University of Tübingen (Germany), and holds PhD degrees in mathematics from the University of Southampton (UK, 1978) and in physics from RWTH Aachen (Germany, 1981), and an Honorary Doctorate from Saratov State University (Russia, 2017). He is an expert in the field of nonlinear dynamical systems and head of the group Nonlinear Dynamics and Control. His work pertains to research in the fields of mathematics and physics, particularly semiconductor physics, laser physics, neurodynamics, complex systems and networks, and bifurcation theory. His latest research is also related to topics in biology and the social sciences, e.g. simulation of the dynamics in socioeconomic, physiological, or neuronal networks and power grids. He is one of the forerunners into the research of chimera states.

Abstract

Discrete models may have hybrid features due to a variety of mechanisms.  We will present two examples of hybrid models, one with some mechanisms between time steps and the other with a shorter time scale embedded in the main time scale processes. In our first example, we present mechanistic models featuring within‐season harvest timing and level. Between discrete population census times, there are continuous density-dependent mortality rates. We explore optimal control of the harvest level and timing of these population models. Maximizing the yield while minimizing the costs of management can lead to unexpected oscillation patterns in the population. In our second example, we find the relationship between air temperature and emergence success of hatchlings across multiple nesting seasons to better understand the potential impact of climate change on Loggerhead sea turtle populations.  We want to investigate the effect of changing hatchling emergence success on the juvenile and adult populations. The results of a statistical model of emergence success feed into the dynamics during the nesting seasons of the eggs and hatchlings in a submodel on daily time scale. The submodel is connected to an age-structure model with two juvenile and one adult classes on a yearly time scale.  We illustrate the effect of temperature changes across these life stages.

Biography

Suzanne Lenhart is a Chancellor's professor in the Department of Mathematics at the University of Tennessee, Knoxville. She was a part-time research staff member at Oak Ridge National Laboratory for 22 years. She is a recognized expert in optimal control and ordinary and partial differential equations, with modeling applications to populations, natural resources, invasive species, and diseases. She has authored many journal articles, as well as two texts, Optimal Control applied to Biological Models  and Mathematics for the Life Sciences.

She was the President of the Association for Women in Mathematics in 2001-2003. She received fellow awards from SIAM, AMS, AWM, and AAAS. She was the Associate Director for Education and Outreach of the National Institute for Mathematical and Biological Synthesis for the last 12 years. Lenhart has been the director of Research Experiences for Undergraduates summer programs on her campus for 27 years.

Abstract

Systems and control theory has developed many techniques borrowing tools from different branches of mathematics. Interestingly, many of the techniques conceived and routinely used to solve control problems can be quite successfully adapted to solve new relevant problems, both practical and curiosity-driven, in other fields.
In this talk we discuss how the mathematical analysis of systems can be very effective in explaining how mechanisms work, why they work in a certain way and to which extent they perform their task properly even in the presence of perturbations and disturbances.
The first part of the talk briefly introduces some preliminary motivating examples of mechanisms, borrowed from other disciplines alien to control theory, to show how a control approach can be very powerful to understand fundamental principles.
The second part introduces the definitions of structural versus robust properties, discussing paradigmatic case studies from the literature. These include a discussion about robust stability/instability analysis, presented in an inverse form: "We know this is stable, but why is it so incredibly stable?". Other fundamental concepts such as adaptation, oscillations, bistability and graph loop analysis are considered.
The third part discusses application examples from biology and biochemistry, to showcase the potential impact that the mathematical approach of control and system theory, suitably revised, can have in these disciplines and how interdisciplinary research can bring fresh ideas to theorists.

Biography

Franco Blanchini was born on 29 December 1959, in Legnano (Italy). He is the Director of the Laboratory of System Dynamics at the University of Udine. He has been involved in the organization of several international events: in particular, he was Program Vice-Chairman of the conference Joint CDC-ECC 2005, Seville, Spain; Program Vice-Chairman of the Conference CDC 2008, Cancun, Mexico; Program Chairman of the Conference ROCOND, Aalborg, Denmark, June 2012 and Program Vice-Chairman of the Conference CDC 2013, Florence, Italy. He is co-author of the book "Set theoretic methods in control", Birkhauser. He received the 2001 ASME Oil & Gas Application Committee Best Paper Award as a co-author of the article "Experimental evaluation of a High-Gain Control for Compressor Surge Instability", the 2002 IFAC prize Survey Paper Award as the author of the article "Set Invariance in Control - a survey", Automatica, November 1999, for which he also received the High Impact Paper Award in 2017, and the 2017 NAHS Best Paper Award as a co-author of the article "A switched system approach to dynamic race modelling", Nonlinear Analysis: Hybrid Systems, 2016. He has been plenary speaker at the IFAC Joint Conference, Grenoble, February 2013, plenary speaker at the 32nd Benelux Meeting on Systems and Control, and semi-plenary speaker at the IEEE CDC 2020, Jeju, Japan. He has been an Associate Editor for Automatica and for IEEE Transactions on Automatic Control.  He has been a Senior Editor for IEEE Control Systems Letters.

