NeuroPSI – Université Paris-Saclay

Hidden complexity in biologically inspired neural networks : emergent properties and dynamical behavior

This thesis investigates the neural dynamics during attentive wakefulness, specifically focusing on the « asynchronous and irregular » (AI) type of dynamics observed in the cerebral cortex. The research aims to gain a deeper understanding of neural network behaviors, with a primary emphasis on two models: the Adaptive Exponential (AdEx) integrate and fire model, and the Hodgkin-Huxley (HH) model, with a particular focus on the AdEx model.
The thesis uncovers intriguing differences among seemingly similar neural networks. In a first part, it will shed light on how neural networks respond to external stimuli, particularly in the context of epilepsy, examining why certain systems control and kill the paroxysmal input while others reproduce and propagate it. In a second part, the thesis explores how sparsely connected networks of AdEx or HH neurons can exhibit AI states in two distinct ways: self-sustained AI states, or AI states requiring external input (Driven). In a third part, we will introduce the Dissipation and focus our analysis of models and different networks around this tool.
To unravel those differences, a combination of classical signal processing techniques, structural analysis of the configuration of the network, and dynamical systems tools – including Lyapunov exponents and system dissipation – are employed. The investigation also makes use of mean-field models of AdEx networks to comprehend how self-sustained and driven variants manifest at a global level. Exploring these properties and variations enhances our understanding of the complex emergent properties and distinct dynamical behaviors that exist within apparently similar biological neural networks.

Composition du Jury

• • Sacha Van Albada
  • Serafim Rodrigues
  • Bruno Cessac
  • Antoine Chaillet