Dynamical systems : theory, applications and future directions / Jean Michel Tchuenche, editor.

Format:

Book

Contributor:

Tchuenche, Jean Michel.

Series:

Mathematics Research Developments

Mathematics reseach developments

Language:

English

Subjects (All):

Chaotic behavior in systems.

Dynamics.

Physical Description:

1 online resource (368 p.)

Place of Publication:

Hauppauge, NY : Nova Science Publishers, Inc., 2013.

Language Note:

English

Summary:

Virtually any advance in disease dynamics requires a sophisticated mathematical approach in order to map out the parameters that drive the system. This book exploits some of the fundamental theory of dynamical systems and applies them to biological and social sciences. Topics include the asymptotic stability of almost periodic systems; modeling and vibration-based system identification and damage inspection of flexible structures; the stability and persistence of dynamical systems using Lyapunov functions; Krylov and Schur subspaces in construction of prediction error filter and its computatio

Contents:

""DYNAMICAL SYSTEMS: THEORY, APPLICATIONS AND FUTURE DIRECTIONS""; ""DYNAMICAL SYSTEMS: THEORY, APPLICATIONS AND FUTURE DIRECTIONS""; ""LIBRARY OF CONGRESS CATALOGING-IN-PUBLICATION DATA""; ""CONTENTS""; ""PREFACE""; ""Chapter 1: MARKUS-SELL�S THEOREM FOR ASYMPTOTICALLY ALMOST PERIODIC SYSTEMS""; ""Abstract""; ""1. Introduction""; ""2. Asymptotic Stability of Dynamical Systems""; ""3. Asymptotic Stability of NDS with Asymptotically Recurrent Base""; ""4. Some Applications""; ""References""

""Chapter 2: A SURVEY OF THE METHOD OF LYAPUNOV FUNCTIONS OF TWO VARIABLES IN THE STUDY OF STABILITY AND PERSISTENCE OF DYNAMICAL SYSTEMS""""Abstract""; ""1. Introduction""; ""2. Linear Hyperbolic Systems in Rn and Their Perturbations""; ""3. Quadratic Forms and Hyperbolic Behavior""; ""4. Almost Hyperbolic Systems""; ""5. Expansive Homeomorphisms""; ""6. Expansivity, Persistence and Pseudo-Anosov Maps""; ""Conclusion""; ""References""; ""Chapter 3: KRYLOV AND SCHUR SUBSPACES IN CONSTRUCTION OF PREDICTION ERROR FILTER: COMPUTATIONAL COMPLEXITY AND PERFORMANCE COMPARISON""; ""Abstract""

""1. Introduction""""2. Krylov Subspace and Schur Subspace""; ""3. Covariance of Prediction Error and PE Sampling Procedure""; ""4. Ritz Values and Ritz Vectors. Krylov Subspace and Schur Subspace""; ""5. Application of Krylov Subspace and Schur Subspace in Filtering""; ""6. Altimetric Data Assimilation in the Ocean Model MICOM""; ""7. Summary and Conclusion""; ""References""; ""Chapter 4: HIGH-FIDELITY MODELING AND VIBRATION-BASED SYSTEM IDENTIFICATION AND DAMAGE INSPECTION OF FLEXIBLE STRUCTURES""; ""Abstract""; ""I. Introduction""; ""II. Geometrically Exact Modeling Technique""

""III. Full-field Damage Inspection Technique""""IV. Online Health Monitoring and System Identification Techniques""; ""V. Numerical and Experimental Results""; ""Conclusion""; ""Acknowledgment""; ""References""; ""Chapter 5: COMPLEXITY AND CHAOS THEORY IN SOCIAL SCIENCES: SCIENTIFIC PHILOSOPHY OR QUANTITATIVE SCIENCE?""; ""Abstract""; ""Introduction""; ""The Curse of Dimensionality""; ""The Data Requirement Question: A Question Far from Being a Closed Issue""; ""A Social Science Model: The Logistic Model""; ""Complexity and Chaos Theory: Implications for Social Science Research""

""Conclusion""""References""; ""Chapter 6: LOCAL STABILITY ANALYSIS OF AN AGE-STRUCTURED HEPATITIS B TRANSMISSION MODEL""; ""Abstract""; ""1. Introduction""; ""2. The Model""; ""3. Stability of the Disease-Free State""; ""4. Existence and Stability of the Endemic States""; ""Conclusion""; ""References""; ""Chapter 7: PARAMETRIC RESONANCE AND HOMOCLINIC CHAOS IN A BULLARD-TYPE DYNAMO""; ""Abstract""; ""1. Introduction""; ""2. The Model and Governing Equations""; ""3. Parametric Excitation""; ""4. Detection of the Instability Threshold in the Model""; ""Conclusion""; ""Appendix""

""Acknowledgments""

Notes:

Description based upon print version of record.

Description based on print version record.

Includes bibliographical references and index.

ISBN:

1-62808-043-4

OCLC:

854583723