Abstract

Inspired by Karr's summation algorithm (1981), an advanced summation framework has been developed in the last 20 years that can deal with indefinite and definite multi-sum expressions. The underlying backbone is an algorithmic difference ring theory which enables one to rephrase expressions in terms of indefinite nested sums and products completely automatically to canonical form representations. As a by-product, the computed expressions are built by sums and products that are algebraically independent among each other. Together with general and highly efficient difference ring algorithms for recurrence finding (based on Zeilberger's creative telescoping paradigm) and recurrence solving, one can simplify huge expressions of multi-sums (and related multi-integrals) to certain classes of special functions defined by iterated sums (and integrals).  In a nutshell, the developed algorithms for symbolic summation and special functions provide a flexible toolbox that can tackle challenging problems coming, e.g., from combinatorics, special functions, number theory, statistics, or particle physics (a long-term collaboration with DESY, the Deutsches Elektronen-Synchrotron). In this talk the underlying difference ring theory and the available summation tools in this setting will be illustrated by concrete examples that are hard to solve or that could not be solved by other methods so far.

Biography

After his computer science studies at the Friedrich-Alexander-University Erlangen-Nürnberg, Carsten Schneider could intensify his scientific interests in the field of computer algebra at the internationally well recognized Research Institute for Symbolic Computation (RISC) of the Johannes Kepler University Linz. There he completed his PhD in 2001, obtained the Habilitation in the field of mathematics in 2008, and serves recently as full processor and vice-director of RISC.

His main research area is symbolic computation: he explores advanced mathematical theories in algebra, in particular in formal rings equipped with ring automorphisms. In this general setting of difference rings, he puts special emphasis on the design of non-trivial algorithms in symbolic summation and finding solutions of linear recurrences. Besides the development of new algorithmic theories, he devotes energy in the design and implementation of user friendly computer algebra packages. Notably, his research has been motivated strongly by concrete and challenging problems, e.g., in number theory (harmonic number identities related to zeta-values and generalizations of them), numerics (Pade approximations, finite element methods), and in particular in combinatorics. In addition, he started 15 years ago an interdisciplinary project with the theory group of the Deutsches Elektronen-Synchrotron (DESY, Zeuthen, Prof. Dr. Johannes Blümlein and Dr. Peter Marquard). In this intensive and fruitful cooperation, they are developing new algorithms for quantum field theories and elementary particle physics. These ongoing large-scale calculations of massive 3--loop Feynman integrals (leading so far to about 80 joint publications) will be used, e.g., for the precision measurements of the Hadron Electron Ring Accelerator (HERA) of the Deutsches Elektronen Synchrotron and of the Large Hadron Collider (LHC) of CERN.

Abstract

In this talk I will discuss selected properties of generic continuous maps of the interval and circle which preserve the Lebesgue measure. I will focus on a few natural properties such as entropy, the structure of periodic points, mixing properties, shadowing properties, etc. I will also highlight properties of generic maps compared to other possible dynamical behaviors within maps preserving Lebesgue measure.

In the second part of the talk, I will present the consequences of obtained results for interval maps (not necessarily preserving Lebesgue measure) and two-dimensional dynamics. In this context, I will consider how a parametrized family of maps induces a continuously varying family of one-dimensional attractors in the unit disc. As a possible tool for distinguishing the obtained embeddings, I will refer to the prime ends rotation number on the circle of prime ends associated with these attractors.
The third part discusses application examples from biology and biochemistry, to showcase the potential impact that the mathematical approach of control and system theory, suitably revised, can have in these disciplines and how interdisciplinary research can bring fresh ideas to theorists.

Biography

Piotr Oprocha is full Professor of Mathematics and Dean at Faculty of Applied Mathematics at AGH University of Science and Technology, Kraków, Poland. He received Ph.D. from Jagiellonian University, Kraków, Poland in 2005. In 2018 he was awarded the title of professor of mathematics by the President of Poland.
From 2002 he is employed at AGH University of Science and Technology, where he was promoted to full professor in 2018. From 2012 to 2020 he was Deputy Dean for Science and became Dean at the Faculty of Applied Mathematics in 2020.
He is an expert in the field of low dimensional discrete dynamical systems with main emphasis on topological and symbolic dynamics. He is authors of numerous papers on topological entropy, notions and mixing, qualitative properties of dynamical systems and chaos.

