A reaction-diffusion model for inter-species competition and intra-species cooperation
This thesis deals with a two component reaction-diffusion system (RDS) for competing and cooperating species. We have analyse in detail the stability and bifurcation structure of equilibrium solutions of this system, a natural extension of the Lotka-Volterra system. We find seven topologically diffe...
| Main Author: | |
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| Format: | Thesis (University of Nottingham only) |
| Language: | English |
| Published: |
2013
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| Online Access: | https://eprints.nottingham.ac.uk/13545/ |
| _version_ | 1848791758397243392 |
|---|---|
| author | Rasheed, Shaker M. |
| author_facet | Rasheed, Shaker M. |
| author_sort | Rasheed, Shaker M. |
| building | Nottingham Research Data Repository |
| collection | Online Access |
| description | This thesis deals with a two component reaction-diffusion system (RDS) for competing and cooperating species. We have analyse in detail the stability and bifurcation structure of equilibrium solutions of this system, a natural extension of the Lotka-Volterra system. We find seven topologically different regions separated by bifurcation boundaries depending on the number and stability of equilibrium solutions, with four regions in which the solutions are similar to those in the Lotka-Volterra system. We study RDS in the small parameter of the range $0< \lambda \ll 1 $ (fast diffusion and slow reaction), and in a few cases we assume $\lambda=O(1)$. We consider three types of initial conditions, and we find three types of travelling wave solutions using numerical and asymptotic methods. However, neither numerical nor asymptotic methods were able to find a particular travelling wave solution which connects a coexistence state say, $(u_0,w_0)$ to an extinction state $(0,0)$ when $0< \lambda \ll 1 $. This type can be found when the reaction-diffusion system satisfy the symmetry property and $\lambda=1$. |
| first_indexed | 2025-11-14T18:33:36Z |
| format | Thesis (University of Nottingham only) |
| id | nottingham-13545 |
| institution | University of Nottingham Malaysia Campus |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-14T18:33:36Z |
| publishDate | 2013 |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | nottingham-135452025-02-28T11:25:49Z https://eprints.nottingham.ac.uk/13545/ A reaction-diffusion model for inter-species competition and intra-species cooperation Rasheed, Shaker M. This thesis deals with a two component reaction-diffusion system (RDS) for competing and cooperating species. We have analyse in detail the stability and bifurcation structure of equilibrium solutions of this system, a natural extension of the Lotka-Volterra system. We find seven topologically different regions separated by bifurcation boundaries depending on the number and stability of equilibrium solutions, with four regions in which the solutions are similar to those in the Lotka-Volterra system. We study RDS in the small parameter of the range $0< \lambda \ll 1 $ (fast diffusion and slow reaction), and in a few cases we assume $\lambda=O(1)$. We consider three types of initial conditions, and we find three types of travelling wave solutions using numerical and asymptotic methods. However, neither numerical nor asymptotic methods were able to find a particular travelling wave solution which connects a coexistence state say, $(u_0,w_0)$ to an extinction state $(0,0)$ when $0< \lambda \ll 1 $. This type can be found when the reaction-diffusion system satisfy the symmetry property and $\lambda=1$. 2013-10-15 Thesis (University of Nottingham only) NonPeerReviewed application/pdf en arr https://eprints.nottingham.ac.uk/13545/1/SHAKER_THESIS.pdf Rasheed, Shaker M. (2013) A reaction-diffusion model for inter-species competition and intra-species cooperation. PhD thesis, University of Nottingham. |
| spellingShingle | Rasheed, Shaker M. A reaction-diffusion model for inter-species competition and intra-species cooperation |
| title | A reaction-diffusion model for inter-species competition and intra-species cooperation |
| title_full | A reaction-diffusion model for inter-species competition and intra-species cooperation |
| title_fullStr | A reaction-diffusion model for inter-species competition and intra-species cooperation |
| title_full_unstemmed | A reaction-diffusion model for inter-species competition and intra-species cooperation |
| title_short | A reaction-diffusion model for inter-species competition and intra-species cooperation |
| title_sort | reaction-diffusion model for inter-species competition and intra-species cooperation |
| url | https://eprints.nottingham.ac.uk/13545/ |