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
Two new embedded pairs of explicit Runge-Kutta methods adapted to the numerical solution of oscillatory problems
TL;DR: The construction of new embedded pairs of explicit Runge-Kutta methods specially adapted to the numerical solution of oscillatory problems is analyzed and their efficiency is compared with some standard and specially adapted pairs proposed in the scientific literature for solving oscillatory Problems.
Journal ArticleDOI
A discrete-time model with vaccination for a measles epidemic.
TL;DR: The results of the simulations indicate that a rate of immunity greater than 98% may be required to prevent an epidemic in a university population and the model has applications to other contagious diseases of SIR type.
School of Mathematical Sciences
TL;DR: A wide variety of archaeological applications involve the study of the geometrical properties of objects as discussed by the authors, with a view to relating size and shape to sets of covariates such as age, location, group etc.
Journal ArticleDOI
Evolutionary predictions should be based on individual-level traits.
TL;DR: A two‐habitat version of the logistic and Ricker equations from individual‐level processes is derived and the evolutionary dynamics of habitat‐specific carrying capacities with those of underlying individual‐ level traits contributing to the carrying capacities are compared.
Journal ArticleDOI
Diffusion-induced instability in chemically reacting systems: Steady-state multiplicity, oscillation, and chaos.
Istvan Lengyel,Irving R. Epstein +1 more
TL;DR: The dynamical behavior of two coupled cells or reactors is described, and three two-variable kinetic models are examined: the Brusselator, a model of the chlorine dioxide-iodine-malonic acid reaction, and the Degn-Harrison model.