Mathematics of Living Matter – Abstracts

2:00 PM – 2:45 PM, Wednesday, October 17, 2018; Room: 114 McAllister bldg.

Complexity of large multi-agent systems with positive reinforcement

Pierre-Emmanuel Jabin, University of Maryland, USA

The aim of this talk is to investigate the behavior of large networks of interacting agents with positive reinforcement. In this setting agents are not indistinguishable but instead the possible interactions between agents are described through a connectivity graph with the corresponding connections involving according to the synchronization between each pair of agents. This framework encompasses a broad set of applications from synchronized oscillators, to neuron networks (biological or artificial).

In classical many particle or multi-agent systems (as they are used in physics…), propagation of chaos (i.e. the almost independence of each agent) can lead to a reduction in complexity through the direct calculation of various macroscopic densities. However the positive reinforcement in the system under consideration here ensures that correlations between neurons never vanish such that the traditional concept do not apply.

Still in a joint work with D. Poyato, we first study the case where agents are essentially fully connected and we are able to show that in spite of this simple topology, the networks may exhibit different measures of complexity which can be characterized through the type of initial connections.

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