How additive noise generates a phantom attractor in a model with cubic nonlinearity / Bashkirtseva Irina,Ryashko Lev // PHYSICS LETTERS A. - 2016. - V. 380, l. 41. - P. 3359-3365.

ISSN/EISSN:

0375-9601 / 1873-2429

Type:

Article

Abstract:

Two-dimensional nonlinear system forced by the additive noise is studied. We show that an increasing noise shifts random states and localizes them in a zone far from deterministic attractors. This phenomenon of the generation of the new ``phantom{''} attractor is investigated on the base of probability density functions, mean values and variances of random states. We show that increasing noise results in the qualitative changes of the form of pdf, sharp shifts of mean values, and spikes of the variance. To clarify this phenomenon mathematically, we use the fast-slow decomposition and averaging over the fast variable. For the dynamics of the mean value of the slow variable, a deterministic equation is derived. It is shown that equilibria and the saddle-node bifurcation point of this deterministic equation well describe the stochastic phenomenon of ``phantom{''} attractor in the initial two-dimensional stochastic system. (C) 2016 Elsevier B.V. All rights reserved.

Author keywords:

Random disturbances; Stochastic bifurcations; Basins of attraction; Fast-slow decomposition; Averaging HOPF-BIFURCATION; STOCHASTIC RESONANCE; COHERENCE RESONANCE; SYSTEM; TRANSITIONS; CHAOS

DOI:

10.1016/j.physleta.2016.08.001

Web of Science ID:

ISI:000383303400008

Соавторы в МНС:

Другие поля

Поле	Значение
Month	OCT 7
Publisher	ELSEVIER SCIENCE BV
Address	PO BOX 211, 1000 AE AMSTERDAM, NETHERLANDS
Language	English
EISSN	1873-2429
Keywords-Plus	HOPF-BIFURCATION; STOCHASTIC RESONANCE; COHERENCE RESONANCE; SYSTEM; TRANSITIONS; CHAOS
Research-Areas	Physics
Web-of-Science-Categories	Physics, Multidisciplinary
Author-Email	lev.ryashko@urfu.ru
Funding-Acknowledgement	Russian Science Foundation {[}16-11-10098]
Funding-Text	The work was supported by Russian Science Foundation (N 16-11-10098).
Number-of-Cited-References	25
Usage-Count-Last-180-days	1
Usage-Count-Since-2013	4
Journal-ISO	Phys. Lett. A
Doc-Delivery-Number	DW0AN