A reaction-diffusion system of a predator-prey-mutualist model
dc.contributor.author | Zheng, Sining | en_US |
dc.date.accessioned | 2006-04-07T19:32:27Z | |
dc.date.available | 2006-04-07T19:32:27Z | |
dc.date.issued | 1986-04 | en_US |
dc.identifier.citation | Zheng, Sining (1986/04)."A reaction-diffusion system of a predator-prey-mutualist model." Mathematical Biosciences 78(2): 217-245. <http://hdl.handle.net/2027.42/26211> | en_US |
dc.identifier.uri | http://www.sciencedirect.com/science/article/B6VHX-45FKDN0-5/2/242c1830b406ca1cd79a0d0a6852c73d | en_US |
dc.identifier.uri | https://hdl.handle.net/2027.42/26211 | |
dc.description.abstract | Mutualism is part of many significant processes in nature. Mutualistic benefits arising from modification of predator-prey interactions involve interactions of at least three species. In this paper we investigate the Homogeneous Neumann problem and Dirichlet problem for a reaction-diffusion system of three species--a predator, a mutualist-prey, and a mutualist. The existence, uniqueness, and boundedness of the solution are established by means of the comparison principle and the monotonicity method. For the Neumann problem, we analyze the constant equilibrium solutions and their stability. For the Dirichlet problem, we prove the global asymptotic stability of the trivial equilibrium solution. Specifically, we study the existence and the asymptotic behavior of two nonconstant equilibrium solutions. The main method used in studying of the stability is the spectral analysis to the linearized operators. The O.D.E. problem for the same model was proposed and studied in [13]. Through our results, we can see the influences of the diffusion mechanism and the different boundary value conditions upon the asymptotic behavior of the populations. | en_US |
dc.format.extent | 1166118 bytes | |
dc.format.extent | 3118 bytes | |
dc.format.mimetype | application/pdf | |
dc.format.mimetype | text/plain | |
dc.language.iso | en_US | |
dc.publisher | Elsevier | en_US |
dc.title | A reaction-diffusion system of a predator-prey-mutualist model | en_US |
dc.type | Article | en_US |
dc.rights.robots | IndexNoFollow | en_US |
dc.subject.hlbsecondlevel | Public Health | en_US |
dc.subject.hlbsecondlevel | Statistics and Numeric Data | en_US |
dc.subject.hlbsecondlevel | Natural Resources and Environment | en_US |
dc.subject.hlbsecondlevel | Mathematics | en_US |
dc.subject.hlbsecondlevel | Ecology and Evolutionary Biology | en_US |
dc.subject.hlbsecondlevel | Biological Chemistry | en_US |
dc.subject.hlbtoplevel | Social Sciences | en_US |
dc.subject.hlbtoplevel | Science | en_US |
dc.subject.hlbtoplevel | Health Sciences | en_US |
dc.description.peerreviewed | Peer Reviewed | en_US |
dc.contributor.affiliationum | Department of Mathematics, University of Michigan, Ann Arbor, Michigan 48109, U.S.A.; Department of Applied Mathematics, Dalian Institute of Technology, Dalian, People's Republic of China | en_US |
dc.description.bitstreamurl | http://deepblue.lib.umich.edu/bitstream/2027.42/26211/1/0000291.pdf | en_US |
dc.identifier.doi | http://dx.doi.org/10.1016/0025-5564(86)90126-4 | en_US |
dc.identifier.source | Mathematical Biosciences | en_US |
dc.owningcollname | Interdisciplinary and Peer-Reviewed |
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