title: Extreme-value statistics of networks with inhibitory and excitatory couplings.
abstract: Inspired by the importance of inhibitory and excitatory couplings in the brain, we analyze the largest eigenvalue statistics of random networks incorporating such features. We find that the largest real part of eigenvalues of a network, which accounts for the stability of an underlying system, decreases linearly as a function of inhibitory connection probability up to a particular threshold value, after which it exhibits rich behaviors with the distribution manifesting generalized extreme value statistics. Fluctuations in the largest eigenvalue remain somewhat robust against an increase in system size but reflect a strong dependence on the number of connections, indicating that systems having more interactions among its constituents are likely to be more unstable.
authors.affiliation: Complex Systems Lab, Indian Institute of Technology Indore, M-Block, IET-DAVV Campus Khandwa Road, Indore 452017, India.
authors.forename: Sanjiv Kumar
authors.initials: SK
authors.lastname: Dwivedi
authors.forename: Sarika
authors.initials: S
authors.lastname: Jalan
mesh_terms: D001921:Brain / Q000166:cytology / Q000502:physiology*; D008959:Models, Neurological; D009415:Nerve Net / Q000166:cytology / Q000502:physiology*; D013569:Synapses / Q000502:physiology