MonographDOI
Mathematical Models in Biology
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TLDR
The theory of linear difference equations applied to population growth and the applications of nonlinear difference equations to population biology are explained.Abstract:
Part I. Discrete Process in Biology: 1. The theory of linear difference equations applied to population growth 2. Nonlinear difference equations 3. Applications of nonlinear difference equations to population biology Part II. Continuous Processes and Ordinary Differential Equations: 4. An introduction to continuous models 5. Phase-plane methods and qualitative solutions 6. Applications of continuous models to population dynamics 7. Models for molecular events 8. Limit cycles, oscillations, and excitable systems Part III. Spatially Distributed Systems and Partial Differential Equation Models: 9. An introduction to partial differential equations and diffusion in biological settings 10. Partial differential equation models in biology 11. Models for development and pattern formation in biological systems Selected answers Author index Subject index.read more
Citations
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Journal ArticleDOI
Recent advances in modeling sleep: from the clinic to society and disease
John H. Abel,John H. Abel,Kimaya Lecamwasam,Melissa A. St. Hilaire,Melissa A. St. Hilaire,Elizabeth B. Klerman,Elizabeth B. Klerman +6 more
TL;DR: This review of recent updates in modeling the timing and durations of sleep and wake, the underlying neurophysiology of sleepand wake, and the application of these models in understanding cognition and disease proposes the utility of individualized models of sleep for precision sleep medicine.
Journal ArticleDOI
Number of common sites visited by N random walkers.
TL;DR: In this paper, the mean number of common sites, W(N), visited by N independent random walkers each of length t and all starting at the origin at t = 0 in d dimensions is computed analytically.
Journal ArticleDOI
Generalized Allee effect model.
TL;DR: Offering a new view point on the weak and strong demographic Allee effect, it is proposed to combine them with the Richards growth model and model validation with ecological data is presented for some special situations.
Journal ArticleDOI
On the risk of extinction of a wild plant species through spillover of a biological control agent: Analysis of an ecosystem compartment model
TL;DR: The analysis indicates that a high attack rate on the target species, which is a selection criterion for biocontrol agents with respect to their effectiveness, also mitigates risks resulting from spillover and non-target effects.
Journal ArticleDOI
The effect of pollen competition on maintenance of variation in fertilisation ability
Åsa Lankinen,Io Skogsmyr +1 more
TL;DR: The dynamic model shows that maintenance of variation in male competitive ability is more probable when differences in pollen competitive ability influence male fitness, i.e., in cases with pollen competition, than when Differences in this trait only is a side effect of selection for more viable individuals.