Abstract

We develop a discrete-time model that describes tick-host population dynamics and incorporates the developmental stages for an individual tick. We study the global dynamics of this system and show that if the inherent net reproductive number is greater than one, then the unique interior equilibrium is globally asymptotically stable. We extend the model to a tick-host-pathogen model to describe the spread of a disease in a hard-bodied tick species. We apply the model to two pathogens and numerically study properties of the invasion and establishment of a disease. In particular, we consider the basic reproduction number, which determines whether a disease can invade the tick-host system, as well as disease prevalence and time to establishment in the case of successful disease invasion.  Using Monte Carlo simulations, we calculate the means of each of these disease metrics and their elasticities with respect to various model parameters. We then extend the population model to include spatial movement of ticks and their hosts and analyze the dynamics of the model under a nonlinear fecundity term that exhibits an Allee effect. We show that the system has rich dynamics including monostable and bistable dynamics. We incorporate demographic stochasticity into the model and use numerical simulations to understand spatial invasion patterns of ticks as they relate to different dispersal mechanisms.

Biography

Azmy S. Ackleh is the R.P. Authement Eminent Scholar and Endowed Chair in Computational Mathematics and the Dean of the College of Sciences at the University of Louisiana at Lafayette. He received his Ph.D. from the University of Tennessee at Knoxville in 1993 and then joined the Center for Research in Scientific Computation at North Carolina State University as a postdoctoral fellow. In 1995 he joined the Department of Mathematics at the University of Louisiana as an Assistant Professor. In 2000 he became an Associate Professor of Mathematics and in 2003 he became a Full Professor of Mathematics in that Department.  

Ackleh’s main research interest is in the area of Mathematical Biology. He co-authored over 150 peer-reviewed articles and a book “Classical and Modern Numerical Analysis: Theory, Methods and Practice”. He is particularly interested in the development of continuous and discrete models in population ecology and epidemiology and in using theoretical and numerical tools to understand the short-term and long-term behavior of solutions to these models. Particular applications that he has worked on include selection-mutation models, amphibian dynamics and associated diseases, and the impact of toxicants on aquatic animals and the role of evolution to resist such toxicants on the system dynamics.

Abstract

Discrete-time dynamical systems naturally arise in economic and social modelling, because changes in the state of a system occur as a consequence of decisions (event-driven time). Given a characteristic time interval, taken as a unit of time advancement, then the state at the next time period is obtained by the application of a map, i.e. a point transformation defined in a n-dimensional state space into itself.

Indeed, in social sciences rational agents are assumed to choose their actions through an optimal decision process, with complete information about the environment and the other agents’ choices. However, humans are sometimes not so rational nor informed, and they behave following adaptive methods, such as learning-by-doing or trial-and-error practices. This leads to replace one-shot optimal decisions with repeated adaptive decisions, in other words a dynamic process that may or may not converge to a rational equilibrium. Moreover, several attracting sets may coexist, so that the step-by-step adaptive process may act as a selection device and a global study of the basins of attraction can gives information about the path dependence, i.e. how the long-run time evolution depends on historical accidents (represented by exogenous shifts of initial conditions). For example, in repeated oligopoly games strategic choices may never settle to a Nash equilibrium, and continue to move around it, following some periodic or chaotic time patterns, or they may even irreversibly depart from it. Sometimes different decision strategies may be adopted by heterogeneous interacting agents, leading to different time adjustment processes characterized by different performances. In these cases evolutionary games can be used to model populations of players subdivided into fractions adopting different strategies, and considering endogenous switching process driven by payoff gradients (such as replicator dynamics or imitate the better mechanisms). Evolutionary game theory, initially developed in the context of biological systems, considers the behavior of large populations of agents who repeatedly engage in strategic interactions. In the biological interpretation, a population consists of animals which are genetically programmed to use some strategy that is inherited by its offspring, whereas in the economic interpretation the agents are assumed to play the game many times and consciously switch strategies driven by imitation of more successful opponents.

