Plenary Talks

René Lozi

Laboratory Jean-Alexandre Dieudonné, University Côte d’azur, Nice, France

Do chaotic dynamical systems contribute to the advancement of science or are they just a mathematical curiosity?

Abstract: Since the seminal work of Henri Poincaré on the three-body problem, and more recent research dating back to the second half of the 20th century on chaotic dynamical systems, many applications have emerged in different domains (biology, economics, electronic, cryptography, physics, etc.).

The “butterfly effect” reveled by Edward Lorenz in 1963 and the word “chaos” coined by James A. Yorke in 1975 have brought global awareness of these concepts often not actually understood by the public. However, it is only at the beginning of 90’ that the applications of chaotic properties of dynamical systems were introduced with the pioneering idea of synchronization of two chaotic attractors of Louis M. Pecora and Thomas L. Carroll.

We try to describe the evolution of the last 50 years on the subject and to find out whether applications are useful for the advancement of science, and what might be the future trends for this domain of mathematics.

Bio: Rene LOZI is emeritus Professor at University Cote d’Azur, Dieudonné Center of Mathematics, France. He completed a PhD in 1975 and the French State Thesis (on chaotic dynamical systems) under the supervision of Prof. Rene Thom (Fields medallist) in 1983.

In 1991, he became Full Professor at University of Nice and IUFM (Institute for teacher trainees). He has served as Director of this institute (2001-2006) and as Vice-Chairman of the French Board of Directors of IUFM (2004- 2006). He is a member of several editorial boards of international journals. In 1977, he discovered a particular mapping of the plane having a strange attractor (now, commonly known as “Lozi map”). Nowadays, his research areas include complexity and emergence theory, dynamical systems, bifurcations, control of chaos, cryptography based on chaos, and recently memristors (physical devices for neurocomputing) and artificial intelligence. He is working in those fields with renowned researchers from many countries. He received the Dr. Zakir Husain Award 2012 from the Indian Society of Industrial and Applied Mathematics during the 12th biannual conference of ISIAM at the University of Punjab, Patialia, (India) in January 2015.

Since August 2023, he is Vice-President of the International Society of Difference Equations.

Arkady Pikovsky

University of Potsdam, Germany

Populations of oscillators as a complex system benchmark: from integrability to disorder 

Abstract: Fifty years ago, Yoshiki Kuramoto formulated his famous model of coupled oscillators, showing a transition from disorder to synchrony. Since then, it has been generalized in different directions and used in many applications, but it remains a paradigmatic example of a complex system out of equilibrium. In this talk, I first introduce the classical approaches of Kuramoto and Ott and Antonsen. Then, I discuss the integrability of the population ensemble in the thermodynamic limit of a large number of units. The second part of the talk is devoted to the effects of disorder in interactions of oscillators. I show how to perform averaging to reduce a disordered system to an effective regular ensemble. Finally, a maximally disordered system is shown to possess certain regularity, but a non-traditional order parameter is needed for its characterization. 

Bio: To be updated.

Alexander Pisarchik

Isaac-Peral Chair in Computational Systems Biology Center for Biomedical Technology
Universidad Politécnica de Madrid, Spain

Ring of Synchrony: Exploring the Intricate Dynamics of Rotating Waves in Coupled Oscillator Networks

Abstract: Synchronous dynamics in networks of coupled oscillators has attracted high interest, considering the pervasive presence of complex networks in our daily lives, such as various transport, energy, communication, social, and neural networks. Among different network structures, the ring configuration holds special significance due to its capacity to generate rotating waves propagating along the ring of interconnected nodes. These waves manifest as stable periodic, quasiperiodic, or chaotic orbits, arising from the phase difference between neighboring oscillators. The intricate dynamics of rotating waves is elucidated through various techniques, including time series analysis, phase-space analysis, bifurcation diagrams, spectral analysis, and basins of attraction. These methods carefully uncover the complex routes from coexisting stable equilibria to hyperchaos. The vast body of research on rotating waves provides insights that are essential for a wide range of scientific disciplines and real-world applications, including lasers, chemical reactions, cardiorespiratory systems, and even beyond, with particular relevance to neural networks and brain functions.

Bio: Alexander Pisarchik is Chair of Computational Systems Biology at the Center for Biomedical Technology, Universidad Politécnica de Madrid, Spain. In 1990, he earned a PhD degree in Physics and Mathematics from the Institute of Physics of the Belarus Academy of Science, and in 1997 completed special courses on “Nonlinear Dynamics in Physiology and Medicine” at McGill University, Montreal, Canada and “Time Evolution of Complex Systems” in Lisbon, Portugal. Since 1992, he has been awarded grants from governments of various countries and has conducted research in Belgium, Spain, Iceland, and Mexico. His impactful contributions span a wide range of fields, including neural and laser dynamics, nonlinear and stochastic analyses of neuronal networks, synchronization, multistability, cognitive neuroscience, and brain-computer interfaces. He is the author of several monographs, diverse book chapters, and patents, in addition to having authored more than 300 papers published in peer-reviewed scientific journals. Furthermore, he serves as a Board Member of International Physics and Control Society (IPACS) and holds membership in the Consorcio de Investigación Biomédica en Red (CIBER).

Sergey Prants

Corresponding member of Russian Academy of Sciences,
Head of Dept. of Ocean and Atmospheric Physics at Pacific Oceanological Institute of Russian Academy of Sciences, Vladivostok, Russia

Transport Barriers in Oceanic Flows

Abstract: Large-scale transport barriers in the oceanic flows are considered from the point of view of dynamical systems theory. Transport barriers are material lines in 2D flows and surfaces in 3D flows across which the flux is zero due to purely advective processes. They can be classified into elliptic, parabolic and hyperbolic barriers. I discuss the dynamical systems theory methods for extracting elliptic and parabolic transport barriers in simple kinematic and dynamic models of vortical and jet flows. Special attention is paid to discussion of importance of hyperbolic transport barriers in some practical issues as anthropogenic and natural pollution.

The work was supported by the Russian Science Foundation (project no. 23-17-00068).

Bio: Sergey’s research activities have been varied, ranging from quantum study on atom-light interactions, to investigation of sound propagation in the ocean using Hamiltonian mechanics methods and to study of transport and mixing processes in geophysical flows using dynamical systems theory methods. He is actively delevoping Lagrangian methods to study ocean fronts, eddies and marine life. He received PhD in Phys. and Math. in 1981 and Dr. Sci. degree in 1992 from Institute of Physics, Minsk, USSR and was elected to Russian Academy of Sciences in 2022. Sergey worked as visiting researcher in P. Lebedev Physical Institute, Moscow, Courant Institute of Mathematical Sciences at New York University, Institute for Pure and Applied Mathematics at University of California in Los Angeles, Galilei Institute for Theoretical Physics, Florence, Italy and gave lectures at Xi’an Jiao Tong University and Nanjing University of Information Science and Technology, China. He authored around 200 peer-reviewed articles in journals indexed in the Web of Science core collection and a few books with the present Hirsch citation index of 29. Prof. Sergey Prants entered the top 2% of the most cited scientists in the world by number of citations in Scopus (2023) https://elsevier.digitalcommonsdata.com/datasets/btchxktzyw/6. He is a member of editorial boards of Journal of Russian Laser Research (Springer), Journal of Environmental Accounting and Management (L& H Scientific Publishing) and Russian Journal of Nonlinear Dynamics. Sergey is the winner of the International Zaslavsky Award in nonlinear science and complexity (2014). In 2006, he was awarded Award in theoretical physics by the Far Eastern Branch of the Russian Academy of Sciences.