Jian-Qiao Sun, Ph.D., M.S., B.S., University of Delaware, Department of Mechanical Engineering, Newark, U.S.A.
Albert Luo, Ph.D., Southern Illinois University, Department of
Mechanical and Industrial Engineering, Edwardsville, U.S.A.
BIFURCATION AND CHAOS IN COMPLEX SYSTEMS
Description
The book presents the recent achievements on bifurcation studies
of nonlinear dynamical systems. The contributing authors of the
book are all distinguished researchers in this interesting
subject area. The first two chapters deal with the fundamental
theoretical issues of bifurcation analysis in smooth and non-smooth
dynamical systems. The cell mapping methods are presented for
global bifurcations in stochastic and deterministic, nonlinear
dynamical systems in the third chapter. The fourth chapter
studies bifurcations and chaos in time-varying, parametrically
excited nonlinear dynamical systems. The fifth chapter presents
bifurcation analyses of modal interactions in distributed,
nonlinear, dynamical systems of circular thin von Karman plates.
The theories, methods and results presented in this book are of
great interest to scientists and engineers in a wide range of
disciplines. This book can be adopted as references for
mathematicians, scientists, engineers and graduate students
conducting research in nonlinear dynamical systems.
Audience
Mechanical Engineers, Electrical Engineers, Physicists,
Mathematicians, Bio-Physicisists, Engineers and Students
Contents
Dedication Preface Chapter 1. Bifurcation, Limit Cycle and Chaos
of Nonlinear Dynamical Systems (Pei Yu) Chapter 2. Grazing Flows
in Discontinuous Dynamic Systems (Albert C.J. Luo) Chapter 3.
Global Bifurcations of Complex Nonlinear Dynamical Systems with
Cell Mapping Methods (Ling Hong and Jian-Qiao Sun) Chapter 4.
Bifurcation Analysis of Nonlinear Dynamic Systems with Time-Periodic
Coefficients (Alexandra David and S.C. Sinha) Chapter 5. Modal
Interactions in Asymmetric Vibrations of Circular Plates (Won
Kyoung Lee)
Series : Advances in Nonlinear Science and Complexity,vol.1.
Hardbound, ISBN: 0-444-52229-8, publication date: 2006
Valentin Afraimovich, Universidad Autonoma de San Luis Potosi, Mexico.
Edgardo Ugalde, Universidad Autonoma de San Luis Potosi, Mexico.
Jesus Urias, Universidad Autonoma de San Luis Potosi, Mexico.
Albert Luo, Ph.D., Southern Illinois University, Dept. of Mechanical and
Industrial Engineering, Edwardsville, U.S.A.
George Zaslavsky
FRACTAL DIMENSIONS FOR POINCARE RECURRENCES
Description
This book is devoted to an important branch of the dynamical
systems theory : the study of the fine (fractal) structure of
Poincare recurrences -instants of time when the system almost
repeats its initial state. The authors were able to write an
entirely self-contained text including many insights and
examples, as well as providing complete details of proofs. The
only prerequisites are a basic knowledge of analysis and topology.
Thus this book can serve as a graduate text or self-study guide
for courses in applied mathematics or nonlinear dynamics (in the
natural sciences). Moreover, the book can be used by specialists
in applied nonlinear dynamics following the way in the book. The
authors applied the mathematical theory developed in the book to
two important problems: distribution of Poincare recurrences for
nonpurely chaotic Hamiltonian systems and indication of
synchronization regimes in coupled chaotic individual systems.
Contents
1. Introduction
Part 1: Fundamentals
2. Symbolic Systems 3. Geometric Constructions 4. Spectrum of
Dimensions for Recurrences
Part II: Zero-Dimensional Invariant Sets
5. Uniformly Hyperbolic Repellers 6. Non-Uniformly Hyperbolic
Repellers 7. The Spectrum for a Sticky Set 8. Rhythmical Dynamics
Part III: One-Dimensional Systems
9. Markov Maps of the Interval 10. Suspended Flows
Part IV: Measure Theoretical Results
11. Invariant Measures 12. Dimensional for Measures 13. The
Variational Principle
Part V: Physical Interpretation and Applications
14. Intuitive Explanation 15. Hamiltonian Systems 16. Chaos
Synchronization
Part VI: Appendices
17. Some Known Facts About Recurrences 18. Birkhoff's Individual
Theorem 19. The SMB Theorem 20. Amalgamation and Fragmentation
Index
Series : Advances in Nonlinear Science and Complexity,vol.2.
