Nonlinear Systems with Stochastic Fluctuations

ISBN: 978-3-11-031305-5
Verlag: De Gruyter

Buch, Englisch, 200 Seiten, Format (B × H): 170 mm x 240 mm

Nonlinear dynamics and its applications have been under intensive studies during last two decades. However, trivial random noise may lead to unpredictable consequences. Nowadays stochastic dynamics has raised interests in many fields, such as physical science, life science, chaotic electric circuits, and nonlinear psychology. This book describes the models of random dynamics which are from applications in various fields. Some illustrative models are presented to demonstrate how to model random phenomena sciences and engineering, how to quantify rare or significant events in these models, how to investigate stochastic dynamics of complex systems, and how to interpret dynamical results in real applications. Some efficient methods, both numerical and theoretical, to study stochastic systems are presented in an accessible way. This book will be an ideal starting point for those who needs a basic fundamental understanding of stochastic dynamical systems. The audience will be graduate students, engineers, junior researchers in applied mathematics, mechanics, probability and statistics and other professionals who are interested in the subject. Dr. Wei Xu is Professor of applied mathematics at Northwestern Polytechnical University, CHINA. His expertise is in stochastic dynamics and its applications. He has made numerous contributions to stochastic dynamics.

Autoren/Hrsg.

Xu, Wei

Xu, Yong

Weitere Mitwirkende

Press, Higher Education

Fachgebiete

• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Angewandte Mathematik, Mathematische Modelle
• Mathematik | Informatik Mathematik Stochastik Wahrscheinlichkeitsrechnung

Inhaltsverzeichnis

1. Introduction and Preliminaries
1.1 Problems
1.2 Concepts
1.3 Book layout
2. A brief introduction to nonlinear dynamical systems
2.1 Basic concepts of dynamical systems
2.2 Approximate analytical methods
2.3 Stability
2.4 Bifurcation and Chaos
2.5 Chaos control
2.6 Applications
3. Some issues in random dynamical systems
3.1 Random noise in dynamical systems
3.2 Basic concepts of random dynamical systems
3.3 Stochastic stability
3.4 Stochastic bifurcation
3.5 FPK equation
3.6 Applications
4. The beam-beam interaction model with narrow-band random noise
4.1 The beam-beam interaction model
4.2 Narrow-band random noise
4.3 Modified multiple scale method
4.4 Mean squared response
4.5 Numerical analysis
4.6 Applications
5. The Duffing oscillator with Gaussian white noise
5.1 Stochastic Duffing oscillator revisited
5.2 The generation of Gaussian white noise5.3 Stochastic stability
5.4 Chaotic response
5.5 Applications
6. Chaos control of nonlinear systems using stochastic force
6.1 Complex Duffing system with random force
6.2 Top Lyapunov exponent
6.3 Chaos control via random phase
6.4 Applications
7. Stochastic bifurcation of the mechanical model
7.1 The model of mechanics
7.2 Method of generalized cell mapping
7.3 Stochastic bifurcation
7.4 Applications
8. Response analysis for the model of earthquake
8.1 The model of earthquake
8.2 Response and stability analysis
8.3 Applications
9. Stochastic dynamics in the model of love
9.1 The model of love
9.2 Modified model of love
9.3 Love dynamics
9.4 Chaos in stochastic model
9.5 Applications

Über Autor(innen)

Wei Xu and Yong Xu, Northwestern Polytechnical University, Xi’an, Shaanxi, PR China.