The iterated maps that model such time evolutions in discrete time are generally nonlinear and are often noninvertible. Hence their folding and unfolding properties characterize the attractors and their basins respectively

Biography

Gian-Italo Bischi. Full professor of “Mathematics for economic and social sciences” at the department DESP (Department of Economics, Society, Politics) of the University of Urbino (Italy) is author of several articles and books on nonlinear dynamic models and their applications to the description of complex systems, ranging from physics and biology up to economics and social sciences. He mainly uses methods from the qualitative theory of nonlinear dynamical systems, also in connection with game theory and in particular evolutionary games. He also deals with the popularisation and communication of mathematical ideass, with a particular focus on connections between mathematics and other cultural fields, like literature and art.

URL. http://www.mdef.it/gian-italo-bischi/

Abstract

Biography

Abstract

Biography

Abstract

Conjugacy describes how two maps may be related via a change of coordinate. In [1] we show that the dynamics induced by a simple geometric construction on elliptic curves (taking the tangents to the curve at a point and mapping to the other intersection of the tangent to the curve or the point at infinity) creates a map topologically conjugate to the chaotic map x -->2-x^2 on [-2; 2]. Moreover, despite the fact that the numerically computed maps obtained in this way can look very different depending on the parameters of the elliptic curve, they are in fact C1-conjugate. Differentiable conjugacies preserve the stability multipliers of periodic orbits, so in chaotic maps with infinitely many periodic orbits, the existence of differentiable conjugacies is rare.
In the talk I will discuss this result (awarded the best paper for JDEA in 2021) and also address questions about topological versus differentiable conjugacy for normal forms of elementary bifurcations (recent work with David J.W. Simpson, Massey, New Zealand).

P. Glendinning and S. Glendinning (2021) Smooth conjugacy of difference equations derived from elliptic curves, J. Di. Equ. & Appl.
doi.org/10.1080/10236198.2021.1984441

Biography

Paul Glendinning is Professor of Applied Mathematics at the University of Manchester. He works on bifurcation theory and piecewise smooth dynamics. He was awarded a PhD from the University of Cambridge in 1985, and after post-docs in Warwick and Cambridge he was a lecturer in Cambridge and then moved to chairs at Queen Mary, University of London, and Manchester (UMIST and University of Manchester). He was the founding Head of School in Mathematics during the merger of UMIST and Manchester (2003-2008), and has been Scientific Director of ICMS, Edinburgh (2016-2021). He is currently President of the IMA, one of the UK Learned Societies for mathematics. He was elected a Fellow of the Royal Society of Edinburgh in 2021.

Photograph by Sasha Glendinning

Abstract

To better grasp the heterogeneity of the temporal phenomena in systems' dynamics, knowledge of “past” may appear as essential to derive appropriate models, and there exists a wide variety of processes in nature with such characteristics. In these cases, the use of delays in the representation of such phenomena may help to better understand the underlying mechanisms or of the interactions/coupling with other (eventually spatial) phenomena. In this context, a particular case is represented by the interconnection of dynamical systems. It is well-known that the interconnection of two or more dynamical systems leads to an increasing complexity of the behavior of the global system due to the effects induced by the emerging dynamics (in the presence or not of feedback loops) in strong interactions (sensing, communication) with environment changes. One of the major problems appearing in such interconnection schemes is related to the propagation, transport, and communication delays acting “through” and/or “inside” the interconnections. Such systems are governed by a particular type of differential equations, namely delay-differential equations.

The purpose of this talk is to briefly present some “user-friendly” (frequency-domain) methods and techniques for the analysis and control of the dynamical systems in the presence of constant (pointwise) delays by emphasizing how the delay, seen as a parameter, can affect the exponential stability of the system. As a by-product of such an analysis, the use of the delay as a control parameter will open up interesting perspectives to exploit further. The presentation is as simple as possible, emphasizing the main intuitive ideas to develop theoretical results, and their potential use in practical applications. Various illustrative examples complete the presentation (joint work with Keqin GU, Southern Illinois University at Edwardsville, USA).

Biography

Silviu-Iulian NICULESCU received the B.S. degree from the Polytechnical Institute of Bucharest, Romania, the M.Sc., and Ph.D. degrees from the Institut National Polytechnique de Grenoble, France, and the French Habilitation (HDR) from Université de Technologie de Compiègne, all in Automatic Control, in 1992, 1993, 1996, and 2003, respectively. He is currently Research Director at CNRS (French National Center for Scientific Research), L2S (Laboratory of Signals and Systems), a joint research unit of CNRS with CentraleSupélec and Université Paris-Saclay located at Gif-sur-Yvette.

