Bumps and oscillons in networks of spiking neurons

0546902 - ÚI 2022 US eng J - Článek v odborném periodiku
Schmidt, Helmut - Avitabile, D.
Bumps and oscillons in networks of spiking neurons.
Chaos. Roč. 30, č. 3 (2020). ISSN 1054-1500. E-ISSN 1089-7682
Klíčová slova: wave-propagation failure * conductance-based models * neural field equation * localized structures * attractor dynamics * ladders * snakes * patterns * systems * snaking
Impakt faktor: 3.642, rok: 2020

We study localized patterns in an exact mean-field description of a spatially extended network of quadratic integrate-and-fire neurons. We investigate conditions for the existence and stability of localized solutions, so-called bumps, and give an analytic estimate for the parameter range, where these solutions exist in parameter space, when one or more microscopic network parameters are varied. We develop Galerkin methods for the model equations, which enable numerical bifurcation analysis of stationary and time-periodic spatially extended solutions. We study the emergence of patterns composed of multiple bumps, which are arranged in a snake-and-ladder bifurcation structure if a homogeneous or heterogeneous synaptic kernel is suitably chosen. Furthermore, we examine time-periodic, spatially localized solutions (oscillons) in the presence of external forcing, and in autonomous, recurrently coupled excitatory and inhibitory networks. In both cases, we observe period-doubling cascades leading to chaotic oscillations.
Trvalý link: http://hdl.handle.net/11104/0323287