Time Lags in Biological Models:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Berlin, Heidelberg
Springer Berlin Heidelberg
1978
|
| Schriftenreihe: | Lecture Notes in Biomathematics
27 |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | 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 integro-differential equations. In these lecture notes I discuss the reasons for including lags, especially distributed lags, in biological models. These reasons may be inherent in the system studied, or may be the result of simplifying assumptions made in the model used. I examine some of the techniques available for studying the solution of the equations. A large proportion of the material presented relates to a special method that can be applied to a particular class of distributed lags. This method uses an extended set of ordinary differential equations. I examine the local stability of equilibrium points, and the existence and frequency of periodic solutions. I discuss the qualitative effects of lags, and how these differ according to the choice of discrete or distributed lag. The models studied are drawn from the population dynamiCS of single species (logistic growth, the chemostat) and of interacting pairs of species (predation, mutualism), from cell population dynamiCS (haemopoiesis) and from biochemical kinetics (the Goodwin oscillator). The last chapter is devoted to a population model employing difference equations. All these models include non-linear terms |
| Beschreibung: | 1 Online-Ressource (VIII, 114 p) |
| ISBN: | 9783642931079 9783540090922 |
| ISSN: | 0341-633X |
| DOI: | 10.1007/978-3-642-93107-9 |
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| 500 | |a 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 integro-differential equations. In these lecture notes I discuss the reasons for including lags, especially distributed lags, in biological models. These reasons may be inherent in the system studied, or may be the result of simplifying assumptions made in the model used. I examine some of the techniques available for studying the solution of the equations. A large proportion of the material presented relates to a special method that can be applied to a particular class of distributed lags. This method uses an extended set of ordinary differential equations. I examine the local stability of equilibrium points, and the existence and frequency of periodic solutions. I discuss the qualitative effects of lags, and how these differ according to the choice of discrete or distributed lag. The models studied are drawn from the population dynamiCS of single species (logistic growth, the chemostat) and of interacting pairs of species (predation, mutualism), from cell population dynamiCS (haemopoiesis) and from biochemical kinetics (the Goodwin oscillator). The last chapter is devoted to a population model employing difference equations. All these models include non-linear terms | ||
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| dewey-hundreds | 500 - Natural sciences and mathematics |
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| discipline | Mathematik |
| doi_str_mv | 10.1007/978-3-642-93107-9 |
| format | Electronic eBook |
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| isbn | 9783642931079 9783540090922 |
| issn | 0341-633X |
| language | English |
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| spelling | MacDonald, Norman Verfasser aut Time Lags in Biological Models by Norman MacDonald Berlin, Heidelberg Springer Berlin Heidelberg 1978 1 Online-Ressource (VIII, 114 p) txt rdacontent c rdamedia cr rdacarrier Lecture Notes in Biomathematics 27 0341-633X 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 integro-differential equations. In these lecture notes I discuss the reasons for including lags, especially distributed lags, in biological models. These reasons may be inherent in the system studied, or may be the result of simplifying assumptions made in the model used. I examine some of the techniques available for studying the solution of the equations. A large proportion of the material presented relates to a special method that can be applied to a particular class of distributed lags. This method uses an extended set of ordinary differential equations. I examine the local stability of equilibrium points, and the existence and frequency of periodic solutions. I discuss the qualitative effects of lags, and how these differ according to the choice of discrete or distributed lag. The models studied are drawn from the population dynamiCS of single species (logistic growth, the chemostat) and of interacting pairs of species (predation, mutualism), from cell population dynamiCS (haemopoiesis) and from biochemical kinetics (the Goodwin oscillator). The last chapter is devoted to a population model employing difference equations. All these models include non-linear terms Mathematics Mathematics, general Mathematik Biologisches System (DE-588)4122930-7 gnd rswk-swf Mathematisches Modell (DE-588)4114528-8 gnd rswk-swf Biologisches System (DE-588)4122930-7 s Mathematisches Modell (DE-588)4114528-8 s 1\p DE-604 https://doi.org/10.1007/978-3-642-93107-9 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | MacDonald, Norman Time Lags in Biological Models Mathematics Mathematics, general Mathematik Biologisches System (DE-588)4122930-7 gnd Mathematisches Modell (DE-588)4114528-8 gnd |
| subject_GND | (DE-588)4122930-7 (DE-588)4114528-8 |
| title | Time Lags in Biological Models |
| title_auth | Time Lags in Biological Models |
| title_exact_search | Time Lags in Biological Models |
| title_full | Time Lags in Biological Models by Norman MacDonald |
| title_fullStr | Time Lags in Biological Models by Norman MacDonald |
| title_full_unstemmed | Time Lags in Biological Models by Norman MacDonald |
| title_short | Time Lags in Biological Models |
| title_sort | time lags in biological models |
| topic | Mathematics Mathematics, general Mathematik Biologisches System (DE-588)4122930-7 gnd Mathematisches Modell (DE-588)4114528-8 gnd |
| topic_facet | Mathematics Mathematics, general Mathematik Biologisches System Mathematisches Modell |
| url | https://doi.org/10.1007/978-3-642-93107-9 |
| work_keys_str_mv | AT macdonaldnorman timelagsinbiologicalmodels |