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Wilson, Howard Boyd (1993) Applications of dynamical systems in ecology. PhD thesis, University of Warwick.
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Official URL: http://webcat.warwick.ac.uk/record=b1416277~S15
Abstract
This thesis consists of five original pieces of work contained in chapters 2, 4, 6, 7 and 8. These cover four topics within the subject area of theoretical ecology: epidemiology, chaos in ecology, evolution and spatially extended ecological systems.
Chapter 2 puts forward a new mechanism for producing chaos in ecology. We show that near extinctions in the SEIR model stabilise a chaotic repeller. This mechanism works for a wide-range of parameter values and so resolves the debate about which dynamic regime is associated with realistic values. It also highlights the problem of treating fluctuations as being either deterministically or stochastically produced.
Chapter 4 describes a new technique for identifying chaos based on measuring the divergence of trajectories over a range of spatial scales. It correctly identifies noise scales and chaos in model systems and is also applied to some real ecological data sets.
In chapters 4 and 5 we set evolutionary game theory in a nonlinear dynamical framework. We introduce a powerful new tool, the selective pressure, for analysing ecological models and identifying evolutionary stable states. It allows analysis of systems where complex attractors exist. We also study the evolution of phenotypic distributions and provide a new mechanism for evolutionary discontinuities.
In chapter 6 we look at an individually-based spatially extended system. This model is spatially heterogeneous and stochastic. However we show that the dynamics on a certain scale are deterministic and low-dimensional. We show how to identify the most efficient spatial scale at which to monitor the system.
| Item Type: | Thesis (PhD) | ||||
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| Subjects: | Q Science > QA Mathematics Q Science > QH Natural history R Medicine > RA Public aspects of medicine |
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| Library of Congress Subject Headings (LCSH): | Ecology -- Mathematical models, Epidemiology -- Mathematical models, Chaotic behavior in systems , Dynamics | ||||
| Official Date: | November 1993 | ||||
| Dates: |
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| Institution: | University of Warwick | ||||
| Theses Department: | Mathematics Institute | ||||
| Thesis Type: | PhD | ||||
| Publication Status: | Unpublished | ||||
| Supervisor(s)/Advisor: | Rand, D. A. (David A.) | ||||
| Extent: | 162 leaves | ||||
| Language: | eng |
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