39 research outputs found

    Stability index for orbits with nonvanishing diffusion

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    The known concepts of Lyapunov exponent, moment Lyapunov exponents, and stability index for stationary points of stochastic systems are carried over for invariant orbits with nonvanishing diffusion. The obtained general results are applied to investigating stochastic stability and stabilization of orbits on the plane. (orig.)Available from TIB Hannover: RR 5549(359)+a / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekSIGLEDEGerman

    The probability approach to numerical solution of nonlinear parabolic equations

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    A number of new layer methods for solving semilinear parabolic equations and reaction-diffusion systems is derived by using probabilistic representations of their solutions. These methods exploit the ideas of weak sense numerical integration of stochastic differential equations. In spite of the probabilistic nature these methods are nevertheless deterministic. A convergence theorem is proved. Some numerical tests are presented. (orig.)Available from TIB Hannover: RR 5549(380) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekSIGLEDEGerman

    Evaluation of moment Lyapunov exponents for second order linear autonomous SDE

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    Deterministic methods for evaluation of moment Lyapunov exponents are derived for two-dimensional systems with non-degenerate noise. (orig.)Available from TIB Hannover: RR 5549(216)+a / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekSIGLEDEGerman
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