Dr. Niculescu is a member of the Inria team “DISCO” and he was the head of L2S for a decade (2010-2019). He is author/coauthor of 11 books and of more than 600 scientific papers. His research interests include delay systems, robust control, operator theory, and numerical methods in optimization, and their applications to the design of engineering systems. Since 2017, he is the Chair of the IFAC TC “Linear Control Systems” and he served as Associate Editor for several journals in Control area, including the IEEE Transactions on Automatic Control (2003-2005). IEEE Fellow since 2018, Doctor Honoris Causa of University of Craiova (Romania) since 2016, Founding Editor and Editor-in-Chief of the Springer Nature Series “Advances in delays and dynamics” since its creation in 2012, Dr. Niculescu was awarded the CNRS Silver and Bronze Medals for scientific research and the Ph.D. Thesis Award from Grenoble INP (France) in 2011, 2001 and 1996, respectively. For further information, please visit https://cv.archives-ouvertes.fr/silviu-iulian-niculescu

Abstract

For LTI (ordinary) difference equations, the Jury (and mapped Routh-Hurwitz) tests provide necessary and sufficient conditions for stability. Our first aim is to show some sufficient conditions of much lower complexity for stability of a subclass of “sparse” systems, and show that this is can be accomplished by a Riccati-equation type condition. These criteria can also be expressed in terms of function-theoretic concepts. We then extend these results to time-variant (delay) difference equations, where problems with wellposedness and causality may occur. Such analyses are instrumental for stability analysis of delay equations and as a singular limit for delay-differential equations. Much of this is joint work with A. Ivanov. The second part of the talk deals with difference equations defined over and ℝ rather than ℤ. In particular, the cases with time-varying and state-dependent delay present new problems. First, an appropriate state space for such systems is sought, as this is a prerequisite for precise notions of what is meant by a trajectory and its stability. Then we discuss the infinitesimal generator. This leads then to implicit iterations of the form x(t) = f(x(t−1), x(t−τ(x(t))), modeling certain systems with state-dependent delay, τ(x). While here t ∈ ℝ, we show that a discrete event-structure (i.e, space-time structure) is appropriate for its description, and certain iterated functional equations are instrumental for characterizing solutions. Finally, for nonhomogeneous linear difference equations, i.e., models of discrete input-output systems, we present in part 3 some intricate problems regarding loss of causality and its consequences if the delay is switched. Fixes, known as lossless causalization and forgetful causalization are discussed.

Biography

Erik I. Verriest is the Director of the Mathematical System Theory Laboratory (MAST Lab) at the Georgia Institute of Technology. He was with the Control Systems Laboratory and the Hybrid Computation Centre, Ghent, Belgium in 1973-1974, obtained the Ph.D. degrees from Stanford University and joined the faculty of Electrical and Computer Engineering at the Georgia Institute of Technology in 1980. His present interests are in mathematical system theory. He contributed to the theory of periodic and hybrid systems, delay-differential systems, model reduction for nonlinear systems, control with communication constraints, locomotion and optimal control. He served on several conference IPC’s and is a member of the IFAC Committee on Linear Systems, a Fellow of the IEEE (2012), a member of the Royal Flemish Academy of Belgium for Science and the Arts (elected 2012), and a Distinguished Professor of ECE, Georgia Tech (2014). He was a plenary speaker at the 2nd IFAC Workshop on Linear Time Delay Systems in Grenoble (2000) and the 13-th IFAC Workshop on Time Delay Systems in Istanbul (2016). Presently he holds the Giovanni Prodi Chair at the Mathematics Institute of the Julius Maximilians Universität Würzburg, Germany.

Abstract

Stability assessment of large power systems is usually performed using time domain simulation. Numerical schemes have been developed in the last decades, based on hybrid DAE solvers (with switches) using a predictor-corrector approach (typically IDA from sundials: IDA | Computing (llnl.gov)). They are quite efficient in the deterministic case. But in fact, there are always short-term stochastic effects in large power systems that are neglected in this type of stability assessment, Unfortunately, the deterministic approach does not verify that these stochastic effects do not excite instabilities and our classical predictor-corrector approach seems incompatible with noise addition. In the presentation, we will present an example and a formulation of the problem.

Biography

Patrick Panciatici is a graduate of Supélec. He joined EDF R&D in 1985 and then RTE in 2003 when he participated in the creation of an internal R&D department at RTE. He has more than 35 years of experience in power systems: modeling, simulation, control and optimization. Currently, as a scientific advisor, he inspires and coordinates RTE's long-term research on the "system" dimension. He interacts with a large network of international experts and with academic teams worldwide on these topics. He is a member of CIGRE, Fellow of IEEE, RTE representative in PSERC and Bits & Watts.