Stochastic sensitivity analysis of noise-induced order-chaos transitions in discrete-time systems with tangent and crisis bifurcations

Irina Bashkirtseva and Lev Ryashko

Physica A: Statistical Mechanics and its Applications, 2017, vol. 467, issue C, 573-584

Abstract: We study noise-induced order-chaos transitions in discrete-time systems with tangent and crisis bifurcations. To study these transitions parametrically, we suggest a generalized mathematical technique using stochastic sensitivity functions and confidence domains for randomly forced equilibria, cycles, and chaotic attractors. This technique is demonstrated in detail for the simple one-dimensional stochastic system, in which points of crisis and tangent bifurcations are borders of the order window lying between two chaotic parametric zones. A stochastic phenomenon of the extension and shift of this window towards crisis bifurcation point, under increasing noise, is presented and analyzed. Shifts of borders of this order window are found as functions of the noise intensity. By our analytical approach based on stochastic sensitivity functions, we construct a parametric diagram of chaotic and regular regimes for the stochastically forced system.

Keywords: Discrete systems; Random disturbances; Stochastic sensitivity functions; Chaos (search for similar items in EconPapers)
Date: 2017
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0378437116306732
Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:467:y:2017:i:c:p:573-584

DOI: 10.1016/j.physa.2016.09.048

Access Statistics for this article

Physica A: Statistical Mechanics and its Applications is currently edited by K. A. Dawson, J. O. Indekeu, H.E. Stanley and C. Tsallis

More articles in Physica A: Statistical Mechanics and its Applications from Elsevier
Bibliographic data for series maintained by Catherine Liu ().