Stochastic sensitivity of systems driven by colored noise

We study a response of the general nonlinear dynamic system to the colored noise. A stochastic sensitivity analysis of equilibria forced by small exponentially-correlated Gaussian noise is carried out. For the stochastic sensitivity matrix of the equilibrium, a system of matrix equations is derived, and explicit solution is found in 2D case. Applying these theoretical results, we study a response of FitzHugh-Nagumo model to colored noise. We analyze how dispersion of random states near the deterministic equilibrium depends on the characteristic time of the power-limited colored noise. The effect of the colored-noise-induced excitability is discussed.