Spatial Dynamics and Pattern Formation in Biological Populations (Original PDF from Publisher)
The book offers an introduction to the modeling of spatiotemporal phenomena in ecology , epidemiology and brain systems using deterministic (and some stochastic) methods .
A review of the traditional models in the areas with contemporary applications is provided . The dynamics of biological populations are influenced by spatial dynamics and diffuse processes , as is explained in detail in the beginning of the book . These procedures are crucial to comprehending the onset and progression of pandemics , which aids in the development of public health focused control measures .
Using traditional models of neuronal dynamics in space and time , a brief description of the functioning mechanisms of the brain (single neuron models and network level) is provided . In ecology , epidemiology and neuroscience , pertinent phenomena and current modeling techniques are given , which give examples of pattern development in these models . We can examine the dynamics of the macroscopic and microscopic behavior of underlying systems as well as the travelling wave-type patterns seen in dispersive systems by analyzing patterns .
As they move on to discussing virus dynamics , the authors provide a thorough study of many types of infectious illness models , including two for influenza , five for the Ebola virus and seven for the Zika virus with diffusion and time delay . The study of brain dynamics (neural systems in space and time) is covered in a separate chapter. The presentation of significant developments in reaction-diffusion system modeling and a study of spatiotemporal patterning in the systems . The creation of suitable mathematical models as well as thorough analysis (including those of linear stability , weakly nonlinear analysis, bifurcation analysis , control theory and numerical simulation) are discussed .
Key Elements
includes a discussion of the basic ideas and mathematical abilities needed to analyze reaction-diffusion models for biological populations. The analysis is explained in such a way that readers with a rudimentary understanding of differential equations and numerical techniques can follow along . Figures are also used to illustrate the results . leverages traditional models of population dynamics , virus dynamics and brain dynamics to focus on mathematical modeling and numerical simulations . wide range of models employing both spatial and non-spatial methods are covered . includes one , two and multispecies reaction-diffusion models from biochemical and ecological perspectives .
The stability of equilibrium points , Turing instability , Hopf bifurcation and pattern forms are all examined in models . uses MATLAB to create patterns and Mathematica to solve problems . Exercises contain examples and problems that have been solved . For advanced undergraduate , graduate and research students , the book is appropriate . It offers information from the majority of the most current works for individuals who are working in the aforementioned fields . The text covers all the foundational ideas and mathematical techniques required to create models and conduct analysis .
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