Analysis of Critical Phenomena in a Dynamic System Under the Influence of Random Perturbations

• Published in: Journal of mathematical sciences (New York, N.Y.) Vol. 272; no. 6; pp. 783 - 790
• Main Author: Firstova, N. M.
• Format: Journal Article
• Language: English
• Published: Cham Springer International Publishing 02.06.2023; Springer; Springer Nature B.V
• Subjects: Dynamical systems; Mathematics; Mathematics and Statistics; Noise intensity; Noise threshold; Oscillation modes; Perturbation; Random processes; Relaxation oscillations; Stochastic models; canard trajectory; white noise; differential equation; 35R60; critical phenomenon; random perturbation; stochastic sensitivity; stochastic equation; 35Q92
• ISSN: 1072-3374; 1573-8795
• DOI: 10.1007/s10958-023-06472-4

The paper is devoted to the study of stochastic models of an electrochemical reaction with a perturbation described by a generalized white-noise random process. Noise-induced transitions are analyzed, the influence of external perturbations on limit cycles is examined, and the sensitivity of the cycle to noise was found. The dependence of the threshold value of the noise intensity on the control parameter of the system is established. The critical value of the noise intensity at which small-amplitude oscillations turn into mixed-type oscillations is obtained. The critical value of noise corresponding to the transition from canard trajectories to relaxation oscillations in the model is found. It is shown that an increase in the intensity of random perturbations can lead to significant changes of oscillation modes of the model up to their destruction.