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.
Sprache
Verlagsort
Zielgruppe
Für Beruf und Forschung
US School Grade: College Graduate Student
Maße
ISBN-13
978-3-11-031305-5 (9783110313055)
Schweitzer Klassifikation
Wei Xu and Yong Xu, Northwestern Polytechnical University, Xi'an, Shaanxi, PR China.
1. Introduction and Preliminaries1.1 Problems1.2 Concepts1.3 Book layout2. A brief introduction to nonlinear dynamical systems2.1 Basic concepts of dynamical systems2.2 Approximate analytical methods2.3 Stability2.4 Bifurcation and Chaos2.5 Chaos control2.6 Applications3. Some issues in random dynamical systems3.1 Random noise in dynamical systems3.2 Basic concepts of random dynamical systems3.3 Stochastic stability3.4 Stochastic bifurcation3.5 FPK equation3.6 Applications4. The beam-beam interaction model with narrow-band random noise4.1 The beam-beam interaction model4.2 Narrow-band random noise4.3 Modified multiple scale method4.4 Mean squared response4.5 Numerical analysis4.6 Applications5. The Duffing oscillator with Gaussian white noise5.1 Stochastic Duffing oscillator revisited5.2 The generation of Gaussian white noise5.3 Stochastic stability5.4 Chaotic response5.5 Applications6. Chaos control of nonlinear systems using stochastic force6.1 Complex Duffing system with random force6.2 Top Lyapunov exponent6.3 Chaos control via random phase6.4 Applications7. Stochastic bifurcation of the mechanical model7.1 The model of mechanics7.2 Method of generalized cell mapping7.3 Stochastic bifurcation7.4 Applications8. Response analysis for the model of earthquake8.1 The model of earthquake8.2 Response and stability analysis8.3 Applications9. Stochastic dynamics in the model of love9.1 The model of love9.2 Modified model of love9.3 Love dynamics9.4 Chaos in stochastic model9.5 Applications
