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Mathematics Webinar | Non-Equilibrium Dynamics and Weak Chaos in Hamiltonian and Driven Systems

Part of the MDPI Mathematics Webinars series
7 July 2025, 14:00 (CEST)

Registration Deadline
7 July 2025

Non-equilibrium dynamics, Weak chaos, Hamiltonian systems, Externally perturbed systems, Chaotic dynamics, Lyapunov exponents, Smaller Alignment Index SALI, chaotic indicators, mappings
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Welcome from the Chair

Understanding the long-term behaviour of complex systems far from equilibrium remains one of the central challenges in nonlinear science. This workshop brings together recent advances in the study of non-equilibrium dynamics and weak chaos in both Hamiltonian many-body systems and externally driven (non-autonomous) models. Topics will include ergodicity breaking, metastable and quasi-stationary states, energy localisation, and anomalous transport, as well as the use of diagnostic tools such as Lyapunov exponents and SALI to characterise dynamical behaviour. Particular emphasis will be placed on systems with long-range interactions and mean-field models that exhibit integrable-like features in the thermodynamic limit, and on periodically forced systems where scattering, resonance, and sensitivity to external parameters play key roles in trajectory evolution. By exploring the interplay between structure, stability, and weak forms of chaos, this workshop aims to deepen our understanding of how order and unpredictability coexist in nonlinear dynamical systems. We invite researchers working across mathematical physics, dynamical systems theory, and computational modelling to attend, with the goal of fostering interdisciplinary dialogue and identifying new directions for exploration.

Date: 7 July 2025

Time: 2:00 pm CEST | 8:00 pm CST Asia | 8:00 am EDT

Webinar ID: 843 5663 2066

Webinar Secretariat: journal.webinar@mdpi.com

Registration

This is a FREE webinar. After registering, you will receive a confirmation email containing information on how to join the webinar.  Registrations with academic institutional email addresses will be prioritized.

Certificates of attendance will be delivered to those who attend the live webinar.


Can’t attend? Register anyway and we’ll let you know when the recording is available to watch.

Event Chair

School of Mathematics, Statistics and Actuarial Science (SMSAS), University of Essex

Introduction
Bio
Dr. Chris Antonopoulos is a Lecturer at the Department of Mathematical Sciences, University of Essex. He obtained his BSc in Mathematics from the University of Crete (1999), and his MSc (2002) and PhD (2007) in Applied Mathematics from the University of Patras, Greece. His PhD focused on the stability and chaos in multi-dimensional Hamiltonian systems and their transition to Statistical Mechanics. He was a postdoctoral researcher at Université Libre de Bruxelles in Prof. P. Gaspard’s group, where he published work on Hamiltonian systems and Statistical Mechanics. He later joined Profs. K. van der Weele and T. Bountis’ group at the University of Patras under the European “Complex Matter” programme. From 2012, he was an EPSRC Research Fellow at the University of Aberdeen’s ICSMB, working on information-dynamical approaches to complex systems. Since 2015, he has taught and conducted research at the University of Essex, focusing on dynamical systems, chaos theory, information theory, computational neuroscience, and complex networks, with applications to brain dynamics and epidemic modelling (e.g., COVID-19). He is a member of the LMS and IMA and serves as editor for Scientific Reports (Nature), Frontiers in Computational Neuroscience, and Open Physics. Dr. Antonopoulos has authored 59 journal publications, 9 conference papers/book chapters, and delivered 59 talks (19 invited). He has organised sessions at BAMC, DDCA, and CHAOS conferences, and taught advanced courses on complex systems at summer schools and PhD programmes. With an h-index of 24 and over 2,800 citations, he currently supervises three PhD students and collaborates internationally to advance mathematical modelling of complex systems.

Keynote Speakers

Nonlinear Dynamics, Chaos and Complex Systems Group, Departamento de Biología y Geología, Física y Química Inorgánica, Universidad Rey Juan Carlos, Madrid, Spain

