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All issues Volume 11 / No 5 (2016) Math. Model. Nat. Phenom., 11 5 (2016) 1-3 References
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Issue
Math. Model. Nat. Phenom.
Volume 11, Number 5, 2016
Bifurcations and Pattern Formation in Biological Applications
Page(s) 1 - 3
DOI https://doi.org/10.1051/mmnp/201611501
Published online 07 December 2016
  1. O. Aydogmus Patterns and transitions to instability in an intraspecific competition model with nonlocal diffusion and interaction, Math. Model. Nat. Phenom, 10 (6) (2015), 17–29. [MathSciNet] [Google Scholar]
  2. M. Banerjee, L. Zhang, Stabilizing role of nonlocal interaction on spatial pattern formation, Math. Model. Nat. Phenom., 11 5 (2016), 103–118. [MathSciNet] [Google Scholar]
  3. A. Bayliss, V.A. Volpert Patterns for competing populations with species specific nonlocal coupling Math. Model. Nat. Phenom, 10 (6) (2015), 30–47. [MathSciNet] [Google Scholar]
  4. T. Biancalani, D. Fanelli, F. Di Patti, Stochastic Turing patterns in the Brusselator model., Phys. Rev. E 81 (2010) 046215. [Google Scholar]
  5. A.E.F. Burgess, P.G. Schofield, S.F. Hubbard, M.A.J. Chaplain, T. Lorenzi, Dynamical patterns of coexisting strategies in a hybrid discrete-continuum spatial evolutionary game model, Math. Model. Nat. Phenom., 11 5 (2016), 49–64. [MathSciNet] [Google Scholar]
  6. M.A.J. Chaplain, G. Lolas, Mathematical modelling of cancer invasion of tissue: dynamic heterogeneity, Netw. Heterog. Media 1, (2006), 399–439. [Google Scholar]
  7. E.J. Crampin, E.A. Gaffney, P.K. Maini, Reaction and diffusion on growing domains: scenarios for robust pattern formation, Bull. Math. Biol. 61 (1999), 1093–1120. [CrossRef] [PubMed] [Google Scholar]
  8. H. Deng, A.V. Holden, L.F. Olsen (Editors), Chaos in Biological Systems, Springer 1987. [Google Scholar]
  9. R. Eftimie, C.K. Macnamara, J. Dushoff, J.L. Bramson, D.J.D. Earn, Bifurcations and chaotic dynamics in a tumour-immune-virus system, Math. Model. Nat. Phenom., 11 5 (2016), 65–85. [MathSciNet] [Google Scholar]
  10. A. Gierer, H. Meinhardt, Theory of biological pattern formation, Kybernetik, 12 (1972), 30–39. [CrossRef] [PubMed] [Google Scholar]
  11. J. Kelkel, C. Surulescu, On a stochastic reaction-diffusion system modeling pattern formation on seashells, J. Math. Biol., 60 (2010), 765–96. [CrossRef] [MathSciNet] [PubMed] [Google Scholar]
  12. S. Kondo, R. Asal, A reaction-diffusion wave on skin of the marine angelfish Pomacanthus, Nature, 376 (1995), 765–768. [CrossRef] [PubMed] [Google Scholar]
  13. A. Madzvamuse, A.H. Chung, Analysis and simulations of coupled bulk-surface reaction-diffusion systems on exponentially evolving volumes, Math. Model. Nat. Phenom., 11 5 (2016), 4–32. [MathSciNet] [Google Scholar]
  14. P.K. Maini, T.E. Woolley, R.E. Baker, E.A. Gaffney, S.S. Lee, Turing’s model for biological pattern formation and the robustness problem, Interface Focus, 2, (2012), 487–496. [CrossRef] [PubMed] [Google Scholar]
  15. A.J. McKane, T. Biancalani, T. Rogers, Stochastic pattern formation and spontaneous polarisation: the linear noise approximation and beyond, Bull. Math. Biol. 76 (2014), 895–921. [CrossRef] [MathSciNet] [PubMed] [Google Scholar]
  16. H. Meinhardt, Modelling of biological pattern formation, Academic Press, London, 1982. [Google Scholar]
  17. J.D. Murray, G. Oster, Generation of biological pattern and form, IMA J. Math. Med. Biol., 1 (1984), 1–25. [CrossRef] [MathSciNet] [PubMed] [Google Scholar]
  18. K.J. Painter, T. Hillen, Spatio-temporal chaos in a chemotaxis model, Physica D, 240, (2011), 363–375. [Google Scholar]
  19. J.A. Sherratt, Using numerical bifurcation analysis to study pattern formation in mussel beds, Math. Model. Nat. Phenom., 11 5 (2016), 86–102. [MathSciNet] [Google Scholar]
  20. I. Siekmann, H. Malchow, Fighting enemies and noise: Competition of residents and invaders in a stochastically fluctuating environment, Math. Model. Nat. Phenom., 11 5 (2016), 137–157. [MathSciNet] [Google Scholar]
  21. A.M. Turing, Chemical basis of morphogenesis, Phil. Trans. R. Soc. Lond., B 237, (1952), 37–72. [Google Scholar]
  22. D. Valenti, A. Giuffrida, G. Denaro, N. Pizzolato, L. Curcio, B. Spagnolo, S. Mazzola, G. Basilone, A. Bonanno, Noise induced phenomena in population dynamics, Math. Model. Nat. Phenom., 11 5 (2016), 158–174. [Google Scholar]
  23. D. Valenti, G. Denaro, F. Giarratana, A. Giuffrida, S. Mazzola, G. Basilone, S. Aronica, A. Bonanno, B. Spagnolo, Modeling of sensory characteristics based on the growth of food spoilage bacteria, Math. Model. Nat. Phenom., 11 5 (2016), 119–136. [Google Scholar]
  24. H.A. Wallace, L. Li, F.A. Davidson, Instability in a moving boundary: heterogeneous growth of bacterial biofilms, Math. Model. Nat. Phenom., 11 5 (2016), 33–48. [Google Scholar]

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