Time Lags in Biological Models
In many biological models it is necessary to allow the rates of change of the variables to depend on the past history, rather than only the current values, of the variables. The models may require discrete lags, with the use of delay-differential equations, or distributed lags, with the use of integ...
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| Format: | eBook |
| Language: | English |
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Berlin, Heidelberg
Springer Berlin Heidelberg
1978, 1978
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| Edition: | 1st ed. 1978 |
| Series: | Lecture Notes in Biomathematics
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| Subjects: | |
| Online Access: | |
| Collection: | Springer Book Archives -2004 - Collection details see MPG.ReNa |
Table of Contents:
- 1. Introduction
- a. Discrete and Distributed Lag
- b. Origin of Lags in Biological Models
- c. Lag as an Alternative to Age Structure
- d. Lag as an Alternative to Spatial Structure
- e. The Effects of Lag
- f. Lags and Stochastic Models
- 2. Stability Analysis
- a. The Linear Chain Trick
- b. Instantaneous Models
- c. Models with a Single Discrete Lag
- d. Models with a Single Distributed Lag
- e. An Inequality for Distributed Lag
- f. The Monod Chemostat Model
- g. May’s Model of Obligate Mutualism
- 3. Periodic Solutions
- a. Periodic Solutions of the Linear Chain Equations
- b. The Method of Hastings, Tyson and Webster
- c. Hopf Bifurcation
- d. Numerical Integration
- 4. Logistic Growth of a Single Species
- a. Discrete Lag
- b. Distributed Lag in a Model of a Self-poisoning Population
- c. Linear Chain Calculations
- d. Hopf and H.T.W. Methods
- e. Constant Harvesting of a Population in the Presence of Lag
- f. Poincaré-Lindstedt Method for Discrete Lag
- g. An Epidemic Model Related to the Logistic Equation
- 5. Biochemical Oscillator Model
- a. The Goodwin Model
- b. Necessary Condition for Instability
- c. Expanding the Set of Equations
- d. A Single Goodwin Equation with Lag
- e. Discrete Lag in the Goodwin Equation
- 6. Models of Haemopoiesis
- a. Wheldon’s Model of Chronic Granulocytic Leukemia
- b. Two-lag Models of Cyclical Neutropenia
- c. Time Lag with Attrition; a Model of Cyclical Pancytopenia
- 7. Predation Models of the Volterra Type
- 8. Difference Equation Models
- a. Stability Analysis
- b. Conditions under which Spreading the Lag does not affect Local Stability
- c. Chaos in Discrete Dynamical Systems
- d. Extended Diapause in a Single Species Population Model
- e. Analogous Treatment of a Functional Differential Equation
- SupplementaryBibliography
- References