Partial Differential Equations in Ecology : 80 Years and Counting

doi:10.3390/books978-3-0365-0297-7

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https://mdpi.com/books/pdfview/book/3501

Contributor(s)

Petrovskii, Sergei (editor)

Language

English

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Abstract

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.

URI

https://directory.doabooks.org/handle/20.500.12854/68481

Keywords

cross diffusion; Turing patterns; non-constant positive solution; animal movement; correlated random walk; movement ecology; population dynamics; taxis; telegrapher’s equation; invasive species; linear determinacy; population growth; mutation; spreading speeds; travelling waves; optimal control; partial differential equation; invasive species in a river; continuum models; partial differential equations; individual based models; plant populations; phenotypic plasticity; vegetation pattern formation; desertification; homoclinic snaking; front instabilities; Evolutionary dynamics; G-function; Quorum Sensing; Public Goods; semi-linear parabolic system of equations; generalist predator; pattern formation; Turing instability; Turing-Hopf bifurcation; bistability; regime shift; carrying capacity; spatial heterogeneity; Pearl-Verhulst logistic model; reaction-diffusion model; energy constraints; total realized asymptotic population abundance; chemostat model; social dynamics; wave of protests; long transients; ghost attractor; prey–predator; diffusion; nonlocal interaction; spatiotemporal pattern; Allen–Cahn model; Cahn–Hilliard model; spatial patterns; spatial fluctuation; dynamic behaviors; reaction-diffusion; spatial ecology; stage structure; dispersal