Partial Differential Equations in Ecology 80 Years and Counting

• Other Authors: Petrovskii, Sergei (Editor)
• Format: Electronic Book Chapter
• Language: English
• Published: Basel, Switzerland MDPI - Multidisciplinary Digital Publishing Institute 2021
• Subjects: Research & information: general; Mathematics & science; 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
• Online Access: DOAB: download the publication; DOAB: description of the publication

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...