Competitive Threshold Linear Networks: limit cycles and their response to periodic inputs

ANDREA L. BEL; HORACIO G. ROTSTEIN; WALTER A. REARTES

Digital Edition

Congreso; 2020 International Conference on Mathematical Neuroscience; 2020

Póster Abstract:We study oscillatory properties of the so-called competitive threshold-linear networks (TLNs) where all connections between nodes are inhibitory. TLN are non-smooth models where the contribution of the connectivity terms is linear above some threshold value (typically zero), while the network is disconnected below it. Despite their simplicity, these networks produce complex behavior including multistability, periodic, quasi-periodic and chaotic solutions. We demonstrate the existence of periodic solutions and analyze how their attributes (amplitude and frequency) are affected by changes in (i) the time scale of each node, (ii) the number of nodes in the network, and (iii) the strength of the inhibitory connections. In addition, we investigate the response of these networks to external oscillatory inputs added to one of the nodes and, by defining a Poincaré map, we numerically study the response (entrainment) properties of the networks.