Partial Differential Equations in Ecology : 80 Years and Counting

Partial differential equations (PDEs) have been used in theoretical ecology research for more than eighty years. Nowadays, along with a variety of different mathematical techniques, they remain as an efficient, widely used modelling framework; as a matter of fact, the range of PDE applications has e...

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Other Authors: Petrovskii, Sergei (Editor)
Format: Book Chapter
Published: Basel, Switzerland MDPI - Multidisciplinary Digital Publishing Institute 2021
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245 1 0 |a Partial Differential Equations in Ecology : 80 Years and Counting 
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520 |a Partial differential equations (PDEs) have been used in theoretical ecology research for more than eighty years. Nowadays, along with a variety of different mathematical techniques, they remain as an efficient, widely used modelling framework; as a matter of fact, the range of PDE applications has even become broader. This volume presents a collection of case studies where applications range from bacterial systems to population dynamics of human riots. 
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653 |a cross diffusion 
653 |a Turing patterns 
653 |a non-constant positive solution 
653 |a animal movement 
653 |a correlated random walk 
653 |a movement ecology 
653 |a population dynamics 
653 |a taxis 
653 |a telegrapher's equation 
653 |a invasive species 
653 |a linear determinacy 
653 |a population growth 
653 |a mutation 
653 |a spreading speeds 
653 |a travelling waves 
653 |a optimal control 
653 |a partial differential equation 
653 |a invasive species in a river 
653 |a continuum models 
653 |a partial differential equations 
653 |a individual based models 
653 |a plant populations 
653 |a phenotypic plasticity 
653 |a vegetation pattern formation 
653 |a desertification 
653 |a homoclinic snaking 
653 |a front instabilities 
653 |a Evolutionary dynamics 
653 |a G-function 
653 |a Quorum Sensing 
653 |a Public Goods 
653 |a semi-linear parabolic system of equations 
653 |a generalist predator 
653 |a pattern formation 
653 |a Turing instability 
653 |a Turing-Hopf bifurcation 
653 |a bistability 
653 |a regime shift 
653 |a carrying capacity 
653 |a spatial heterogeneity 
653 |a Pearl-Verhulst logistic model 
653 |a reaction-diffusion model 
653 |a energy constraints 
653 |a total realized asymptotic population abundance 
653 |a chemostat model 
653 |a social dynamics 
653 |a wave of protests 
653 |a long transients 
653 |a ghost attractor 
653 |a prey-predator 
653 |a diffusion 
653 |a nonlocal interaction 
653 |a spatiotemporal pattern 
653 |a Allen-Cahn model 
653 |a Cahn-Hilliard model 
653 |a spatial patterns 
653 |a spatial fluctuation 
653 |a dynamic behaviors 
653 |a reaction-diffusion 
653 |a spatial ecology 
653 |a stage structure 
653 |a dispersal 
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