Stationary solutions of linear stochastic delay differential equations: Applications to biological systems

被引：95

作者：

Frank, TD ^{[1
]}

Beek, PJ ^{[1
]}

机构：

[1] Vrije Univ Amsterdam, Fac Human Movement Sci, NL-1081 BT Amsterdam, Netherlands

来源：

PHYSICAL REVIEW E | 2001年 / 64卷 / 02期

关键词：

D O I：

10.1103/PhysRevE.64.021917

中图分类号：

O35 [流体力学]; O53 [等离子体物理学];

学科分类号：

070204 ; 080103 ; 080704 ;

摘要：

Recently, Kuchler and Mensch [Stochastics Stochastics Rep. 40, 23 (1992)] derived exact stationary probability densities for linear stochastic delay differential equations. This paper presents an alternative derivation of these solutions by means of the Fokker-Planck approach introduced by Guillouzic [Phys. Rev. E 59, 3970 (1999); 61, 4906 (2000)]. Applications of this approach, which is argued to have greater generality, are discussed in the context of stochastic models for population growth and tracking movements.

引用

页数：12

共 69 条

[11] Noise-induced transitions in human postural sway [J].

Eurich, CW ;

Milton, JG .

PHYSICAL REVIEW E, 1996, 54 (06) :6681-6684

[12]

Fender D.H., 1971, CONTROL EYE MOVEMENT, P539

[13] Impacts of noise on a field theoretical model of the human brain [J].

Frank, TD ;

Daffertshofer, A ;

Beek, PJ ;

Haken, H .

PHYSICA D-NONLINEAR PHENOMENA, 1999, 127 (3-4) :233-249

[14] Multivariate Ornstein-Uhlenbeck processes with mean-field dependent coefficients: Application to postural sway [J].

Frank, T.D. ;

Daffertshofer, A. ;

Beek, P.J. .

Physical Review E - Statistical, Nonlinear, and Soft Matter Physics, 2001, 63 (1 I) :011905-011901

[15] Towards a comprehensive theory of brain activity: Coupled oscillator systems under external forces [J].

Frank, TD ;

Daffertshofer, A ;

Peper, CE ;

Beek, PJ ;

Haken, H .

PHYSICA D-NONLINEAR PHENOMENA, 2000, 144 (1-2) :62-86

[16]

FRAUENTHAL JC, 1984, POPULATION BIOL, P9

[17]

Gardiner C. W, 1997, HDB STOCHASTIC METHO

[18] Steady-state movement-related cortical potentials: A new approach to assessing cortical activity associated with fast repetitive finger movements [J].

Gerloff, C ;

Toro, C ;

Uenishi, N ;

Cohen, LG ;

Leocani, L ;

Hallett, M .

ELECTROENCEPHALOGRAPHY AND CLINICAL NEUROPHYSIOLOGY, 1997, 102 (02) :106-113

[19] VOLTERRA AND OTHER NONLINEAR MODELS OF INTERACTING POPULATIONS [J].

GOEL, NS ;

MAITRA, SC ;

MONTROLL, EW .

REVIEWS OF MODERN PHYSICS, 1971, 43 (02) :231-+

[20] NUMERICAL-INTEGRATION OF STOCHASTIC DIFFERENTIAL-EQUATIONS [J].

GREINER, A ;

STRITTMATTER, W ;

HONERKAMP, J .

JOURNAL OF STATISTICAL PHYSICS, 1988, 51 (1-2) :95-108

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