The role of external and endogenous noise in neural network dynamics and statistics
Clément Zankoc · Florence Research (University of Florence) · 2019
Noise is ubiquitous, stemming from the surrounding environment or arising from the inherent stochasticity of the system under consideration. Its presence may qualitatively change the behavior of a physical system, possibly leading to surprising and unexpected phenomena, and, as such, it should be accommodated for in realistic models. In this work, I present several models, that bear interest in neuroscience, in which noise plays a role of paramount importance. Throughout my thesis, investigations are conducted by means of both analytical and computational methods. First, I introduce, and further develop key analytical tools for tackling analytically the dynamics of a stochastic system. More specifically, I develop a perturbative technique which allows for computing the statistics of such systems even if they do not obey a gradient dynamics. Second, I focus on purely stochastic oscillators. I show that a collection of such oscillators, occupying the nodes of a generic network, can organize at the macroscopic level yielding noise-sustained spatiotemporal pattern with long-range correlations. Then, the same oscillators are organized in a directed unidirectional lattice with adjacent connections. The endogenous component of noise, coupled to a certain topology of the embedding space, seeds a coherent amplification of the signal across the lattice. Almost periodic oscillations emerge that I thoroughly investigate. Finally, I demonstrate that the coherent amplification of an imposed noisy perturbation destabilizes the synchronous state of an ensemble made of deterministic oscillators also when a conventional linear stability analysis would deem the system resilient to small external disturbances.