Oscillation and Stability of Delay Models in Biology
Oscillation and Stability of Delay Models in Biology

Author: Ravi P. Agarwal

Publisher: Springer

Published: 2014-06-07

Total Pages: 347

ISBN-13: 3319065572

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Environmental variation plays an important role in many biological and ecological dynamical systems. This monograph focuses on the study of oscillation and the stability of delay models occurring in biology. The book presents recent research results on the qualitative behavior of mathematical models under different physical and environmental conditions, covering dynamics including the distribution and consumption of food. Researchers in the fields of mathematical modeling, mathematical biology, and population dynamics will be particularly interested in this material.

Stability and Oscillations in Delay Differential Equations of Population Dynamics
Stability and Oscillations in Delay Differential Equations of Population Dynamics

Author: K. Gopalsamy

Publisher: Springer Science & Business Media

Published: 2013-03-14

Total Pages: 514

ISBN-13: 9401579202

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This monograph provides a definitive overview of recent advances in the stability and oscillation of autonomous delay differential equations. Topics include linear and nonlinear delay and integrodifferential equations, which have potential applications to both biological and physical dynamic processes. Chapter 1 deals with an analysis of the dynamical characteristics of the delay logistic equation, and a number of techniques and results relating to stability, oscillation and comparison of scalar delay and integrodifferential equations are presented. Chapter 2 provides a tutorial-style introduction to the study of delay-induced Hopf bifurcation to periodicity and the related computations for the analysis of the stability of bifurcating periodic solutions. Chapter 3 is devoted to local analyses of nonlinear model systems and discusses many methods applicable to linear equations and their perturbations. Chapter 4 considers global convergence to equilibrium states of nonlinear systems, and includes oscillations of nonlinear systems about their equilibria. Qualitative analyses of both competitive and cooperative systems with time delays feature in both Chapters 3 and 4. Finally, Chapter 5 deals with recent developments in models of neutral differential equations and their applications to population dynamics. Each chapter concludes with a number of exercises and the overall exposition recommends this volume as a good supplementary text for graduate courses. For mathematicians whose work involves functional differential equations, and whose interest extends beyond the boundaries of linear stability analysis.

Delay Effects on Stability
Delay Effects on Stability

Author: Silviu-Iulian Niculescu

Publisher: Springer Science & Business Media

Published: 2001-05-22

Total Pages: 399

ISBN-13: 1852332913

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This monograph is devoted to the effect of delays on the stability properties of dynamical systems. Stability regions with respect to the delay parameters are considered, and some sufficient characterizations are proposed. This monograph addresses general delay problems and offers solutions in some cases. In other cases, approximations of the stability regions can be proposed. The interpretation of delays as uncertainty allows the authors to use the advances in robust control and robust convex optimization to solve or to approximate the solutions of the corresponding problems.

Time Delay Systems
Time Delay Systems

Author: Tamás Insperger

Publisher: Springer

Published: 2017-03-30

Total Pages: 359

ISBN-13: 3319534262

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This volume collects contributions related to selected presentations from the 12th IFAC Workshop on Time Delay Systems, Ann Arbor, June 28-30, 2015. The included papers present novel techniques and new results of delayed dynamical systems. The topical spectrum covers control theory, numerical analysis, engineering and biological applications as well as experiments and case studies. The target audience primarily comprises research experts in the field of time delay systems, but the book may also be beneficial for graduate students alike.

Delay Systems
Delay Systems

Author: Tomáš Vyhlídal

Publisher: Springer Science & Business Media

Published: 2013-09-07

Total Pages: 417

ISBN-13: 3319016954

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This volume is the first of the new series Advances in Dynamics and Delays. It offers the latest advances in the research of analyzing and controlling dynamical systems with delays, which arise in many real-world problems. The contributions in this series are a collection across various disciplines, encompassing engineering, physics, biology, and economics, and some are extensions of those presented at the IFAC (International Federation of Automatic Control) conferences since 2011. The series is categorized in five parts covering the main themes of the contributions: · Stability Analysis and Control Design · Networks and Graphs · Time Delay and Sampled-Data Systems · Computational and Software Tools · Applications This volume will become a good reference point for researchers and PhD students in the field of delay systems, and for those willing to learn more about the field, and it will also be a resource for control engineers, who will find innovative control methodologies for relevant applications, from both theory and numerical analysis perspectives.

Stability of Time-Delay Systems
Stability of Time-Delay Systems

Author: Keqin Gu

Publisher: Springer Science & Business Media

Published: 2003-06-26

Total Pages: 384

ISBN-13: 9780817642129

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For both its intrinsic scientific interest and practical impact, time-delay dynamical systems have been an enduring theme in the studies of differential equations, stochastic processes, game theory and systems theory, which span a number of broad areas of applications. This book presents recent research results.

Time-delay Systems
Time-delay Systems

Author: Sun Yi

Publisher: World Scientific

Published: 2010

Total Pages: 153

ISBN-13: 9814307408

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1. Introduction. 1.1. Motivation. 1.2. Background. 1.3. Scope of this document. 1.4. Original contributions -- 2. Solutions of systems of DDEs via the matrix Lambert W function. 2.1. Introduction. 2.2. Free systems of DDEs. 2.3. Forced systems. 2.4. Approach using the Laplace transformation. 2.5. Concluding remarks -- 3. Stability of systems of DDEs via the Lambert W function with application to machine tool chatter. 3.1. Introduction. 3.1. The Chatter equation in the turning process. 3.3. Solving DDEs and stability. 3.4. Concluding remarks -- 4. Controllability and observability of systems of linear delay differential equations via the matrix Lambert W function. 4.1. Introduction. 4.2. Controllability. 4.3. Observability. 4.4. Illustrative example. 4.5. Conclusions and future work -- 5. Eigenvalue assignment via the Lambert W function for control of time-delay systems. 5.1. Introduction. 5.2. Eigenvalue assignment for time-delay systems. 5.3. Design of a feedback Controller. 5.4. Conclusions -- 6. Robust control and time-domain specifications for systems of delay differential equations via eigenvalue assignment. 6.1. Introduction. 6.2. Robust feedback. 6.3. Time-domain specifications. 6.4. Concluding remarks -- 7. Design of observer-based feedback control for time-delay systems with application to automotive powertrain control. 7.1. Introduction. 7.2. Problem formulation. 7.3. Design of observer-based feedback controller. 7.4. Application to diesel engine control. 7.5. Conclusions -- 8. Eigenvalues and sensitivity analysis for a model of HIV pathogenesis with an intracellular delay. 8.1. Introduction. 8.2. HIV pathogenesis dynamic model with an intracellular delay. 8.3. Rightmost eigenvalue analysis. 8.4. Sensitivity analysis. 8.5. Concluding remarks and future work