[1]
|
M. S. Alber, M. A. Kiskowski and Y. Jing, Lattice gas cellular automaton model for rippling and aggregation in myxobacteria, Physica D, 191 (2004), 343-358.
|
[2]
|
U. Börner and M. Bär, Pattern formation in a reaction-advection model with delay: A continuum approach to myxobacterial rippling, Annalen der Physik, 13 (2004), 432-441. doi: 10.1002/andp.200410086
|
[3]
|
U. Börner, A. Deutsch, H. Reichenbach and M. Bär, Rippling patterns in aggregates of myxobacteria arise from cell-cell collisions, Physical Review Letters, 89 (2002), 078101.
|
[4]
|
O. Diekmann, M. Gyllenberg, J. A. J. Metz and H. R. Thieme, On the formulation and analysis of general deterministic structured population models I. Linear Theory, J. Math. Biol., 36 (1998), 349-388. doi: 10.1007/s002850050104
|
[5]
|
O. Diekmann, M. Gyllenberg, H. Huang, M. Kirkilionis, J. A. J. Metz and H. R. Thieme, On the formulation and analysis of general deterministic structured population models II. Nonlinear theory, J. Math. Biol., 43 (2001), 157-189. doi: 10.1007/s002850170002
|
[6]
|
M. Dworkin and D. Kaiser eds., "Myxobacteria II," American Society for Microbiology (AMS) Press, 1993.
|
[7]
|
R. Erban and H. J. Hwang, Global existence results for complex hyperbolic models of bacterial chemotaxis, DCDS-B, 6 (2006), 1239-1260. doi: 10.3934/dcdsb.2006.6.1239
|
[8]
|
R. Erban and H. Othmer, From signal transduction to spatial pattern formation in E.coli : A paradigm for multi-scale modeling in biology, Multiscale Modeling and Simulation, 3 (2005), 362-394. doi: 10.1137/040603565
|
[9]
|
E. Geigant, "Nichtlineare Integro-Differential-Gleichungen zur Modellierung interaktiver Musterbildungsprozesse auf $S^{1}$," (German) [Nonlinear Integro-Differential Equations for the Modelling of Interactive Pattern Formation Processes on $S^{1}$], Bonner Mathematische Schriften 323 Ph.D thesis, University of Bonn, 1999.
|
[10]
|
E. Geigant, On peak and periodic solutions of an integro-differential equation on $S^1$, in "Geometric Analysis and Nonlinear Partial Differential Equations", Springer-Verlag, Berlin, (2003), 463-474.
|
[11]
|
E. Geigant and M. Stoll, Bifurcation analysis of an orientational aggregation model, J. Math. Biol., 46 (2003), 537-563. doi: 10.1007/s00285-002-0187-1
|
[12]
|
A. Gierer and H. Meinhardt, A theory of biological pattern formation, Kybernetik, 12, (1972), 30-39. doi: 10.1007/BF00289234
|
[13]
|
T. Hillen, A Turing model with correlated random walk, J. Math. Biol., 35 (1996), 49-72. doi: 10.1007/s002850050042
|
[14]
|
O. Igoshin, J. Neu and G. Oster, Developmental waves in Myxobacteria: A novel pattern formation mechanism, Phys. Rev. E, 7 (2004), 1-11.
|
[15]
|
K. Kang, B. Perthame, A. Stevens and J. J. L. Velázquez, An Integro-differential equation model for alignment and orientational aggregation, J. of Differential Equations, 246 (2009), 1387-1421. doi: 10.1016/j.jde.2008.11.006
|
[16]
|
T. Kato, "Perturbation Theory for Linear Operators," Springer-Verlag, Berlin, 1980. doi: 10.1007/978-3-642-66282-9
|
[17]
|
F. Lutscher and A. Stevens, Emerging patterns in a hyperbolic model for locally interacting cell systems, J. Nonlinear Science, 12 (2002), 619-640. doi: 10.1007/s00332-002-0510-4
|
[18]
|
H. Meinhardt, Morphogenesis of lines and nets, Differentiation, 6 (1976), 117-123.
|
[19]
|
J. D. Murray, "Mathematical Biology I and II," Interdisciplinary Applied Mathematics 17 and 18, Springer-Verlag, New York, 2002/03.
|
[20]
|
H. Othmer, S. Dunbar and W. Alt, Models of dispersal in biological systems, J. Math. Biol., 26 (1988), 263-298. doi: 10.1007/BF00277392
|
[21]
|
B. Perthame, "Transport Equations in Biology," Frontiers in Mathematics, Birkhäuser-Verlag, Basel, 2007.
|
[22]
|
B. Pfistner, "Ein Eindimensionales Modell Zum Schwarmverhalten der Myxobakterien Unter Besonderer Berücksichtigung der Randzonenentwicklung," (German) [A one-dimensional model on the swarming behavior of Myxobacteria, with special consideration of the development of the boundary zone], Ph.D thesis, University of Bonn, 1992.
|
[23]
|
I. Primi, A. Stevens and J. J. L. Velázquez, Mass-selection in alignment models with non-deterministic effects, Communication in PDE, 34 (2009), 419-456. doi: 10.1080/03605300902797171
|
[24]
|
M. Rotenberg, Transport theory for growing cell populations, J. Theor. Biology, 103 (1983), 181-199. doi: 10.1016/0022-5193(83)90024-3
|
[25]
|
J. Scheuer, "Pattern Formation in Reaction-Drift and Diffusion Systems," Diploma thesis, University of Heidelberg, 2009.
|
[26]
|
H. R. Thieme, "Mathematics in Population Biology," Princeton Series in Theoretical and Computational Biology, Princeton University Press, Princeton, NJ, 2003.
|
[27]
|
A. M. Turing, The chemical basis of morphogenesis, Philosophical Transactions of the Royal Society of London. Series B, Biological Sciences, 237 (1952), 37-72.
|