Dynamical Systems: Theory, Applications and Future Directions

Jean Michel Tchuenche (Editor)
Centers for Disease Control and Prevention, Atlanta, GA, USA

Series: Mathematics Research Developments
BISAC: MAT027000

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Volume 10

Issue 1

Volume 2

Volume 3

Special issue: Resilience in breaking the cycle of children’s environmental health disparities
Edited by I Leslie Rubin, Robert J Geller, Abby Mutic, Benjamin A Gitterman, Nathan Mutic, Wayne Garfinkel, Claire D Coles, Kurt Martinuzzi, and Joav Merrick

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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 theories 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 computational complexity and performance comparison, parametric resonance and homoclinic chaos in a Bullard-type dynamo; and birhythmicity, synchonization and chaos in an enzyme-substrate reaction with ferroelectric behavior. Biological applications include the local stability of an age-structured Hepatitis B model, the dynamics of a predator-prey model, avian influenza, tuberculosis, malaria and HIV-TB co-dynamics. A possible application of nonlinear dynamical systems in social sciences is also investigated. (Imprint: Nova)

Preface

Chapter 1- Markus-Sell’s Theorem for Asymptotically Almost Periodic Systems
(David Cheban and Cristiana Mammana, State University of Moldova
Department of Mathematics and Informatics, Moldova, and others)

Chapter 2- A Survey of the Method of Lyapunov Functions of Two Variables in The Study of Stability and Persistence of Dynamical Systems
(Jorge Lewowicz, Jorge Groisman, Juan Tolosa, IMERL, Facultad de Ingeniera, Universidad de la Republica, Montevideo, Uruguay, and others)

Chapter 3- Krylov and Schur Subspaces in Construction of Prediction Error Filter: Computational Complexity and Performance Comparison
(Hong Son Hoang and Remy Baraille, SHOM/CMO, Avenue Gaspard Coriolis Toulouse, France)

Chapter 4- High-Fidelity Modeling and Vibration-Based System Identification and Damage Inspection of Flexible Structures
(P. Frank Pai, Mechanical and Aerospace Engineering Dept., University of Missouri, Columbia, MO, USA)

Chapter 5- Complexity and Chaos Theory in Social Sciences: Scientific Philosophy or Quantitative Science?
(Rosalia Condorelli, Department of Political and Social Sciences, Catania University, Vittorio Emanuele II, Catania, Italy)

Chapter 6- Local Stability Analysis of an Age-Structured Hepatitis B Transmission Model
(Ousmane M. Tessa, Bisso Saley, Herieth Rwezaura and Jean M. Tchuenche, Department of Mathematics and Computer Science, Abdou Moumouni University, Niamey, Niger)

Chapter 7- Parametric Resonance and Homoclinic Chaos in a Bullard-Type Dynamo
(O. Foupouapouognigni, M. Siewe Siewe, C. Tchawoua, Universite de Yaoundé I, Faculté des Sciences, Département de Physique,
Laboratoire de Mécanique, Yaoundé-Cameroun)

Chapter 8- Birhythmicity, Synchonization and Chaos in an Enzyme-Substrate Reaction with a Ferroelectric Behavior
(H.G. Enjieu Kadji, P. Woafo, Monell Chemical Senses Center, Philadelphia, PA, USA, and others)

Chapter 9- Dynamics of Low and High Pathogenic Avian Influenza in Wild Bird Population
(Necibe Tuncer, Juan Torres, and Maia Martcheva, Department of Mathematics, University of Tulsa, Tulsa, OK, USA, and others)
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Chapter 10- Analysis of A Predator-Prey Model with Sigmoidal Response Function and SIS Disease
(J.J. Tewa, P. Tchinda Mouofo, V. Kamla, S. Bowong, Department of Mathematics and Physics, National Advanced School of Engineering (Polytechnic), University of Yaounde I, Yaounde, Cameroon, and others)

Chapter 11- Impact of Multi-Intervention Campaigns on the Malaria Epidemic in Malawi
(P.M. Mwamtobe, J.M. Tchuenche, M. Maliyoni and S.D. Hove-Musekwa, Department of Mathematics and Statistics, University of Malawi, The Malawi Polytechnic, Private Bag, Chichiri, Blantyre, Malawi, and others)

Chapter 12- Modelling the Dynamics of HIV-TB Co-Infection in a Variable Size Population
(Agraj Tripathi, Ram Naresh, Dileep Sharma, Department of Mathematics, Bhabha Institute of Technology, Kanpur, India, and others)

Chapter 13- Case Detection on Tuberculosis Dynamics with Isolation in a Sanatorium
(Nyimvua Shaban, Department of Mathematics, University of Dar es Salaam, Dar es Salaam, Tanzania)

Index

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