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Full Description
Non-linear stochastic systems are at the center of many engineering disciplines and progress in theoretical research had led to a better understanding of non-linear phenomena. This book provides information on new fundamental results and their applications which are beginning to appear across the entire spectrum of mechanics.
The outstanding points of these proceedings are Coherent compendium of the current state of modelling and analysis of non-linear stochastic systems from engineering, applied mathematics and physics point of view. Subject areas include: Multiscale phenomena, stability and bifurcations, control and estimation, computational methods and modelling.
For the Engineering and Physics communities, this book will provide first-hand information on recent mathematical developments. The applied mathematics community will benefit from the modelling and information on various possible applications.
Contents
I Multi-scale Phenomena.- Nonlinear Diffusion Approximation of Slow Motion.- Experiments on Large Fluctuations.- Stochastic Averaging.- Noise Sensitivity of Stochastic Resonance Mark Freidlin.- Stochastic Resonance.- Metastability of Diffusion Processes.- Stochastic Averaging Near Homoclinic Orbits via Singular Perturbations.- II Stability and Bifurcations.- Stochastic Internal Resonance.- Dynamics of Globally Coupled Noisy Excitable Elements.- Stochastic Duffing-van der Pol Oscillator.- Slow Sweep Through a Period-Doubling Cascade.- Multi-Scale Analysis of Noise-Sensitivity Near a Bifurcation.- Hopf Meets Hamilton Under Whitney's Umbrella.- Stochastic Stability of Two Coupled Oscillators in Resonance.- On Stabilizing the Double Oscillator by Mean Zero Noise.- Stability of a Two-Dimensional System.- III Control and Estimation.- The Distributed Nonlinear Stochastic World of Networks.- Noise effects in Nonlinear System Identification.- Structural Vibration Mitigation using Dissipative Smart Damping Devices.- Parameter Estimation for Stochastic Systems.- Control Against Large Deviation for Oscillatory Systems.- Parameter Analysis.- Stochastic Parameter Estimation of Non-Linear Systems.- Lyapunov Exponent and Stability of Controlled Systems.- IV Modeling.- From Earth's Ice Ages to Human Sensory Systems.- Response Spectral Densities.- Stochastic Lotka-Volterra Systems.- Dynamic Systems Driven By Poisson/Lévy White Noise.- Stochastic Dynamics of Friction-Induced Vibration in Disc Brakes.- Multiplicative Random Impulse Process.- Multiscale Impact Models: Multibody Dynamics and Wave Propagation.- Nonstationary Response of Nonlinear Systems.- Hilbert Spectral Description and Simulation.- V Computational Methods.- Random Vibrations of Riding Cars with Bilinear Damping.-Solutions of the First-Passage Problem by Importance Sampling.- Passive Fields and Particles.- Sample Point Uniformity Measures.- Kinks in a Stochastic PDE.- Path Integration as a Tool for Investigating Chaotic Behaviour.- Time-Varying Cardiovascular Oscillations.
