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Cross-diffusive Instabilities and Ag...

deForest, Russ.

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Cross-diffusive Instabilities and Aggregation in Partial Differential Equation Models of Interacting Populations.

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Cross-diffusive Instabilities and Aggregation in Partial Differential Equation Models of Interacting Populations./
作者:	deForest, Russ.
出版者:	Ann Arbor : ProQuest Dissertations & Theses, : 2019,
面頁冊數:	143 p.
附註:	Source: Dissertations Abstracts International, Volume: 80-12, Section: B.
Contained By:	Dissertations Abstracts International80-12B.
標題:	Mathematics. -
電子資源:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=13917897
ISBN:	9781392318300

Cross-diffusive Instabilities and Aggregation in Partial Differential Equation Models of Interacting Populations.
deForest, Russ.

Cross-diffusive Instabilities and Aggregation in Partial Differential Equation Models of Interacting Populations. - Ann Arbor : ProQuest Dissertations & Theses, 2019 - 143 p.

Source: Dissertations Abstracts International, Volume: 80-12, Section: B.

Thesis (Ph.D.)--The Pennsylvania State University, 2019.

We propose several systems of quasilinear partial differential equations as spatial models of interacting biological populations. The key distinctive feature present in each model is a negative self-diffusivity in one of the populations. Despite the presence of negative self-diffusion, under our assumptions the resulting models correspond to normally parabolic systems or degenerate limiting cases of normally parabolic systems.We consider a spatial predator-prey model and show the existence of a cross-diffusive instability leading to spatial patterning. Numerical examples are given in one and two dimensions. Our model demonstrates a mechanism by which prey aggregate in response to predators, potentially reducing their individual risk of predation.We also consider several specific spatial models of polymorphic populations with both a cooperative and exploitative type in a nonlinear public goods game. Each phenotype is represented by a density and the fitness of each type depends locally on the density of all types. We demonstrate conditions for the existence of a cross-diffusive instability, leading to pattern formation and the advantageous aggregation of the cooperative type.

ISBN: 9781392318300Subjects--Topical Terms:

515831
Mathematics.

Cross-diffusive Instabilities and Aggregation in Partial Differential Equation Models of Interacting Populations.
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