Project description
Concrete mathematical descriptions emerge from abstract dynamical systems theories
Mathematical models are critical to our understanding of many phenomena: stock market activity, individual investor choices, and the emergence of neural network functions based on the properties of individual neurons. These models enable us to test hypotheses and make predictions, enhancing understanding and improving decision-making. Their value grows as the problem's complexity increases. However, when it comes to complex systems involving the dynamic interaction of multiple different types of agents, deriving the mathematics leading to the best models that accurately describe and predict emergent network behaviours is even more difficult. The EU-funded ErgThComplexSys project is drawing on abstract theory to solve concrete problems and bridge the gap for mathematical models with real-world features.
Objective
"Nowadays, networks of interacting systems appear in many areas of Science such as physics, chemistry, biology and also engineering and the human sciences. Examples range from solid state physics, to astrophysics, reaction-diffusion equations, transportation systems, the Internet, social networks, opinion models, etc. This vast spectrum of applications has stimulated a broad interdisciplinary endeavour to predict and control the behaviour of so-called ""complex systems"", namely large ensembles of units coupled through an intricate interaction web. While various theoretical and computational approaches to these systems have been developed, from the mathematical perspective, their analysis remains extremely challenging. Very little has been accomplished, especially as the description of the dynamical mechanisms underlying overall functioning is concerned. The proposed project aims to develop a novel rigorous approach to describe the emergence of global behaviour in complex heterogeneous systems, given their microscopic constituents such as individual dynamics and interaction nature/structure. At the interface between pure and applied mathematics, our approach will rely on results from abstract ergodic theory, especially as they have been recently obtained for non-uniformly hyperbolic systems, to address concrete mathematical models exhibiting real-world features."
Fields of science (EuroSciVoc)
CORDIS classifies projects with EuroSciVoc, a multilingual taxonomy of fields of science, through a semi-automatic process based on NLP techniques.
CORDIS classifies projects with EuroSciVoc, a multilingual taxonomy of fields of science, through a semi-automatic process based on NLP techniques.
- natural sciencescomputer and information sciencesinternet
- natural sciencesphysical sciencesastronomyastrophysics
- natural sciencesphysical sciencescondensed matter physicssolid-state physics
- natural sciencesmathematicsapplied mathematicsmathematical model
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Programme(s)
Funding Scheme
MSCA-IF - Marie Skłodowska-Curie Individual Fellowships (IF)Coordinator
75794 Paris
France