Non normal amplification of stochastic quasi-cycles

TL;DR

This paper investigates how non-normal reactivity influences the amplification of stochastic quasi-cycles in a two-species excitatory-inhibitory model, revealing that system structure and thermodynamics affect oscillation magnification.

Contribution

It demonstrates the role of non-normal reactivity in amplifying stochastic oscillations and links thermodynamic properties to system reactivity and phase space exploration.

Findings

Amplification increases as the system approaches Hopf bifurcation.

Non-normal reactivity correlates with oscillation amplification.

Thermodynamics facilitates out-of-equilibrium phase space exploration.

Abstract

Stochastic quasi-cycles for a two species model of the excitatory-inhibitory type, arranged on a triangular loop, are studied. By increasing the strength of the inter-nodes coupling, one moves the system towards the Hopf bifurcation and the amplitude of the stochastic oscillations are 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.