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
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Journal ArticleDOI
Factors influencing the structure and maintenance of fish schools
TL;DR: In this paper, the authors explored the factors that contribute to fish school formation and maintenance using a series of computer simulation experiments, including the functional form of attraction to and repulsion from neighbors, alignment with neighbors, regions of no social force (neutral zones), scaling of neighbor influence, random noise and frictional drag.
Journal ArticleDOI
On the velocity of epidemic waves in model plant disease epidemics
TL;DR: This study considers two simple models based on reaction-diffusion equations with scale-dependent diffusivity based on the theory of turbulent diffusion, which suggests that spread becomes more efficient as the area with diseased plants expands.
Journal ArticleDOI
Consequences of symbiosis for food web dynamics.
TL;DR: It becomes possible that a stable two-nutrient–two-prey population system becomes unstable by invasion of a predator and eventually the predator goes extinct together with the two prey populations, that is, the complete food web is destroyed.
Journal ArticleDOI
The memory effect on fractional calculus: an application in the spread of COVID-19
Laécio Carvalho de Barros,Michele Martins Lopes,Francielle Santo Pedro,Estevão Esmi,José Paulo Carvalho dos Santos,Daniel Eduardo Sánchez +5 more
TL;DR: The main interest of this work is to attest how the hysteresis phenomenon, which describes a type of memory effect present in biological systems, can be treated by fractional calculus.