Slaving principle for stochastic differential equations with additive and multiplicative noise and for discrete noisy maps

Haken, Hermann; Wunderlin, A.

doi:10.1007/bf01441301

Cited by 52 publications

(22 citation statements)

References 2 publications

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“…In this connection, the detailed treatment of the slaving principle inc1uding noise, which was recently presented by Haken and Wunderlin (1982), is worth mentioning, although they treat the problem in a physical or mathematical context rather different from the present one. 5.5 -7, we illustrate how the slaving principle works even when fluctuating forces are present.…”

Section: Synchronization As a Mode Of Self-organizationmentioning

confidence: 99%

Chemical Oscillations, Waves, and Turbulence

Kuramoto

1984

Springer Series in Synergetics

6,195

6,896

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Section: Synchronization As a Mode Of Self-organizationmentioning

confidence: 99%

Chemical Oscillations, Waves, and Turbulence

Kuramoto

1984

Springer Series in Synergetics

6,195

6,896

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“…To model these effects has become of great interest since the increasing technological importance of piezoelectric materials, in particular as electromechanical actuators and sensors [17,18,19]. Key contributions for a treatment of such nonlinear effects using the technique of Green's functions had been presented by Wunderlin and Haken [20,21].…”

Section: Resultsmentioning

confidence: 99%

“…As a consequence the terms (eqs. (21), (22)) t b4 = t c4 = 0 (100) are vanishing. Thus the determinant f (eq.…”

Section: Appendixmentioning

confidence: 99%

Calculation of the electroelastic Green’s function of the hexagonal infinite medium

Michelitsch

1997

Z. Phys. B

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The electroelastic 4 × 4 Green's function of a piezoelectric hexagonal (transversely isotropic) infinitely extended medium is calculated explicitely in closed compact form (eqs. (73) ff. and (88) ff., respectively) by using residue calculation. The results can also be derived from Fredholm's method [2]. In the case of vanishing piezoelectric coupling the derived Green's function coincides with two well known results: Kröner's expressions for the elastic Green's function tensor [4] is reproduced and the electric part then coincides with the electric potential (solution of Poisson equation) which is caused by a unit point charge.The obtained electroelastic Green's function is useful for the calculation of the electroelastic Eshelby tensor [16].

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“…Although provably exact for the simple case described here, taking limits in a brusque fashion like this is generally inadvisable when dealing with stochastic dynamical systems. Nonetheless, the method is quite powerful and the same basic principle has been developed to various levels of rigour and generality by many authors, most notably Haken (Haken and Wunderlin, 1982).…”

Section: Discussionmentioning

confidence: 99%

Dimension reduction for stochastic dynamical systems forced onto a manifold by large drift: a constructive approach with examples from theoretical biology

Parsons¹,

Rogers²

2017

J. Phys. A: Math. Theor.

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Systems composed of large numbers of interacting agents often admit an effective coarsegrained description in terms of a multidimensional stochastic dynamical system, driven by small-amplitude intrinsic noise. In applications to biological, ecological, chemical and social dynamics it is common for these models to posses quantities that are approximately conserved on short timescales, in which case system trajectories are observed to remain close to some lower-dimensional subspace. Here, we derive explicit and general formulae for a reduced-dimension description of such processes that is exact in the limit of small noise and well-separated slow and fast dynamics. The Michaelis-Menten law of enzymecatalyzed reactions, and the link between the Lotka-Voltera and Wright-Fisher processes are explored as a simple worked examples. Extensions of the method are presented for infinite dimensional systems and processes coupled to non-Gaussian noise sources.1 A complementary branch of theory exists dealing with the relaxation of this assumption, see (Arnold and Imkeller, 1998;Roberts, 2008) for starting points in the literature.

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Slaving principle for stochastic differential equations with additive and multiplicative noise and for discrete noisy maps

Cited by 52 publications

References 2 publications

Chemical Oscillations, Waves, and Turbulence

Chemical Oscillations, Waves, and Turbulence

Calculation of the electroelastic Green’s function of the hexagonal infinite medium

Dimension reduction for stochastic dynamical systems forced onto a manifold by large drift: a constructive approach with examples from theoretical biology

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