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Cross-diffusive Instabilities and Aggregation in Partial Differential Equation Models of Interacting Populations
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| 자료유형 | 학위논문 |
|---|---|
| 서명/저자사항 | Cross-diffusive Instabilities and Aggregation in Partial Differential Equation Models of Interacting Populations. |
| 개인저자 | deForest, Russ. |
| 단체저자명 | The Pennsylvania State University. Mathematics. |
| 발행사항 | [S.l.]: The Pennsylvania State University., 2019. |
| 발행사항 | Ann Arbor: ProQuest Dissertations & Theses, 2019. |
| 형태사항 | 143 p. |
| 기본자료 저록 | Dissertations Abstracts International 80-12B. Dissertation Abstract International |
| ISBN | 9781392318300 |
| 학위논문주기 | Thesis (Ph.D.)--The Pennsylvania State University, 2019. |
| 일반주기 |
Source: Dissertations Abstracts International, Volume: 80-12, Section: B.
Publisher info.: Dissertation/Thesis. Advisor: Belmonte, Andrew. |
| 요약 | 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. |
| 일반주제명 | Mathematics. |
| 언어 | 영어 |
| 바로가기 | 
: 이 자료의 원문은 한국교육학술정보원에서 제공합니다. |
