title: Analysis of noise-induced transitions from regular to chaotic oscillations in the Chen system.
abstract: The stochastically perturbed Chen system is studied within the parameter region which permits both regular and chaotic oscillations. As noise intensity increases and passes some threshold value, noise-induced hopping between close portions of the stochastic cycle can be observed. Through these transitions, the stochastic cycle is deformed to be a stochastic attractor that looks like chaotic. In this paper for investigation of these transitions, a constructive method based on the stochastic sensitivity function technique with confidence ellipses is suggested and discussed in detail. Analyzing a mutual arrangement of these ellipses, we estimate the threshold noise intensity corresponding to chaotization of the stochastic attractor. Capabilities of this geometric method for detailed analysis of the noise-induced hopping which generates chaos are demonstrated on the stochastic Chen system.
authors.affiliation: Department of Mathematics, Ural State University, Lenina, 51, Ekaterinburg, Russia.
authors.forename: Irina
authors.initials: I
authors.lastname: Bashkirtseva
authors.forename: Guanrong
authors.initials: G
authors.lastname: Chen
authors.forename: Lev
authors.initials: L
authors.lastname: Ryashko