Hardbound, ISBN: 0-444-52189-5, 280 pages, publication date: 2006
Albert Luo, Ph.D., Southern Illinois University, Dept. of Mechanical and Industrial Engineering, U.S.A.
George Zaslavsky
SINGULARITY AND DYNAMICS ON DISCONTINUOUS VECTOR FIELDS
Description
This book discussed fundamental problems in dynamics, which
extensively exist in engineering, natural and social sciences.
The book presented a basic theory for the interactions among many
dynamical systems and for a system whose motions are constrained
naturally or artificially. The methodology and techniques
presented in this book are applicable to discontinuous dynamical
systems in physics, engineering and control. In addition, they
may provide useful tools to solve non-traditional dynamics in
biology, stock market and internet network et al, which cannot be
easily solved by the traditional Newton mechanics. The new ideas
and concepts will stimulate ones' thought and creativities in
corresponding subjects. The author also used the simple,
mathematical language to write this book. Therefore, this book is
very readable, which can be either a textbook for senior
undergraduate and graduate students or a reference book for
researches in dynamics.
Audience
Mechanical Engineers, Control Engineers, Physicians and
Mathematicians. Also for Bio-Physicians, Managers and Students.
Contents
Preface Chapter 1. Introduction Chapter 2. Flow Passability and
Tangential Flows Chapter 3. Flow Switching Bifurcations Chapter 4.
Transversal Singularity and Bouncing Flows Chapter 5. Real and
Imaginary Flows Chapter 6. Discontinuous Vector Fields with Flow
Barriers Chapter 7. Transport Laws and Mapping Dynamics Chapter 8.
Symmetry and Fragmentized Strange Attractors Appendix References
Subject Index
Series : Advances in Nonlinear Science and Complexity,vol.2.
Hardbound, ISBN: 0-444-52766-4, publication date: 2006
Ed. by Hulpke, Alexander / Liebler, Robert / Penttila, Tim / Seress, Akos
Finite Geometries, Groups, and Computation
Proceedings of the Conference 'Finite Geometries, Groups, and
Computation', Pingree Park, Colorado, USA, September 4-9, 2004
March 2006. 24 x 17 cm. VIII, 278 pages. Cloth.
ISBN 3-11-018220-3
Series: [de Gruyter Proceedings in Mathematics]
Subjects: Mathematics / Algebra, Number theory
Mathematics / Geometry and Topology
Language: English
This volume is the proceedings of a conference on Finite
Geometries, Groups, and Computation that took place on September
4-9, 2004, at Pingree Park, Colorado (a campus of Colorado State
University). Not accidentally, the conference coincided with the
60th birthday of William Kantor, and the topics relate to his
major research areas.
Participants were encouraged to explore the deeper interplay
between these fields. The survey papers by Kantor, O'Brien, and
Penttila should serve to introduce both students and the broader
mathematical community to these important topics and some of
their connections while the volume as a whole gives an overview
of current developments in these fields.
Contents
Grafarend, Erik W.
Linear and Nonlinear Models
Fixed effects, Random effects, and mixed models
March 2006. 24 x 17 cm. XX, 752 pages. Cloth.
ISBN 3-11-016216-4
Subjects: Natural Sciences / Geosciences / Geodesy, Cartography
Language: English
This monograph contains a thorough treatment of methods for
solving over- and underdetermined systems of equations, e.g. the
minimum norm solution method with respect to weighted norms. The
considered equations can be nonlinear or linear, and
deterministic models as well as probabilistic ones are considered.
An extensive appendix provides all necessary prerequisites like
matrix algebra, matrix analysis and Lagrange multipliers, and a
long list of references is also included.
Contents