Analysis of noise-induced transitions in a generalized logistic model with delay near Neimark–Sacker bifurcation

Abstract

We consider an effect of random disturbances on the generalized logistic model with delay in mono- and bistable regimes near Neimark–Sacker bifurcation. Noise-induced transitions between coexisting attractors, and between separate parts of the unique attractor, are studied. We suggest a semi-analytical approach that combines a geometric analysis of the mutual arrangement of attractors, their basins of attraction, and corresponding confidence domains found by the stochastic sensitivity functions technique. Constructive abilities of this approach are demonstrated for the generalized logistic model with delay.

Stochastic sensitivity analysis of noise-induced transitions in a biochemical model with birhythmicity

“…This extended model possesses a coexistence of the equilibrium and cycle, or two stable cycles (birhythmicity). The aim of the present paper is to study effects of noise in this bistable model and show how stochastic phenomena can be investigated with the help of the analytical approach based on the stochastic sensitivity technique [54][55][56].…”

Noise‐induced transformations in corporate dynamics of coupled chaotic oscillators

“…Our analytical approach is based on the stochastic sensitivity technique and confidence domains approximating dispersion of random states around deterministic attractors. 46,47 Mathematical details of this general technique are briefly discussed in Appendix C1. In Section 2, we give an overview of deterministic corporate dynamics of coupled chaotic oscillators depending on the increasing strength of coupling and discuss the variety of attractors and bifurcations.…”

Variability and effect of noise on the corporate dynamics of coupled oscillators

“…A mathematical analysis of these phenomena requires analysing the saddle-node, period-doubling, crisis, and Neimark-Sacker bifurcations [8,9,10]. A presence of inevitable noise can cause another, more complicated, regimes [11,12,13,14,15,16].…”