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Mathematical Biosciences and Engineering (MBE)
 

A tridiagonal patch model of bacteria inhabiting a nanofabricated landscape
Pages: 953 - 973, Issue 4, August 2017

doi:10.3934/mbe.2017050      Abstract        References        Full text (396.8K)           Related Articles

Robert Stephen Cantrell - Department of Mathematics, The University of Miami, Coral Gables, FL 33124, United States (email)
Brian Coomes - Department of Mathematics, The University of Miami, Coral Gables, FL 33124, United States (email)
Yifan Sha - Department of Public Health Division of Biostatistics, Miller School of Medicine, The University of Miami, Miami, FL 33136, United States (email)

1 K. J. Brown and S. S. Lin, On the existence of positive solutions for an eigenvalue problem with an indefinite weight function, Journal of Mathematical Analysis and Applications, 75 (1980), 112-120.       
2 R. S. Cantrell and C. Cosner, Spatial Ecology via Reaction-Diffusion Equations, Wiley and Sons, Chichester, UK, 2003.       
3 F. Centler, I. Fetzer and M. Thullner, Modeling population patterns of chemotactic bacteria in homogeneous porous media, Journal of Theoretical Biology, 287 (2011), 82-91.       
4 B. Fiedler and T. Gedeon, A Lyapunov function for tridiagonal competitive-cooperative systems, SIAM Journal on Mathematical Analysis, 30 (1999), 469-478.       
5 J. K. Hale and P. Waltman, Persistence in infinite-dimensional systems, SIAM Journal on Mathematical Analysis, 20 (1989), 388-395.       
6 J. E. Keymer, P. Galajda, C. Muldoon, S. Park and R. H. Austin, Bacterial metapopulations in nanofabricated landscapes, Proceedings of the National Academy of Sciences, 103 (2006), 17290-17295.
7 S. Senn and P. Hess, On positive solutions of a linear elliptic eigenvalue problem with Neumann boundary conditions, Mathematische Annalen, 258 (1982), 459-470.       
8 J. Smillie, Competitive and cooperative tridiagonal systems of differential equations, SIAM Journal on Mathematical Analysis, 15 (1984), 530-534.       
9 H. R. Thieme, Persistence under relaxed point-dissipativity (with applications to an endemic model), SIAM Journal on Mathematical Analysis, 24 (1993), 407-435.       

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