We reconstruct a nonlinear stochastic model of the cardiorespiratory interaction in terms of a set of polynomial basis functions representing the nonlinear force governing system oscillations. The strength and direction of coupling and noise intensity are simultaneously inferred from a univariate blood pressure signal. Our new inference technique does not require extensive global optimization, and it is applicable to a wide range of complex dynamical systems subject to noise.

A different form of stochastic resonance, in which the weak periodic force is applied multiplicatively (rather than additively) in the noise, has been investigated for a Brownian particle moving in a double-well potential. A regular periodic signal whose amplitude increases sharply with increasing noise intensity is shown to arise when the potential is asymmetric.$-— The experimental measurements are in good agreement with a theoretical analysis.

Topologies of invariant manifolds and optimal trajectories are investigated in stochastic continuous systems and maps. A topological method is introduced that simplifies the solution of boundary value problems: The activation energy is calculated as a function of a set of parameters characterizing the initial conditions of the escape path. The method is applied explicitly to compute the optimal escape path and the activation energy for a variety of dynamical systems and maps.