Introduction
Talk
Forced Chaotic Scattering
Bio
Dr. Jesús M. Seoane earned his degree in Physical Sciences from UNED in 2002 and joined the Nonlinear Dynamics, Chaos, and Complex Systems Group at URJC in 2003. He completed his PhD in 2007 with highest honours (Sobresaliente cum laude, Extraordinary Doctorate Award), focusing on weak perturbations in chaotic scattering, under the supervision of Prof. M. A. F. Sanjuán and in collaboration with Prof. Ying-Cheng Lai (Arizona State University). His thesis results were published in top journals including Physical Review, Chaos, and New Journal of Physics. Dr. Seoane has held several international research positions, including postdoctoral work at Arizona State University and research stays in Italy, where he worked on chaos control and synchronisation in biological systems. His collaboration with Prof. Arecchi and Meucci further broadened his interdisciplinary expertise. He has since expanded his research into areas such as mechanical systems, fractal structures, and more recently, cancer physics. In collaboration with researchers from Portugal and Brazil, this new line of work has resulted in numerous Q1 journal publications. He has co-authored over 80 student theses, supervised 7 doctoral dissertations, and participated in 12 competitive research projects. Dr. Seoane regularly reviews 15–20 articles annually for leading journals (e.g., PRE, Chaos, Scientific Reports) and serves as an editor for PLOS ONE. He has presented his work at over 60 conferences worldwide and remains active in academic leadership, currently serving as the Coordinator of the Doctoral Program in Science at URJC. He has also held roles as an Academic Secretary, a PAU exam coordinator, and a tutor in experimental sciences.
Research Keywords
chaotic dynamics applied to mechanical engineering problems, particularly vehicle suspension issues; fractal structures; cancer physics

Nonlinear Dynamics, Chaos and Complex Systems Group, Departamento de Biología y Geología, Física y Química Inorgánica, Universidad Rey Juan Carlos, Madrid, Spain

Introduction
Talk
Characterising Chaotic Dynamics in Some Astronomical Systems
Bio
Dr. Juan C. Vallejo is an astrophysicist specialised in numerical modelling, nonlinear dynamics and processing of space observatories data. He received his degree in Physics (Astrophysics) from University Complutense of Madrid (UCM) and competed his PhD thesis at University Rey Juan Carlos (URJC). He has been an Associate Professor at URJC since 2024. He is member of the Nonlinear Dynamics, Chaos and Complex Systems Group at URJC. The research at URJC focuses on analysing the impact of chaotic dynamics in numerical simulations in astronomy, mainly by using finite-time Lyapunov exponent distributions to study the predictability of orbits in galactic systems. Another parallel research line is the analysis of chaotic scattering phenomena in stellar systems. From 2017 until 2023, he was also a member of the AEGORA research group at UCM. The main focus of research at UCM was on the analysis of protoplanetary discs around young stars and the impact of X-ray and UV radiation on their evolution. Juan C. Vallejo has broad experience in the field of aerospace, focusing on the development and operation of space telescopes and their associated data processing systems. From 1997 until 2016, he worked in the science operations centres of the European Space Agency (ESA) observatories ISO and XMM-Newton. His areas of expertise include flight dynamics systems, mission operations centres and science operations centres.
Research Keywords
numerical modeling; nonlinear dynamics and processing of space observatories data

School of Mathematics and Physics, University of Lincoln (Brayford Pool Campus), Lincoln, UK

Introduction
Talk
Helen Christodoulidi is a Senior Lecturer in Applied Mathematics at the University of Lincoln. In 2010, she was awarded her PhD in Applied Mathematics from the University of Patras in Greece, with part of her studies carried out at the Max Planck Institute for the Physics of Complex Systems in Germany. She worked as a postdoctoral research fellow for several years, two years at the University of Padova in Italy and the next three years at the University of Patras. In 2017 she was awarded a research fellowship, funded by the Greek State Scholarships Foundation, to study Complex Hamiltonian Systems at the Academy of Athens. Dr Christodoulidi's research focuses on Nonlinear Dynamical Systems, Hamiltonian and Statistical Mechanics, Perturbation Theory, Integrable Systems, Numerical Methods for ODES and PDES and Mathematical Modelling of Complex Systems. She is an expert in large-scale numerical simulations, as well as in applying perturbation theory methods to nonlinear dynamical systems.
Bio
Energy Localisation And Dynamics of a Mean-Field Model With Non-Linear Dispersion
Research Keywords
large-scale numerical simulations; application of perturbation theory methods to nonlinear dynamical systems.

Programme

Speaker/Presentation Time in CEST Time in EST Time in CST
Dr. Chris Antonopoulos
Chair Introduction
14:00–14:10 08:00–08:10 20:00–20:10
Prof. Dr. Jesús M. Seoane
Forced Chaotic Scattering
14:10–14:40 08:10–08:40 20:10–20:40
Q&A Session 14:40–15:00 08:40–09:00 20:40–21:00
Dr. Juan C. Vallejo
Characterising Chaotic Dynamics in Some Astronomical Systems
15:00–15:30 09:00–09:30 21:00–21:30
Q&A Session 15:30–15:50 09:30–09:50 21:30–21:50
Dr Helen Christodoulidi
Energy Localisation and Dynamics of a Mean-Field Model With Non-Linear Dispersion
15:50–16:20 09:50–10:20 21:50–22:20
Q&A Session 16:20–16:40 10:20–10:40 22:20–22:40
Dr Chris Antonopoulos
Closing of Webinar
16:40–16:50 10:40–10:50 22:40–22:50

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