Delays in physiological systems
- 1 December 1979
- journal article
- Published by Springer Nature in Journal of Mathematical Biology
- Vol. 8 (4) , 345-364
- https://doi.org/10.1007/bf00275831
Abstract
In comparison to most physical or chemical systems, biological systems are of extreme complexity. In addition the time needed for transport or processing of chemical components or signals may be of considerable length. Thus temporal delays have to be incorporated into models leading to differential-difference and functional differential equations rather than ordinary differential equations. A number of examples, on different levels of biological organization, demonstrate that delays can have an influence on the qualitative behavior of biological systems: The existence or non-existence of instabilities and periodic or even chaotic oscillations can entirely depend on the presence or absence of delays with appropriate duration.Keywords
This publication has 26 references indexed in Scilit:
- Periodic solutions of ẋ(t) = –f(x(t), x(t – 1))Mathematical Methods in the Applied Sciences, 1979
- Some periodicity criteria for functional differential equationsmanuscripta mathematica, 1978
- Time lag in a model of a biochemical reaction sequence with end product inhibitionJournal of Theoretical Biology, 1977
- Visual control of orientation behaviour in the fly: Part I. A quantitative analysisQuarterly Reviews of Biophysics, 1976
- Simple mathematical models with very complicated dynamicsNature, 1976
- Real-time delayed tracking in fliesNature, 1976
- Time Delays, Density-Dependence and Single-Species OscillationsJournal of Animal Ecology, 1974
- A Quantitative Description of the Dynamics of Excitation and Inhibition in the Eye of Limulus The Journal of general physiology, 1970
- Mathematics of cellular control processes I. Negative feedback to one geneJournal of Theoretical Biology, 1968
- Zur Theorie des BalancierensMathematische Nachrichten, 1948