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Biological Oscillators.

By: Pavlidis, Theodosios.
Material type: TextTextSeries: eBooks on Demand.Publisher: Burlington : Elsevier Science, 2012Description: 1 online resource (222 p.).ISBN: 9780323159821.Subject(s): Biological control systems - Mathematical models | Biological control systems -- Mathematical models | Biological rhythms - Mathematical models | Biological rhythms -- Mathematical models | Oscillations | OscillationsGenre/Form: Electronic books.Additional physical formats: Print version:: Biological Oscillators: Their Mathematical AnalysisDDC classification: 574.1 LOC classification: QH527 .P38Online resources: Click here to view this ebook.
Contents:
Front Cover; Biological Oscillators: Their Mathematical Analysis; Copyright Page; Dedication; Table ofContents; Preface; Acknowledgments; Chapter 1. Fundamentals of the Mathematical Theory of Oscillators; 1.1 Introduction; 1.2 Phase Plane Techniques; 1.3 An Example of Application of Phase Plane Techniques; 1.4 State Space; 1.5 Asymptotic Techniques; 1.6 Describing Function; 1.7 Conservative Systems; Chapter 2. Examples of Biological Rhythms; 2.1 Introduction; 2.2 Circadian Rhythms; 2.3 Circadian Rhythms in an Insect Population; 2.4 Circadian Rhythms in Cell Populations
2.5 Biochemical Oscillators2.6 Neural Oscillators; 2.7 Oscillations in Cultures of Fungi; Chapter 3. Phase Shifts and Phase Response Curves; 3.1 Introduction; 3.2 Timing Sequences, Isochrones, Phase Response Curves, and Phase Transition Curves; 3.3 Experimental Phase Response Curves; 3.4 Analysis of Phase Response Curves; 3.5 Isochrones and Phase Response Curves of a van der Pol Oscillator; 3.6 Phase Response Curves of a Biochemical Oscillator; 3.7 Bibliographical Notes; Chapter 4. Entrainment of Oscillators by External Inputs; 4.1 Introduction; 4.2 Entrainment of a van der Pol Oscillator
4.3 Entrainment of Circadian Clocks by Light and Temperature Cycles4.4 Fringe Entrainment; 4.5 Entrainment of Oscillators by Pulses; 4.6 Entrainment of a Circadian Rhythm by Light Pulses; 4.7 Subharmonic Entrainment; 4.8 Bibliographical Notes; Chapter 5. The Dynamics of Circadian Oscillators; 5.1 Introduction; 5.2 Dependence of the Period of an Oscillator on Constant Environmental Factors; 5.3 Mathematical Formulation of a Model for Biological Oscillators; 5.4 The Independence between the Phase Response Curve and the Effects of Light on the Free-Run Period
5.5 Computer Simulation of Models for the Circadian Clock5.6 Starting and Stopping the Clock; 5.7 Bibliographical Notes; Chapter 6. Effects of Changing Environment on the Dynamics of Biological Oscillators; 6.1 Introduction; 6.2 State Variables and Parameters; 6.3 Temperature Compensation in the Drosophila Pseudoobscura Eclosion Rhythm; 6.4 Temperature Compensation in Unicellular Organisms; 6.5 Effects of Heavy Water; 6.6 Bibliographical Notes; Chapter 7. Populations of Interacting Oscillators; 7.1 Introduction; 7.2 Structural Stability
7.3 Monofrequency Oscillations in Systems of Coupled Oscillators Studied by Asymptotic Techniques7.4 Strategies for the Study of Populations of Oscillators; 7.5 Synchronization of Populations of Oscillators: The Weakly Nonlinear Case; 7.6 Synchronization of Populations of Oscillators: The General Case; 7.7 Concluding Remarks; 7.8 Bibliographical Notes; Chapter 8. Biological Phenomena Attributable to Populations of Oscillators; 8.1 Introduction; 8.2 Frequency Doubling in Circadian Rhythms; 8.3 A System of Coupled Biochemical Oscillators
8.4 Spatial Organization of Populations of Oscillators and an Interpretation of the Pattern of Zonation of Fungi Cultures
Summary: Biological Oscillators: Their Mathematical Analysis
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Front Cover; Biological Oscillators: Their Mathematical Analysis; Copyright Page; Dedication; Table ofContents; Preface; Acknowledgments; Chapter 1. Fundamentals of the Mathematical Theory of Oscillators; 1.1 Introduction; 1.2 Phase Plane Techniques; 1.3 An Example of Application of Phase Plane Techniques; 1.4 State Space; 1.5 Asymptotic Techniques; 1.6 Describing Function; 1.7 Conservative Systems; Chapter 2. Examples of Biological Rhythms; 2.1 Introduction; 2.2 Circadian Rhythms; 2.3 Circadian Rhythms in an Insect Population; 2.4 Circadian Rhythms in Cell Populations

2.5 Biochemical Oscillators2.6 Neural Oscillators; 2.7 Oscillations in Cultures of Fungi; Chapter 3. Phase Shifts and Phase Response Curves; 3.1 Introduction; 3.2 Timing Sequences, Isochrones, Phase Response Curves, and Phase Transition Curves; 3.3 Experimental Phase Response Curves; 3.4 Analysis of Phase Response Curves; 3.5 Isochrones and Phase Response Curves of a van der Pol Oscillator; 3.6 Phase Response Curves of a Biochemical Oscillator; 3.7 Bibliographical Notes; Chapter 4. Entrainment of Oscillators by External Inputs; 4.1 Introduction; 4.2 Entrainment of a van der Pol Oscillator

4.3 Entrainment of Circadian Clocks by Light and Temperature Cycles4.4 Fringe Entrainment; 4.5 Entrainment of Oscillators by Pulses; 4.6 Entrainment of a Circadian Rhythm by Light Pulses; 4.7 Subharmonic Entrainment; 4.8 Bibliographical Notes; Chapter 5. The Dynamics of Circadian Oscillators; 5.1 Introduction; 5.2 Dependence of the Period of an Oscillator on Constant Environmental Factors; 5.3 Mathematical Formulation of a Model for Biological Oscillators; 5.4 The Independence between the Phase Response Curve and the Effects of Light on the Free-Run Period

5.5 Computer Simulation of Models for the Circadian Clock5.6 Starting and Stopping the Clock; 5.7 Bibliographical Notes; Chapter 6. Effects of Changing Environment on the Dynamics of Biological Oscillators; 6.1 Introduction; 6.2 State Variables and Parameters; 6.3 Temperature Compensation in the Drosophila Pseudoobscura Eclosion Rhythm; 6.4 Temperature Compensation in Unicellular Organisms; 6.5 Effects of Heavy Water; 6.6 Bibliographical Notes; Chapter 7. Populations of Interacting Oscillators; 7.1 Introduction; 7.2 Structural Stability

7.3 Monofrequency Oscillations in Systems of Coupled Oscillators Studied by Asymptotic Techniques7.4 Strategies for the Study of Populations of Oscillators; 7.5 Synchronization of Populations of Oscillators: The Weakly Nonlinear Case; 7.6 Synchronization of Populations of Oscillators: The General Case; 7.7 Concluding Remarks; 7.8 Bibliographical Notes; Chapter 8. Biological Phenomena Attributable to Populations of Oscillators; 8.1 Introduction; 8.2 Frequency Doubling in Circadian Rhythms; 8.3 A System of Coupled Biochemical Oscillators

8.4 Spatial Organization of Populations of Oscillators and an Interpretation of the Pattern of Zonation of Fungi Cultures

Biological Oscillators: Their Mathematical Analysis

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