Symposiums

Recent Developments in Fractional Dynamics and Applications

Symposium Organizers:

  • Mark Edelman, Yeshiva University and Courant Institute, New York, USA; edelman@cims.nyu.edu

  • Minvydas Ragulskis, Kaunas University of Technology, Kaunas, Lithuania; minvydas.ragulskis@ktu.lt

Scope:

The purpose of this mini symposium is to discuss recent trends in the development of the theory of fractional dynamics.

The theoretical aspects of this proposal include the recent developments in continuous and discrete generalized fractional calculus, maps of matrices, diffusion in fractional (with memory) systems, complex fractional dynamics, etc.

The applications include (but not restricted to) biological and socio-economic systems with memory and engineering (secure communication, signal and image processing, memristors, neural networks, control theory, etc.).

The organizers welcome reviews of recently published books on fractional calculus.

Solitons and other localized structures in physical and mathematical sciences

Symposium Organizers:

  • Yury Stepanyants, University of Southern Queensland, Toowoomba, Australia;Yury.Stepanyants@unisq.edu.au
  • Victor Shrira, University of Keele, UK; V.I.Shrira@keele.ac.uk;
  • Lev Ostrovsky, University of Colorado, Boulder, USA; Lev.Ostrovsky@gmail.com.

Scope:

The symposium focus on the following topics:

  • New developments in the soliton theory;

  • Solitary waves and soliton-like structures in non-integrable equations;

  • Multisoliton formations, rogue waves, and collapses;

  • Experimental results on solitary waves and their observations in nature (oceans, atmosphere, solar plasma, space).

The main thrust of the symposium is to discuss the soliton-like structures in various physical contexts and to break down the artificial walls separating researchers working in different fields.

Theoretical, numerical, and experimental works are welcome.

Scaling Laws, Phase Transitions, and Criticality in Nonlinear Dynamical Systems

Symposium Organizers:

  • Edson Denis Leonel, São Paulo State University (UNESP), Rio Claro, Brazil; edson-denis.leonel@unesp.br
  • José Antonio Méndez-Bermúdez
    Benemérita Universidad Autónoma de Puebla (BUAP), Puebla, Mexico; jmendez@ifuap.buap.mx

Scope:

The purpose of this symposium is to discuss recent developments in the characterization of scaling laws, phase transitions, and critical phenomena in discrete (described by difference equations/maps) and continuous (described by differential equations) nonlinear dynamical systems.

From the theoretical perspective, the symposium aims to bring together contributions addressing the emergence of critical behavior in deterministic systems, including transitions between integrable and non-integrable regimes, transitions between bounded and unbounded transport, and the suppression or enhancement of diffusion. Topics of interest include, but are not limited to, the identification of order parameters and susceptibilities in dynamical systems, scaling hypotheses and universality classes, crossover phenomena, and the role of symmetry breaking, topological defects, and elementary excitations in driving dynamical phase transitions.

From an applied and interdisciplinary viewpoint, the symposium also welcomes contributions connecting scaling and criticality in dynamical systems to problems in statistical physics, transport phenomena, networks, synchronization, control theory, and complex systems, including applications in biological, physical, and engineered systems.

The organizers encourage both original research contributions and overview or review-type presentations that highlight recent advances, open problems, and emerging directions in the study of scaling laws and phase transitions in nonlinear dynamical systems.

Complexity, Chaos, Complex Systems and Applications in Medicine, Biology, to Mathematical Sciences and Engineering

Symposium Organizers:

  • Yeliz Karaca, University of Massachusetts (UMass), Worcester, USA; yeliz.karaca@ieee.org

  • Dumitru Baleanu, Lebanese American University, Lebanon, and Institute of Space Science, Romania; dumitru.baleanu@gmail.com

  • António Manuel Ferreira Mendes Lopes, University of Porto, Porto, Portugal; aml@fe.up.pt

  • Albert Luo, Southern Illinois University Edwardsville, IL, USA; e-mail: aluo@siue.edu

Scope:

Complexity, as a scientific theory, forges a connection between the quantitative and qualitative facets of life, which enables the comprehensive contemplation of diverse systems from as cells to human beings, possible to be comprehended partially by traditional scientific methods merely. This derives from the premise that some systems display pattern-wise and behavioral phenomena which could be utterly inexplicable by only conventional analyses regarding the systems’ constituent parts. Complexity reflects the disentangling of complex, dynamic, complicated, random, nonlinear, adaptive, emergent systems, amongst many more, bringing about collective dynamics along with the interaction of components in multiple manners. Besides these, complexity provides facilitation and lenses in observing the problems through multiple perspectives. Complexity science merges the two solitudes of both micro (analysis of the parts) and macro analyses (holistic analysis), ranging across human genome to evolutionary biology across the spectrum natural and human systems. In that regard, complexity science seeks to discover the underlying principles, theoretical aspects of emergence with an orientation to use them through applications so that biological, physical and social worlds can be understood at the pedestal of emergence of chaos and order as the hallmarks of natural systems as well as designed systems.

