Luo A.C.J. (Ed.) Dynamical Systems: Discontinuity, Stochasticity and Time-Delay
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Dynamical Systems
Albert C.J. Luo
Editor
Dynamical Systems
Discontinuity, Stochasticity and Time-Delay
123
Editor
Albert C.J. Luo
Department of Mechanical and Industrial Engineering
Southern Illinois University Edwardsville
Edwardsville, IL 62026-1805
USA
aluo@siue.edu
ISBN 978-1-4419-5753-5 e-ISBN 978-1-4419-5754-2
DOI 10.1007/978-1-4419-5754-2
Springer New York Dordrecht Heidelberg London
Library of Congress Control Number: 2010924743
c
Springer Science+Business Media, LLC 2010
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Preface
Dynamics, vibrations, and control of dynamical systems with discontinuity,
stochasticity, and time delay are presented in this book. Dynamical systems with
discontinuity, stochasticity, and time delay exist extensively in practical systems.
This book provides the reader with a better understanding of control of dynami-
cal behaviors of complex dynamical systems. Recent developments in dynamical
systems with discontinuity, stochasticity, and time delay are discussed along with
topics normally associated with discontinuous systems including but not limited to
impact systems, friction-induced systems, and impulsive systems. Also presented
are classic vibration and control of dynamical systems.
This content presented is based on the Second Conference on Dynamics, Vibra-
tion and Control, held in Chengdu-Jiuzhaigou, Sichuan, China, 2009 (DVC2009).
The goal of this conference is to provide a place to exchange recent developments,
discoveries, and progresses on dynamics, vibration, and control. This second con-
ference is the continuation of the 2007 Arctic Summer Conference on Dynamics,
Vibrations and Control. Papers and presentations relative to all areas pertaining
to theoretical, symbolic, computational, and experimental aspects of dynamics, vi-
brations, and control were solicited. There were 57 papers initially submitted for
presentation and publications. After peer review, only 34 papers were selected for
publication in this book; these contributions are divided into four groups:
Group 1 discusses nonlinear and discontinuous dynamical systems and includes
11 contributions that cover fractional dynamics, chaos and bifurcations in non-
linear dynamical systems, discontinuous dynamical systems, and applications in
manufacturing and rotor dynamics.
Group 2 discusses time-delay systems and includes four contributions that cover
the method of time-continuous approximation and time-delay systems, the time-
delay control for nonlinear dynamical systems, bifurcation and stability for
neuronal systems with time delay.
Group 3 discusses switching and stochastic systems and includes six contri-
butions that cover nonlinear dynamics of switching and impulsive dynamical
systems, neuron synchronization under noise excitation, nonequilibrium transi-
tion, and stochastic resonance.
v
vi Preface
Group 4 discusses classic vibration and control with 13 contributions that cover
structural dynamics wave propagation in soil and foundations, fluid-induced
vibration and control systems, and system identification.
The conference organizers would like to take this opportunity to thank all volunteers
for conference preparation and hotel arrangement. We would also like to express
appreciation to Ms. Yi Sun who made all the necessary arrangements for the con-
ference and special events in China.
