Stochastic differential equations

L Arnold - New York, 1974 - books.google.com
... These objects are provided by Oseledec's multiplicative ergodic theorem and its generalizations.
Now the door is open for stochastic stability, stochastic invariant manifolds (in particular stochastic
center manifolds), stochastic bifurcation theory, stochastic normal forms, etc. ...
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Random attractors-General properties, existence and applications to stochastic bifurcation theory

KR Schenk-Hoppé - Discrete and Continuous Dynamical Systems, 1998 - aimsciences.org
Abstract. This paper is concerned with attractors of randomly perturbed dynamical systems,
called random attractors. The framework used is provided by the theory of random
dynamical systems. We first define, analyze, and prove existence of random attractors. ...
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Recent progress in stochastic bifurcation theory

L Arnold - IUTAM Symposium on Nonlinearity and Stochastic …, 2001 - Springer
Abstract We report on new results in stochastic bifurcation theory obtained in 1997 and
1998. These include:(i) a rather complete classification of the one-dimensional case by
Crauel, Imkeller and Steinkamp,(ii) new insight into the stochastic Hopf bifurcation (made ...
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[BOOK][B] Elements of applied bifurcation theory

YA Kuznetsov - 2013 - books.google.com
... 45. Marsden/McCracken: Hopf Bifurcation and Its Applications ... Davies: Integral Transforms and
Their Applications, 2nd ed. Kushner/Clark: Stochastic Approximation Methods for ...
Guckenheimer/Holmes: Nonlinear Oscillations, Dynamical Systems and Bifurcations of Vector ...
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Stochastic bifurcation

NS Namachchivaya - Applied Mathematics and Computation, 1990 - Elsevier
... Stochastic Differential EquationsSpringer-Verlag, New York (1972). 34; M. Golubitsky, DG
Schaeffer; Singularities and Groups in Bifurcation Theory, Vol. 1Springer-Verlag, New York (1985).
35; R. Graham; Hopf bifurcations with fluctuating control parameter. Phys. Rev. ...
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[BOOK][B] Singularities and groups in bifurcation theory

M Golubitsky, I Stewart - 2012 - books.google.com
... I. . Marsden/McCracken: Hopf Bifurcation and Its Applications. ... Davies: Integral Transforms and
Their Applications, 2nd ed. Kushner/Clark: Stochastic Approximation Methods for ...
Guckenheimer/Holmes: Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector ...
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[BOOK][B] Stochastic bifurcation: instructive examples in dimension one

L Arnold, P Boxler - 1992 - Springer
... It tells us that the most simple bifurcations of equilibria in dimension one appear in ... The examples
below support our belief that the proper level to discuss stochastic bifurcation is the ... and more
general) measures: New invariant measures are expected to bifurcate from reference ...
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[BOOK][B] Elementary stability and bifurcation theory

G Iooss, DD Joseph - 2012 - books.google.com
... Chung: Elementary Probability Theory with Stochastic Processes. ... X.2 Direct Computation of
Asymptotically Quasi-Periodic Solutions Which Bifurcate at Rational Points ... xii Contents CHAPTER
XI Secondary Subharmonic and Asymptotically Quasi-Periodic Bifurcation of Periodic ...
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[BOOK][B] Acoustic and electromagnetic equations: integral representations for harmonic problems

JC Nédélec - 2001 - books.google.com
... Theory, Vol. I. 19. Marsden/McCracken: Hopf Bifurcation and Its 47. Applications. 20. ... 26.
Kushner/Clark: Stochastic Approximation 55. ... Guckenheimer/Holmes: Nonlinear Oscillations,
Dynamical Systems, and Bifurcations of Vector Fields. Ockendon/Taylor: In viscid Fluid Flows. ...
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[BOOK][B] Self-organization in nonequilibrium systems

G Nicolis, I Prigogine - 1977 - tocs.ulb.tu-darmstadt.de
... Qualitative Properties of Dissipative Structures in Vicinity of First Bifurcation; 115 7.9. Successive
Instabilities and Secondary Bifurcations, 120 7.10. ... Bifurcation of Time-periodic Dissipative
Structures, 140 7.13. ... PART III. STOCHASTIC METHODS 9. General Comments 223 9.1. ...
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