DYNSYSAPLL

DYNAMICAL SYSTEMS AND THEIR APPLICATIONS

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 Obiettivo del progetto (Objective)

'The main objective of this project is to create fundamental understanding in dynamical systems theory and to apply this theory in formulating and analyzing real world models met especially in Neuroscience, Plasma Physics and Medicine. The specific objectives, tasks and methodology of this proposal are contained in the 5 WPs of the project. In WP1 we want to develop new methods for the center and isochronicity problems for analytic and non-analytic systems, study bifurcations of limit cycles and critical periods, including time-reversible systems with perturbations, and investigate reaction-diffusion and fractional differential equations. In WP2 we deal with the problem of integrability for some differential systems with invariant algebraic curves, classification of cubic systems with a given number of invariant lines, study global attractors of almost periodic dynamical systems and their topological structure, respectively, Levitan/Bohr almost periodic motions of differential/difference equations. The main objective of WP3 is to study dynamics of some classes of continuous and discontinuous vector fields, preserving, respectively, breaking some symmetries, study of their singularities and closed orbits for classes of piecewise linear vector fields. WP4 deals with Hamiltonian systems in Plasma Physics, twist and non-twist area preserving maps, further studies of a recent model proposed to study some phenomena occurring in the process of plasma’s fusion in Tokamaks, numerical methods, and the study of symmetries of certain kinds of k-cosymplectic Hamiltonians. The last WP tackles mathematical models in Neuroscience and Medicine. Firstly, we study several ODE-based and map-based neuronal models, survey in vivo results with respect to Autism Spectrum Disorder (ASD) and propose a model for ASD. Secondly, we study several approaches to mathematical models for diabetes. Finally, bone remodeling by means of convection-diffusion-reaction equations is our last task.'

Introduzione (Teaser)

The beauty of mathematics even for non-mathematicians lies in its ability to explain the world around us, to make the seemingly abstract more concrete. Advances in an important field of mathematics are providing a window on physical and biological systems.

Descrizione progetto (Article)

Mathematical formulae explain phenomena like why we do not float off the surface of the Earth and how a neuron fires an action potential to send a signal to another cell. The world around us is a smorgasbord of physical, chemical and biological systems whose evolution in time can often be described using dynamical systems theory.

Given its relevance to so many real-world scenarios, scientists launched the EU-funded DYNSYSAPLL (Dynamical systems and their applications) project to significantly advance dynamical systems theory and use it to gain insight into important phenomena in physics, neuroscience and medicine.

With respect to fundamental mathematics, scientists have tackled topics ranging from bifurcations of limit cycles and almost periodic motions to some classes of continuous and non-continuous vector fields. Numerous new results and simplified or more efficient approaches have been obtained, resulting in several publications in peer-reviewed scientific journals.

Researchers have also studied bifurcations of a model describing variation of plasma parameters in devices for controlled thermonuclear fusion. The model provides insight into the effects of changing parameters as they provide the basis for development of control strategies. Dynamical systems theory was also applied to harmonic oscillators, models of spiking behaviours in both single neurons and populations, and models of bone osteogenesis.

DYNSYSAPLL is creating fundamental knowledge and understanding in the field of dynamical systems theory and providing important insight into the workings of real-world systems. Along the way, it is providing fertile training ground for the researchers whom it supports.