The theories of complex systems besides these points provide the ideas suggestive of the way intractable the world is considering that even the simplest of phenomena involve enormous and even incalculable complexity. Consequently, it has been observed that many applications of science have turned into multimethod case studies based on evolving knowledge over time. 

Bifurcation analysis is employed for compilation of characterizing the dependence of certain classes of solutions of a dynamical system on variations in problem parameters. Thus, it may prove the coexistence of two independent processes of dynamical behavior under conditional symmetry, which emphasizes its advantage compared to simulation-based approaches owing to the capability of mapping out such families independently of the dynamic stability of the periodic orbits or equilibria, which implies that the analyses encompass a multitude of theoretical and algorithmic approaches. In addition, the properties of complex systems stem from the nonlinear interaction of components and constituents, ranging from cells to neurons in the brain, through individuals within a group. In nonlinear dynamics, complex problems foreground the critical support of artificial phenomena in order that each domain of complex systems can yield applicable answers and solutions to the needs of different aspects of complexity and nonlinearity by minimizing the problems of complexity whose solutions are based on advanced mathematical foundations and analogous algorithmic models constituting numerous applied aspects of complexity. These approaches to address complex systems and uncertainty may span across the entire deterministic-stochastic-discrete-continuous mathematical approximations and principled approaches.

Furthermore, the conflux between mathematical formalisms and neurons makes up the set structure of modern computational sciences, expending quantitative frameworks concerning the complexities of cognitive functions, neural coding, patterns, network dynamics, systems, synaptic plasticity and information processing. Given these constructs, mathematical modeling is oriented toward capturing processes of functioning of natural and artificial types of neural networks, indicating the employment of synaptic inputs in chaotic neurons considering spatial and temporal aggregation. All these peculiarities demonstrate the criticality of complexity and modeling of a single neuron to understand the entire brain dynamics, biological systems, patterns, attributes as well as neuromodulation.

The mathematics of data, by encompassing a multifaceted blend of mathematical techniques and models, is pivotal for tackling voluminous datasets and extracting significant inputs from them. Computation of the complexity (computational or algorithmic complexity) of a particular mathematical model necessities the performance of the analyses over the run time, which is related to and based on the type of data (big data) identified, determined and employed along with the methods.  While providing the tools required to explore the complexities of data, Artificial Intelligence (AI) applications, deep learning, machine learning methods as well as data analysis aspects rely on foundational mathematical concepts, which can pave the way for novice perspectives, solutions to challenges and directions for the future elements to arise. 

To these ends, the aim of our symposium is to unify and put into practice the diverse and evolving approaches to complexity theory, mathematical sciences, physical sciences, chaos, nonlinearity and applied complexity science, among others for providing a key into understanding the current and conceivable complex problems so that mathematical frameworks can serve as the plinth to understand the role of AI, modeling, algorithmic mechanisms and future science of complexity. In view of the integrative schemes emerging on dynamic scales, our purpose is to highlight the mutually enriching association between the core of mathematics and data in the ever-evolving digitizing landscape and ecology science, computer science, informatics, medicine, biology, neurobiology, epidemiology, virology, applied sciences, engineering, biomedicine, bioengineering, biomechanics, economics, social sciences, and so forth, towards the integration, analysis, interpreting mechanisms, processing of models and data-centric prediction-based and other respective domains.

Fractional Calculus in Complex and Nonlinear Systems

Symposium Organizers:

    • Dumitru Baleanu, Lebanese American University, Lebanon, and Institute of Space Science, Romania; dumitru.baleanu@gmail.com

    • Yeliz Karaca, University of Massachusetts (UMass), Worcester, USA; yeliz.karaca@ieee.org

    • Yu-Dong Zhang, University of Leicester, Leicester, UK; yudongzhang@ieee.org

    • Akif Akgül, Hitit University, Çorum, Türkiye; akifakgul@hitit.edu.tr

Scope:

Nonlinear dynamic models are spawned by high dimensionality and heterogeneity, having fractional-order derivatives, and constituting fractional calculus, which brings forth a thorough comprehension and control of the related dynamics, patterns and structure. Fractional dynamics with its interdisciplinary aspect examines the nonlocal properties of dynamical systems through the methods pertaining to fractional calculus, integro-differential equations of non-integer orders as well as discrete nonlocal mappings. Regarded as a nonlocal system of any nature, a fractional dynamical system displays states of changes that could be discrete or continuous in time.

