Workshop on Dynamical Systems: Theory, Modelling and AI 19–21 November 2025
(The Day 1 of the workshop will be announced in due course.)
[Mathematical Methods for the treatment of Differential Equations (DEs)]
Lie Symmetries and Group Analysis of DEs, Integrable Systems and Painlevé Analysis, Geometric Theory of DEs and Modern Techniques for the treatment of DEs
1. Sergey V. Meleshko (Keynote): Applications of Equivalence Transformations to Group Classification
2. Abdul Hamid Kara (Keynote): On the Relationship between the Invariance and Conservation Laws of Differential Equations
3. Sachin Kumar: Painlevé Analysis, higher-order rogue waves and dispersive solitons for a new generalized nonlinear evolution equation using a Hirota's N-soliton method
4. Mathew Aibinu: A Solow-Swan framework for economic growth with memory effect
5. Ryad Ghanam: Symmetry Analysis of the geodesic equations of the canonical connection: The n-dimensional case with r-dimensional abelian nilradical
6. Ali Raza: From Single (Symmetry) Reduction via the Optimal System to Double Reduction via Conservation Laws for physically interesting Partial Dierential Equations
7. Jean-Jacq du Plessis: The effect of long range interactions on energy spreading in nonlinear, disordered Klein-Gordon chains
(The Day 2 of the workshop will be announced in due course.)
[Differential Equations in Natural World and in Physics]
Ecological and Epidemic Modeling with Nonlinear Systems, Economic Dynamics and Market Models via DEs, DEs in Climate and Environmental Science
1. Linke Potgieter (Keynote): Ecological and Epidemic Modelling with Nonlinear Systems
2. Andrew Watson: Hydrological and groundwater modelling
3. Jack Jansma: Bayesian inference captures metabolite-bacteria interactions in ODE models of microbial communities
4. Mukhtar Yahaya: Emergence of structure in plant–pollinator adaptive networks
5. Richard Gibbs: Modelling cognitive agent movement with Integro-PDEs
6. Pietro Landi: Fishery modelling with adaptive dynamics
7. Fernando P. da Costa: A coagulation toy model for silicosis
(The Day 3 of the workshop will be announced in due course.)
Modern Computational Approaches
Computer Algebra Systems in DEs Research, Neural DEs and Physics-Informed Neural Networks, From Data to DEs Models and Reduced Order Modeling & Surrogate Modeling with AI
1. Shane Josias: Introduction to matching flows
2. Hugo Touchette: Applications of machine learning for simulations
3. Daniël Cloete: Machine learning methods for sampling rare events
4. Emma Nelson: Laguerre spectral collocation
(The program of the workshop will be announced in due course.)
Title: Applications of Equivalence Transformations to Group Classification
Speaker: Sergey V. Meleshko (Suranaree University of Technology, Thailand)
Abstract: The presentation is devoted to the application of equivalence transformations to the group classification of differential equations. It includes our experience in finding generalized equivalence transformations and performing preliminary group classification. As the construction of an optimal system of subalgebras is an essential part of using equivalence transformations for group classification, this topic will also be discussed. Part of the talk will focus on overdetermined systems of partial differential equations. Both partial differential equations and integro-differential equations will be considered. The presentation includes applications to the Boltzmann equation, the construction of invariant solutions for Gromeka–Beltrami flows, and the analysis of flows of chemically reacting gases in Eulerian and Lagrangian variables (for both unsteady and steady flows).
Title: A coagulation toy model for silicosis
Speaker: Fernando P. da Costa (Univ. Aberta, and CAMGSD, Técnico, Univ. Lisboa, Portugal)
Abstract: We present a system with a countable number of ordinary differential equations of coagulation type that can be considered a simple model for the silicosis mechanism. Silicosis is a respiratory disease due to the ingestion of quartz dust and their accumulation in the lungs. The mathematical model consists in an ODE for the concentration of free quartz particles, an ODE for the concentration of macrophages without quartz (cells of the immune system that identify, capture and try to expel entities strange to the body), and a countable number of ODEs each one describing the concentration of macrophages with a number $i\in\mathbb{N}$ of captured quartz particles. We briefly describe basic results such as existence, uniqueness, regularity, and semigroup results of the set of solutions. Then we study the dynamics of the infinite dimensional system in the case of a particular class of rate coefficients that allows for the decoupling of the full infinite dimensional system into a finite dimensional one and a lower triangular infinite system. By the analysis of the finite dimensional subsystem, we conclude that it has a saddle-node bifurcation, possessing two equilibria when a bifurcation coefficient which is the ratio of the input rate of quartz to the rate of creation of empty macrophages is below a critical value, and no equilibria above that value. The stability properties of the bifurcating branches of the full infinite dimensional system are studied.
Title: A Solow-Swan framework for economic growth with memory effect
Speaker: Mathew O. Aibinu (University of Regina, Canada)
Abstract: The Solow-Swan equation is a cornerstone in the development of modern economic growth theory and continues to attract significant scholarly attention. This study incorporates memory effects into the classical Solow-Swan model by introducing a formulation based on the Caputo fractional derivative. A comparative analysis is conducted between the integer-order and fractional-order versions of the model to examine the influence of fractional dynamics on capital accumulation. The findings reveal that the inclusion of a fractional-order derivative significantly affects the trajectory and long-term stability of capital, offering a more flexible and comprehensive framework for modeling economic growth processes.
Title: Laguerre spectral collocation
Speaker: Emma Nel (Stellenbosch University, Stellenbosch)
Abstract: In this work, we investigate the use of Laguerre spectral collocation methods for solving differential equations on the semi-infinite line. While spectral methods are known for their high accuracy, the unbounded domain and the exponential weighting associated with Laguerre polynomials present notable challenges. For example, the direct computation of the entries in the Laguerre spectral differentiation matrix leads to underflow and overflow issues in IEEE-754 arithmetic for large degrees N, even though the entries themselves are well-behaved. We discuss recent progress in addressing these numerical difficulties and explore approaches for improving convergence. By employing these techniques, one can achieve significantly higher values of N in Laguerre spectral methods, ultimately leading to better numerical results.
Title: The effect of long range interactions on energy spreading in nonlinear, disordered Klein-Gordon chains
Speaker: Jean-Jacq du Plessis (University of Cape Town)
Abstract: We investigate the dynamics of energy spreading and thermalisation in a one-dimensional nonlinear Klein-Gordon lattice with long-range interactions and disorder. Pairwise in- teraction terms in the potential are scaled by 1/r^α, where r is the distance between lattice sites and α ≥ 0 is a parameter which governs the range of interactions. Using measures such as the participation number, second moment and entropy, we study how energy spreading through the lattice depends on the range of interaction by varying the α parameter. In addition, we study the normal modes of the linearised system to understand their influence on the energy spreading dynamics.
Title:: Painlevé Analysis, higher-order rogue waves and dispersive solitons for a new generalized nonlinear evolution equation using a Hirota's N-soliton method
Speaker: Sachin Kumar (University of Delhi)
Abstract: We investigate the dynamics of energy spreading and thermalisation in a one-dimensional nonlinear Klein-Gordon lattice with long-range interactions and disorder. Pairwise in- teraction terms in the potential are scaled by 1/r^α, where r is the distance between lattice sites and α ≥ 0 is a parameter which governs the range of interactions. Using measures such as the participation number, second moment and entropy, we study how energy spreading through the lattice depends on the range of interaction by varying the α parameter. In addition, we study the normal modes of the linearised system to understand their influence on the energy spreading dynamics.