Extreme-value statistics of networks with inhibitory and excitatory couplings
Sanjiv Kumar Dwivedi and Sarika Jalan
Accepted
Inspired by the importance of inhibitory and excitatory couplings in brain, we analyze largest eigenvalue statistics of random networks incorporating such features. We find that the largest real part of eigenvalues of network, which accounts for stability of 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 largest eigenvalue remain somewhat robust against increase in system size, but reflect a strong dependence on number of connections indicating that systems having more interactions among its constituents are likely to be more unstable.