Fractional calculus, extending traditional calculus by enabling the differentiation and integration of non-integer orders, proves itself as a robust means of interdisciplinary applications, biology, mechanics and engineering, among other fields. Fractional-order system refers to a dynamical system whose modeling can be attained by a fractional differential equation that includes derivatives of non-integer order. Accordingly, fractional models have become relevant to dealing with phenomena with memory effects in contrast with traditional models of ordinary and partial differential equations. Compared with integer-order calculus, which constitutes the mathematical basis of most control systems, fractional calculus can provide better equipment to handle the observed time-dependent impacts and generalized memory.

The advances in science, engineering and applied mathematics have led to the exploration of limitations and solutions to challenges concerning physical, natural and biological systems described with differential fractional-order equations in which a fractional derivative order is used. Analysis and control of fractional order nonlinear systems are also significant, along with the observation of unknown inputs, subtle details and concepts being used and derived analytically. Chaos synchronization, fluctuations and periodic behaviors in systems have differing states, while chaotic systems are characterized by sensitivity to initial conditions with their complexity manifesting the relevance to theoretical aspects and practical applications.

The theoretical foundations and interdisciplinary applications with their advances of fractional calculus, through the investigation of fractional-order integral and derivative operators with real or complex domain, has rendered computational processing analyses as a method of reasoning and the main pillar of current research. These can be of aid in tackling nonlinear dynamic problems through novel strategies based on observations and complex experimental data. In that regard, fractional calculus in epidemiology-related settings provides a comprehensive model to investigate real-world problems through explaining the history of infection and recovery rates. Data fitting emerges as an important process of fitting models to data and analyzing the accuracy of the fit used to address the problem of determining the curve passing close to a set of points in a multidimensional space. This allows for a rich variety of diagnostic means and outputs to ensure the adequacy of the selected model to be efficiently assessed.

The purpose of our symposium is to foreground this integrative approach, with the theoretical and applied dimensions of nonlinear dynamic systems merging fractional calculus and advancing technologies, demonstrating the significance of distinctive approaches in the related realms. These particular aspects are critical in the optimal prediction solutions, critical decision-making processes, optimization, quantification, automation, controllability, observability, synchronization and stabilization of fractional, neural, dynamical and computational systems amongst many others. Thus, it is aimed at facilitating to achieve viable, more effective and reliable solutions, optimization processes, numerical simulations besides technical analyses and related applications in areas, including mathematics, medicine, engineering, physics, mechanics, biology, neurobiology, biomedicine, virology, epidemiology, psychology, chemistry, genetics, information science, data science, computer science, space sciences, applied sciences, economics and social sciences, to name some.

Phase Space Dynamics: Methods, Computation, and Applications

Symposium Organizers:

    • Makrina Agaoglou,Universidad Politecnica de Madrid, Spain; makrina.agaoglou@upm.es
  •  
    • Aikaterini Maria Vergiopoulou, Universidad Politecnica de Madrid, Spain; aikaterini.vergiopoulou@upm.es
  •  
    • Matthaios Katsanikas, Academy of Athens, Greece; mkatsan@academyof athens.gr

Scope:

This mini symposium aims to explore methods of analysing phase space dynamics in non-linear dynamical systems. Emphasis is placed on practical tools for constructing and interpreting phase portraits, including not only classical methods such us Poincaré surfaces of section, but also more recent methods like Lagrangian Descriptors (LDs), SALI and GALI etc. These techniques are widely used to identify invariant structures, distinguish regular and chaotic motion, and understand transport mechanisms in realistic models. The session also highlights emerging applications of machine learning for data-driven exploration and classification of dynamical behavior in phase space. The aim is to connect theory with applications and promote the exchange of effective computational and analytical methodologies across disciplines.

