Retrieval of the quasi-optimal signal activating the excitable systems using preceding noise samples

We propose a method for obtaining a signal leading to the activation of an excitable dynamic system for a signal energy close to minimal. The efficiency of this technique, which is based on recording and processing of noise samples preceding the activation was tested using the FitzHugh–Nagumo, Hodgkin–Huxley, and Luo–Rudy models as examples. It is shown that the proposed procedure gives good results when the noise intensity is smaller than or close to the system activation energy. The criteria of “low” and “high” intensities of fluctuations are proposed. The method of increasing the stability of the excitable system with respect to “low-intensity” noise by filtering or another way of suppression of the spectral components that make the main contribution to the energetically optimal activation signal is justified. The relation between eigenvalues of the linearized system of the Hamiltonian equations, which describe the optimal trajectories and the activation signal, and eigenvalues of the excitable system linearized near the initial equilibroum state is found.