Dynamical Models in Biology (eBook)

Miklos Farkas (Autor)

eBook Download: PDF

2001 | 1. Auflage
187 Seiten
Elsevier Science (Verlag)
978-0-08-053060-4 (ISBN)

Infos

use back cover copy

* A 'down-to-earth' introduction to the growing field of modern mathematical biology
* Also includes appendices which provide background material that goes beyond advanced calculus and linear algebra

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Dynamic Models in Biology offers an introduction to modern mathematical biology. This book provides a short introduction to modern mathematical methods in modeling dynamical phenomena and treats the broad topics of population dynamics, epidemiology, evolution, immunology, morphogenesis, and pattern formation. Primarily employing differential equations, the author presents accessible descriptions of difficult mathematical models. Recent mathematical results are included, but the author's presentation gives intuitive meaning to all the main formulae. Besides mathematicians who want to get acquainted with this relatively new field of applications, this book is useful for physicians, biologists, agricultural engineers, and environmentalists. Key Topics Include:- Chaotic dynamics of populations- The spread of sexually transmitted diseases- Problems of the origin of life- Models of immunology- Formation of animal hide patterns- The intuitive meaning of mathematical formulae explained with many figures- Applying new mathematical results in modeling biological phenomena Miklos Farkas is a professor at Budapest University of Technology where he has researched and instructed mathematics for over thirty years. He has taught at universities in the former Soviet Union, Canada, Australia, Venezuela, Nigeria, India, and Columbia. Prof. Farkas received the 1999 Bolyai Award of the Hungarian Academy of Science and the 2001 Albert Szentgyorgyi Award of the Hungarian Ministry of Education. - A 'down-to-earth' introduction to the growing field of modern mathematical biology- Also includes appendices which provide background material that goes beyond advanced calculus and linear algebra

Inhalt

Front Cover 1
Dynamical Models in Biology 4
Copyright Page 5
Contents 10
Preface 8
Chapter 1. Discrete Population Models 12
1.1 Nonoverlapping Generations and Discrete Time Models 12
1.2 Population with Age Structure 23
Chapter 2. Population Dynamics in Continuous time 28
2.1 The Logistic Equation and Human Demography 28
2.2 Two Interacting Species-Predator and Prey 31
2.3 Two Interacting Species-Competition and Cooperation 41
2.4 More Species 49
2.5 More Realism 59
Chapter 3. Epidemics 74
3.1 The Spread of Diseases and Susceptibles/Infectives/Removed Models 74
3.2 Sexually Transmitted Diseases 78
3.3 A Model of Pair Formation 80
3.4 The Spread of Epidemics in Space 84
Chapter 4. Evolution And population Genetics 90
4.1 The Phase Space of Genotypes and the Hardy-Weinberg Law 90
4.2 Equations of Selection, Recombination, and Mutation 94
4.3 The Origins of Life and Eigen's Hypercycle 102
4.4 The Immune System 109
Chapter 5. Morphogenesis And Pattern Formation 116
5.1 Modeling the Embryo-Thom's Catastrophe Theory 116
5.2 Animal Hide and Shell Patterns 125
Appendix 1. Discrete Mathematics 136
A1.1 Linear Algebra 136
A1.2 One-Dimensional Discrete Semiflows 140
A1.3 Discrete Dynamical Systems 147
A1.4 Branching Processes 150
Appendix 2. Ordinary Differential Equations 154
A2.1 Basic Facts 154
A2.2 Stability 157
A2.3 Bifurcations 162
Appendix 3. Partial Differential Equations 168
A3.1 First-Order Linear Equations 168
A3.2 Reaction-Diffusion Equations 172
A3.3 Turing Bifurcation 175
Appendix 4. Riemannian Geometry 182
A4.1 Local Riemannian Geometry 182
A4.2 Shahshahani's Metric 187
References 190
Index 195

Produkt-Details

• Erscheint lt. Verlag: 15.6.2001
• Sprache: englisch
• Themenwelt: Sachbuch/Ratgeber
• Themenwelt: Mathematik / Informatik ► Informatik
• Themenwelt: Mathematik / Informatik ► Mathematik ► Algebra
• Themenwelt: Mathematik / Informatik ► Mathematik ► Angewandte Mathematik
• Themenwelt: Naturwissenschaften ► Biologie
• Themenwelt: Naturwissenschaften ► Physik / Astronomie
• Themenwelt: Technik
• ISBN-10: 0-08-053060-5 / 0080530605
• ISBN-13: 978-0-08-053060-4 / 9780080530604