Nonlinear & Discontinuous Dynamical Systems

Symposium Organizers:

    •  Yu Guo, McCoy College of Science Mathematics and Engineering, Midwestern State University Texas, USA;  yu.guo@msutexas.edu
    • Jianzhe Huang, School of Aeronautics and Astronautics, Shanghai Jiao Tong University, Chinal; hjianzhe@sjtu.edu.cn

Scope:

This symposium focusses on nonlinear and discontinuous dynamical systems. This symposium provides a platform for researchers to exchange ideas in recent development and advances of nonlinear dynamics and methods. All papers will be peer-reviewed, and upon acceptance, they will be published in the special issue of Journal of Vibration Testing and System Dynamics. Manuscripts are solicited in the following topics but not limited to:

  • Bifurcation, stability and chaos in dynamical systems

  • Singularity and switchability in discontinuous dynamical systems

  • Nonlinear wave dynamics and structural vibration

  • Discontinuity mechanism of controlled dynamical systems

  • Dynamics and Acoustics in Linear and Nonlinear Systems

  • Flow-Induced and Thermal-Induced Vibrations in Continuous Medium

  • Nonlinear Vibrations and Random Vibrations

Nonlinear Dynamics in Lattice Systems

Symposium Organizers:

    • Haris Skokos, University of Cape Town, South Africa; haris.skokos@gmail.com.

      Georgios Theocharis, CNRS – Le Mans Université, France; georgios.theocharis@univ-lemans.fr

Scope:

This symposium aims to bring together recent advances in the study of nonlinear dynamics in lattice systems, with particular emphasis on the interplay between nonlinearity, topology, disorder, and activity. Paradigmatic lattice models such as the Fermi–Pasta–Ulam–Tsingou (FPUT), discrete nonlinear Schrödinger (dNLS), and Klein–Gordon (KG) chains continue to provide fundamental insight into key physical processes, including energy localization, thermalization, and transport in nonlinear media.

The session will cover both theoretical, computational and experimental developments in nonlinear lattice dynamics, addressing phenomena such as energy localization and equipartition, wave propagation, and stability in ordered, disordered, and quasiperiodic settings. Particular attention will be given to emerging directions at the interface of nonlinear dynamics and the topological properties of waves, as well as to nonreciprocal, excitable, and active lattice systems, including non-Hermitian and driven nonlinear lattices. The aim of this minisymposium is to provide a forum for the exchange of ideas across communities working on nonlinear dynamics, lattice models, and novel wave phenomena, and to stimulate interaction between theory, computation, and applications in nonlinear science.

Dynamical Systems Meet Deep Learning: From Classical ANNs to PINNs and Reservoir Computing

Symposium Organizers:

  • Ioannis Antoniades, Aristotle University of Thessaloniki; iantoniades@auth.gr.
  • Ioannis Kafetzis, AI Group Leader, Interventional and Experimental Endoscopy ; ioanniskaf@gmail.com
  • Constantinos Siettos, University of Naples Federico II; constantinos.siettos@unina.it

Scope: Artificial Intelligence and Deep Learning have revolutionized scientific modeling, yet they face two critical barriers, namely the high energy cost of digital hardware and the “black box” nature of model predictions. This symposium explores two transformative focus areas that address these challenges by leveraging nonlinear dynamics and physical laws.

The first focus area, Reservoir Computing (RC), treats computation as a physical process. By exploiting the inherent nonlinear dynamics of physical substrates, such as optical, memristive, and neuromorphic computing systems, RC provides high-performance, low-power alternatives to traditional digital architectures.

The second focus area, Physics-Informed Neural Networks (PINNs), treats physics as a computational constraint. By embedding governing equations (PDEs, conservation laws) and uncertainty quantification directly into the learning process, PINNs ensure that AI outputs are physically consistent and interpretable.

The goal of this symposium is to bring together theorists and practitioners to discuss the synergy between nonlinear dynamics and machine learning, bridging the gap between abstract neural models and real-world physical applications.

Indicative Topics of Interest

The symposium welcomes contributions focusing on either Focus Area (RC or PINNs) or their intersection. Specific topics include:

Hardware & Dynamical Computing

  • Physical Reservoirs: Optical, Memristive, and Spintronic implementations.
  • Quantum Reservoir Computing and Quantum Neural Networks.
  • Chaos, Stochastic, and Time-Delay Reservoir Computing.
  • Neuromorphic and Analog computing for edge IoT applications.

Physics-Informed & Interpretable AI

  • Physics-Informed Neural Networks (PINNs) and Neural Operators (DeepONets).
  • Explainable AI (xAI) for identifying governing physical dynamics.
  • Uncertainty Quantification (UQ) in AI-based physical simulations.
  • Symmetry-preserving and Equivariant Neural Networks.

Cross-Disciplinary Applications

  • Neural network-based time-series analysis for complex systems.
  • Nonlinear dynamics in generative models and Reinforcement Learning.
  • Hybrid AI-nonlinear systems for secure communication and robotics.
  • AI for discovering governing equations from experimental data.