Stochastic sensitivity analysis of noise-induced excitement in a prey–predator plankton system

Generation of stochastic mixed-mode oscillations in a pair of VDP oscillators with direct-indirect coupling

Environmental noise can lead to complex stochastic dynamical behavior in nonlinear systems. In this paper, we studied the phenomenon of a pair of Van der Pol (VDP) oscillators with direct-indirect coupling affected by Gaussian white noise. That is to say, a noise-induced equilibrium transition oscillation was observed in three types of different parameter regions, where the deterministic system had two kinds of stable equilibrium points. Meanwhile, with the noise intensity increasing, we found that the stochastic system will constantly switch between two stable equilibrium points. To analyze the stochastic behavior, we used the stochastic sensitivity equation and confidence ellipse method. When the confidence ellipsoid crossed the boundary of the attraction basin of the equilibrium point, the system entered into the state of stochastic mixed-mode oscillations, which was consistent with the simulation results.

Sensitivity analysis of the noise-induced oscillatory multistability in Higgins model of glycolysis

A phenomenon of the noise-induced oscillatory multistability in glycolysis is studied. As a basic deterministic skeleton, we consider the two-dimensional Higgins model. The noise-induced generation of mixed-mode stochastic oscillations is studied in various parametric zones. Probabilistic mechanisms of the stochastic excitability of equilibria and noise-induced splitting of randomly forced cycles are analysed by the stochastic sensitivity function technique. A parametric zone of supersensitive Canard-type cycles is localized and studied in detail. It is shown that the generation of mixed-mode stochastic oscillations is accompanied by the noise-induced transitions from order to chaos.

Analysis of the noise-induced regimes in Ricker population model with Allee effect via confidence domains technique

We consider a discrete-time Ricker population model with the Allee effect under the random disturbances. It is shown that noise can cause various dynamic regimes, such as stable stochastic oscillations around the equilibrium, noise-induced extinction, and a stochastic trigger. For the parametric analysis of these regimes, we develop a method based on the investigation of the dispersions and arrangement of confidence domains. Using this method, we estimate threshold values of the noise generating such regimes.