Beschreibung
Focusing on the mathematical description of stochastic dynamics in discrete as well as in continuous time, this book investigates such dynamical phenomena as perturbations, bifurcations and chaos. It also introduces new ideas for the exploration of infinite dimensional systems, in particular stochastic partial differential equations. Example applications are presented from biology, chemistry and engineering, while describing numerical treatments of stochastic systems.
Inhaltsverzeichnis
Stability along Trajectories at a Stochastic Bifurcation Point.- Bifurcations of One-Dimensional Stochastic Differential Equations.- P-Bifurcations in the Noisy Duffing-van der Pol Equation.- The Stochastic Brusselator: Parametric Noise Destroys Hopf Bifurcation.- Numerical Approximation of Random Attractors.- Random Hyperbolic Systems.- Some Questions in Random Dynamical Systems Involving Real Noise Processes.- Topological, Smooth, and Control Techniques for Perturbed Systems.- Perturbation Methods for Lyapunov Exponents.- The Lyapunov Exponent of the Euler Scheme for Stochastic Differential Equations.- Towards a Theory of Random Numerical Dynamics.- Canonical Stochastic Differential Equations based on Levy Processes and their Supports.- On the Link between Fractional and Stochastic Calculus.- Asymptotic Curvature for Stochastic Dynamical Systems.- Stochastic Analysis on (Infinite-Dimensional) Product Manifolds.- Evolutionary Dynamics in Random Environments.- Microscopic and Mezoscopic Models for Mass Distributions.
Autorenporträt
InhaltsangabeStability Along Trajectories at a Stochastic Bifurcation Point.- Bifurcations of One-Dimensional Stochastic Differential Equations.- P-Bifurcations in the Noisy Duffing-van der Pol Equation.- The Stochastic Brusselator: Parametric Noise Destroys Hoft Bifurcation.- Numerical Approximation of Random Attractors.- Random Hyperbolic Systems.- Some Questions in Random Dynamical Systems Involving Real Noise Processes.- Topological, Smooth, and Control Techniques for Perturbed Systems.- Perturbation Methods for Lyapunov Exponents.- The Lyapunov Exponent of the Euler Scheme for Stochastic Differential Equations.- Towards a Theory of Random Numerical Dynamics.- Canonical Stochastic Differential Equations based on Lévy Processes and Their Supports.- On the Link Between Fractional and Stochastic Calculus.- Asymptotic Curvature for Stochastic Dynamical Systems.- Stochastic Analysis on (Infinite-Dimensional) Product Manifolds.- Evolutionary Dynamics in Random Environments.- Microscopic and Mezoscopic Models for Mass Distributions.
