IUTAM Symposium on Nonlinear Stochastic Dynamics: Proceedings of the IUTAM Symposium held in Monticello, Illinois, U.S.A., 26–30 August 2002

✍ Scribed by Ludwig Arnold (auth.), N. Sri Namachchivaya, Y. K. Lin (eds.)

• Publisher: Springer Netherlands
• Year: 2003
• Tongue: English
• Leaves: 469
• Series: Solid Mechanics and Its Applications 110
• Edition: 1
• Category: Library

✦ Synopsis

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.

✦ Table of Contents

Front Matter....Pages i-xix
Front Matter....Pages 1-3
Linear and Nonlinear Diffusion Approximation of the Slow Motion in Systems with Two Time Scales....Pages 5-18
Experiments on Large Fluctuations....Pages 19-28
Stochastic Averaging: Some Methods and Applications....Pages 29-41
Noise Sensitivity of Stochastic Resonance and Other Problems Related to Large Deviations....Pages 43-55
The Reduction of Potential Diffusions to Finite State Markov Chains and Stochastic Resonance....Pages 57-69
Metastability of Diffusion Processes....Pages 71-81
Stochastic Averaging Near Homoclinic Orbits Via Singular Perturbations....Pages 83-94
Front Matter....Pages 95-96
Stochastic Stability of Coupled Oscillators in Internal Resonance....Pages 97-110
Dynamics of Globally Coupled Noisy Excitable Elements: The Fitzhugh-Nagumo Case....Pages 111-124
Lyapunov Exponents and Stability for the Stochastic Duffing-Van der Pol Oscillator....Pages 125-135
Slow Sweep Through a Period-Doubling Cascade: An Example of a Noisy Parametric Bifurcation....Pages 137-146
Multi-Scale Analysis of Noise-Sensitivity Near a Bifurcation....Pages 147-156
Hopf Meets Hamilton Under Whitney’s Umbrella....Pages 157-165
Stochastic Stability of Two Coupled Oscillators in Resonance....Pages 167-177
On Stabilizing the Double Oscillator by Mean Zero Noise....Pages 179-190
Stability of a Two-Dimensional System Under Combined Harmonic and Real Noise Parametric Excitations....Pages 191-201
Front Matter....Pages 203-204
The Distributed Nonlinear Stochastic World of Networks....Pages 205-216
Noise Effects in Nonlinear System Identification with Applications to Structures and Systems with Viscoelastic Elements....Pages 217-225
Structural Vibration Mitigation Using Dissipative Smart Damping Devices....Pages 227-236
On Parameter Estimation for Linear and Nonlinear Stochastic Systems....Pages 237-245
Front Matter....Pages 203-204
Control Against Large Deviation for Oscillatory Systems....Pages 247-256
On Parameter Analysis of the Differential Model of Hysteresis....Pages 257-268
Stochastic Parameter Estimation of Non-Linear Systems....Pages 269-278
Lyapunov Exponent and Stability of Optimally Controlled Quasi Partially Integrable Hamiltonian Systems....Pages 279-288
Front Matter....Pages 289-290
Stochastic Resonance: From Earth’s Ice Ages to Human Sensory Systems....Pages 291-298
Response Spectral Densities of Systems Under Both Additive and Multiplicative Excitations....Pages 299-306
Stochastic Lotka-Volterra System....Pages 307-317
Dynamic Systems Driven by Poisson/Lévy White Noise....Pages 319-330
Stochastic Dynamics of Friction- Induced Vibration in Disc Brakes....Pages 331-342
Dynamical Systems with Multiplicative Random Impulse Process Excitation....Pages 343-352
Multiscale Impact Models: Multibody Dynamics and Wave Propagation....Pages 353-362
Use of Orthogonal Decomposition of Data-Based Excitation Processes for Nonstationary Response of Nonlinear Systems....Pages 363-373
Hilbert Spectral Description and Simulation of Nonstationary Random Processes....Pages 375-384
Front Matter....Pages 385-386
Random Vibrations of Riding Cars with Bilinear Damping....Pages 387-399
Solutions of the First-Passage Problem by Importance Sampling....Pages 401-413
Passive Fields and Particles in Chaotic Flows....Pages 415-424
Sample Point Uniformity Using Discrepancy Measures....Pages 425-434
Kinks in a Stochastic PDE....Pages 435-443
Path Integration as a Tool for Investigating Chaotic Behaviour....Pages 445-454
Time-Varying Cardiovascular Oscillations....Pages 455-464
Back Matter....Pages 465-467

✦ Subjects

Probability Theory and Stochastic Processes; Mechanical Engineering; Signal, Image and Speech Processing; Structural Mechanics; Ordinary Differential Equations