Inaugural Francqui Chair Lecture

Thanks to the Francqui foundation, the Department of Mathematics of the University of Namur is proud to host a FRANCQUI Chair during the 2019-2020 academic year.

Complex systems: physics beyond physics

Complex systems are systems composed of many microscopic entities, subject to mutual interactions. Starting from the microscopic rules of interaction, systems self-organize in time and in space, yielding ordered macroscopic patterns which are needed for implementing dedicated functions.

Cellular biology, chemical oscillating reactions, the organization of social communities are all examples of complex systems, covering different scales and involving distinct populations, which can be quantitatively addressed via statistical mechanics and non linear dynamics tools.

The classical approach to population dynamics relies indeed on characterizing the densities of species through a system of ordinary differential equations, which incorporates the interactions being at play. In other words, pure competition, predator-prey interactions, or even cooperative effects could be translated into specific interaction terms. Noise and other disturbances can be eventually hypothesized to alter the ideal deterministic, hence reproducible, dynamics but always acting as a macroscopic bias. 

As opposed to this formulation, a different level of modeling can be invoked by focusing instead on the individual-based description, which is intrinsically stochastic. Individuals entities interact when e.g. they happen to meet and the ensuing reactions might occur with a given success rate. The system becomes probabilistic and the idealized deterministic picture can be solely recovered when considering very large populations of interacting units.

For finite size populations, demographic noise, as the probabilistic contributions are  customarily referred to, acts as a source of endogenous perturbation, shaking the system from the inside. In this talk I will discuss, in simple terms and building on examples, how the noisy component of the dynamics, as stemming from the discreteness of the scrutinized sample, can yield the emergence of quasi-regular patterns.

Microscopic disorder can hence materialize in macroscopic order, a counterintruitive mechanism which could be exploited by living systems to orchestrate a multitude of different functions. If time allows, I will also make reference to networks, another source of heterogeneity which positively interferes with the ability of a multi-species system to generate coherent patterns of collective activity. This latter topic will be also addressed within the planned lectures.

More information is available on the website below.  Registration is kindly recommended.

 

Image en bandeau du site web: COPYRIGHT: © 2017 UNIVERSITÀ DEGLI STUDI DI FIRENZE.

 

 

Contact : Anne-Sophie Libert - anne-sophie.libert@unamur.be
Plus d'info : https://www.unamur.be/sciences/mathematique/chairfrancqui2020
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