Spatial Dynamics and Pattern Formation in Biological Populations (Original PDF from Publisher)

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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