Non-normal amplification of stochastic quasicycles

Stochastic quasicycles for a two-species model of the excitatory-inhibitory type, arranged on a triangular loop, are studied. By increasing the strength of the internode coupling, one moves the system towards the Hopf bifurcation, and the amplitude of the stochastic oscillations is consequently magnified. When the system is instead constrained to evolve on specific manifolds, selected so as to return a constant rate of deterministic damping for the perturbations, the observed amplification correlates with the degree of non-normal reactivity, here quantified by the numerical abscissa. The thermodynamics of the reactive loop is also investigated and the degree of inherent reactivity shown to facilitate the out-of-equilibrium exploration of the available phase space.