IUTAM Symposium on Nonlinear Stochastic Dynamics

1. Front Matter

   Pages i-xix

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2. Multi-Scale Phenomena

   1. Front Matter

      Pages 1-3

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   2. Linear and Nonlinear Diffusion Approximation of the Slow Motion in Systems with Two Time Scales

      • Ludwig Arnold

      Pages 5-18

   3. Experiments on Large Fluctuations

      • A. Bandrivskyy, S. Beri, D. G. Luchinsky, P. V. E. McClintock

      Pages 19-28

   4. Stochastic Averaging: Some Methods and Applications

      • P. Bernard

      Pages 29-41

   5. Noise Sensitivity of Stochastic Resonance and Other Problems Related to Large Deviations

      • Mark Freidlin

      Pages 43-55

   6. The Reduction of Potential Diffusions to Finite State Markov Chains and Stochastic Resonance

      • Peter Imkeller, Ilya Pavlyukevich

      Pages 57-69

   7. Metastability of Diffusion Processes

      • C. Schütte, W. Huisinga, S. Meyn

      Pages 71-81

   8. Stochastic Averaging Near Homoclinic Orbits Via Singular Perturbations

      • Richard B. Sowers

      Pages 83-94

3. Stability and Bifurcations

   1. Front Matter

      Pages 95-96

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   2. Stochastic Stability of Coupled Oscillators in Internal Resonance

      • S. T. Ariaratnam, N. M. Abdelrahman

      Pages 97-110

   3. Dynamics of Globally Coupled Noisy Excitable Elements: The Fitzhugh-Nagumo Case

      • J. A. Acebrón, A. R. Bulsara, W.-J. Rappel

      Pages 111-124

   4. Lyapunov Exponents and Stability for the Stochastic Duffing-Van der Pol Oscillator

      • Peter H. Baxendale

      Pages 125-135

   5. Slow Sweep Through a Period-Doubling Cascade: An Example of a Noisy Parametric Bifurcation

      • Huw G. Davies, Philotas Kyriakidis

      Pages 137-146

   6. Multi-Scale Analysis of Noise-Sensitivity Near a Bifurcation

      • R. Kuske

      Pages 147-156

   7. Hopf Meets Hamilton Under Whitney’s Umbrella

      • William F. Langford

      Pages 157-165

   8. Stochastic Stability of Two Coupled Oscillators in Resonance

      • N. Sri Namachchivaya, N. Ramakrishnan, H. J. Van Roessel, L. Vedula

      Pages 167-177

   9. On Stabilizing the Double Oscillator by Mean Zero Noise

      • Volker Wihstutz

      Pages 179-190

   10. Stability of a Two-Dimensional System Under Combined Harmonic and Real Noise Parametric Excitations

       • Wei-Chau Xie

       Pages 191-201

4. Control and Estimation

   1. Front Matter

      Pages 203-204

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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.

• Measure
• Sage
• Sweep
• diffusion process
• information
• modeling
• simulation
• vibration
• ordinary differential equations

• University of Illinois at Urbana-Champaign, USA

  N. Sri Namachchivaya

• Florida Atlantic University, USA

  Y. K. Lin

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