Edwardsville, IL Albert C.J. Luo
Contents
Part I Nonlinear and Discontinuous Dynamical Systems
1 General Solution of a Vibration System with Damping
Force of Fractional-Order Derivative ...................................... 3
Z.H. Wang and X. Wang
2 An Analytic Proof for the Sensitivity of Chaos to Initial
Condition and Perturbations ................................................ 13
J.H. Peng and J.S. Tang
3 Study on the Multifractal Spectrum of Local Area
Networks Traffic and Their Correlations .................................. 23
Yan Liu and Jia-Zhong Zhang
4 A Boundary Crisis in High Dimensional Chaotic Systems............... 31
Ling Hong, Yingwu Zhang, and Jun Jiang
5 Complete Bifurcation Behaviors of a Henon Map ........................ 37
Albert C.J. Luo and Yu Guo
6 Study on the Performance of a Two-Degree-of-Freedom
Chaotic Vibration Isolation System ........................................ 49
Jing-Jun Lou, Ying-Chun Wang, and Shi-Jian Zhu
7 Simulation and Nonlinear Analysis of Panel Flutter
with Thermal Effects in Supersonic Flow.................................. 61
Kai-Lun Li, Jia-Zhong Zhang, and Peng-Fei Lei
8 A Parameter Study of a Machine Tool with Multiple
Boundaries .................................................................... 77
Brandon C. Gegg, Steve C.S. Suh, and Albert C.J. Luo
vii
viii Contents
9 A New Friction Model for Evaluating Energy Dissipation
in Carbon Nanotube-Based Composites ................................... 95
Yaping Huang and X.W. Tangpong
10 Nonlinear Response in a Rotor System With a Coulomb
Spline...........................................................................105
C. Nataraj and Karthik Kappaganthu
11 The Influence of the Cross-Coupling Effects
on the Dynamics of Rotor/Stator Rubbing.................................121
Zhiyong Shang, Jun Jiang, and Ling Hong
Part II Time-delay Systems
12 Some Control Studies of Dynamical Systems with Time
Delay ...........................................................................135
Bo Song and Jian-Qiao Sun
13 Stability and Hopf Bifurcation Analysis in Synaptically
Coupled FHN Neurons with Two Time Delays ............................157
Dejun Fan and Ling Hong
14 On the Feedback Controlling of the Neuronal System
with Time Delay ..............................................................169
Hao Liu, Wuyin Jin, Chi Zhang, Ruicheng Feng,
and Aihua Zhang
15 Control of Erosion of Safe Basins in a Single
Degree of Freedom Yaw System
of a Ship with a Delayed Position Feedback ...............................177
Huilin Shang
Part III Switching and Stochastic Dynamical Systems
16 On Periodic Flows of a 3-D Switching System with Many
Subsystems ....................................................................189
Albert C.J. Luo and Yang Wang
17 Impulsive Control Induced Effects on Dynamics
of Complex Networks ........................................................203
Xiuping Han and Xilin Fu
18 Study on Synchronization of Two Identical Uncoupled
Neurons Induced by Noise ...................................................217
Ying Wu, Ling Hong, Jun Jiang, and Wuyin Jin
Contents ix
19 Non-equilibrium Phase Transitions in a Single-Mode
Laser Model Driven by Non-Gaussian Noise ..............................223
Yanfei Jin
20 Dynamical Properties of Intensity Fluctuation
of Saturation Laser Model Driven by Cross-Correlated
Additive and Multiplicative Noises .........................................233
Ping Zhu
21 Empirical Mode Decomposition Based on Bistable
Stochastic Resonance Denoising ............................................251
Y.-J. Zhao, Y. Xu, H. Zhang, S.-B. Fan, and Y.-G. Leng
Part IV Classic Vibrations and Control
22 Order Reduction of a Two-Span Rotor-Bearing System
Via the Predictor-Corrector Galerkin Method ............................263
Deng-Qing Cao, Jin-Lin Wang, and Wen-Hu Huang
23 Stiffness Nonlinearity Classification Using Morlet
Wavelets .......................................................................275
Rajkumar Porwal and Nalinaksh S. Vyas
24 Dynamics of Wire-Driven Machine Mechanisms:
Literature Review ............................................................285
Timo Karvinen and Erno Keskinen
25 Dynamics of Wire-Driven Machine Mechanisms,
Part II: Theory and Applications ...........................................299
Erno Keskinen, Timo Karvinen, and Jori Montonen
26 On Analytical Methods for Vibrations of Soils
and Foundations ..............................................................319
H.R. Hamidzadeh
27 Inversely Found Elastic and Dimensional Properties.....................341
Darryl K. Stoyko, Neil Popplewell, and Arvind H. Shah
28 Nonlinear Self-Defined Truss Element Based on the Plane
Truss Structure with Flexible Connector ..................................357
Yajun Luo, Xinong Zhang, and Minglong Xu