How additive noise forms and shifts phantom attractors in slow-fast systems

被引：10

作者：

Bashkirtseva, Irina ^{[1
]}

Ryashko, Lev ^{[1
]}

机构：

[1] Ural Fed Univ, Inst Nat Sci & Math, Lenina 51, Ekaterinburg, Russia

来源：

JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL | 2020年 / 53卷 / 37期

基金：

俄罗斯科学基金会;

关键词：

noise; slow-fast systems; phantom attractors; freezing and averaging; stochastic shifts;

D O I：

10.1088/1751-8121/aba76f

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

We present a peculiar phenomenon of the formation and shift of a localized random distribution in slow-fast systems forced by additive white Gaussian noise. Location of such 'phantom' attractors in zones far from deterministic attractors is theoretically analysed by the method of freezing and averaging. This method is applied to the analysis of the Goldbeter enzymatic model and FitzHugh-Nagumo neural model, in which noise-induced formation and shifts of 'phantom' attractors are detected.

引用

页数：10

共 28 条

[1] Anomalous stochastic dynamics induced by the slip-stick friction and leading to phantom attractors [J].

Alexandrov, D., V ;

Bashkirtseva, I. A. ;

Ryashko, L. B. .

PHYSICA D-NONLINEAR PHENOMENA, 2019, 399 :153-158

[2]

Anishchenko V S, 1988, NONLINEAR DYNAMICS C

[3]

[Anonymous], 1984, Noise-Induced Transitions in Physics, Chemistry, and Biology

[4]

Arnold L, 1995, LECT NOTES MATH, V1609, P1

[5]

Arnold L, 1992, DIFFUSION PROCESSES, V2

[6] Analysis of nonlinear stochastic oscillations in the biochemical Goldbeter model [J].

Bashkirtseva, Irina ;

Ryashko, Lev ;

Zaitseva, Svetlana .

COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION, 2019, 73 :165-176

[7] How additive noise generates a phantom attractor in a model with cubic nonlinearity [J].

Bashkirtseva, Irina ;

Ryashko, Lev .

PHYSICS LETTERS A, 2016, 380 (41) :3359-3365

[8] Stochastic bifurcations caused by multiplicative noise in systems with hard excitement of auto-oscillations [J].

Bashkirtseva, Irina ;

Ryazanova, Tatyana ;

Ryashko, Lev .

PHYSICAL REVIEW E, 2015, 92 (04)

[9] Bifurcations of one-dimensional stochastic differential equations [J].

Crauel, H ;

Imkeller, P ;

Steinkamp, M .

STOCHASTIC DYNAMICS, 1999, :27-47

[10] IMPULSES AND PHYSIOLOGICAL STATES IN THEORETICAL MODELS OF NERVE MEMBRANE [J].

FITZHUGH, R .

BIOPHYSICAL JOURNAL, 1961, 1 (06) :445-&

← 1 2 3 →