-
1
-
-
0031230367
-
Properties of solutions for a chemotaxis system
-
Allegretto, W., Xie, H., Yang, S.: Properties of solutions for a chemotaxis system. J. Math. Biol. 35, 949-966 (1997)
-
(1997)
J. Math. Biol.
, vol.35
, pp. 949-966
-
-
Allegretto, W.1
Xie, H.2
Yang, S.3
-
2
-
-
0019188958
-
Biased random walk model for chemotaxis and related diffusion approximation
-
Alt, W.: Biased random walk model for chemotaxis and related diffusion approximation. J. Math. Biol. 9, 147-177 (1980)
-
(1980)
J. Math. Biol.
, vol.9
, pp. 147-177
-
-
Alt, W.1
-
3
-
-
0023151749
-
Transient behavior of a chemotaxis system modelling certain types of tissue inflammation
-
Alt, W., Lauffenburger, D.A.: Transient behavior of a chemotaxis system modelling certain types of tissue inflammation. J. Math. Biol. 24(6), 691-722 (1987)
-
(1987)
J. Math. Biol.
, vol.24
, Issue.6
, pp. 691-722
-
-
Alt, W.1
Lauffenburger, D.A.2
-
4
-
-
33645215770
-
Signal transduction in bacterial chemotaxis
-
Baker, M.D., Wolanin, P.M., Stock, J.B.: Signal transduction in bacterial chemotaxis. Bioessays 28(1), 9-22 (2006)
-
(2006)
Bioessays
, vol.28
, Issue.1
, pp. 9-22
-
-
Baker, M.D.1
Wolanin, P.M.2
Stock, J.B.3
-
5
-
-
0022253881
-
A mathematical model of tumour-induced capillary growth
-
Balding, D., McElwain, D.L.: A mathematical model of tumour-induced capillary growth. J. Theor. Biol. 114(1), 53-73 (1985)
-
(1985)
J. Theor. Biol.
, vol.114
, Issue.1
, pp. 53-73
-
-
Balding, D.1
McElwain, D.L.2
-
6
-
-
0000657461
-
Local and global solvability of some parabolic systems modelling chemotaxis
-
Biler, P.: Local and global solvability of some parabolic systems modelling chemotaxis. Adv. Math. Sci. Appl. 8(2), 715-743 (1998)
-
(1998)
Adv. Math. Sci. Appl.
, vol.8
, Issue.2
, pp. 715-743
-
-
Biler, P.1
-
7
-
-
0001580322
-
Global solutions to some parabolic-elliptic systems of chemotaxis
-
Biler, P.: Global solutions to some parabolic-elliptic systems of chemotaxis. Adv. Math. Sci. Appl. 9(1), 347-359 (1999)
-
(1999)
Adv. Math. Sci. Appl.
, vol.9
, Issue.1
, pp. 347-359
-
-
Biler, P.1
-
8
-
-
0022604029
-
Model for chemotactic bacterial bands
-
Boon, J.P., Herpigny, B.: Model for chemotactic bacterial bands. Bull. Math. Biol. 48(1), 1-19 (1986)
-
(1986)
Bull. Math. Biol.
, vol.48
, Issue.1
, pp. 1-19
-
-
Boon, J.P.1
Herpigny, B.2
-
9
-
-
10244229064
-
Precise computations of chemotactic collapse using moving mesh methods
-
Budd, C.J., Carretero-Gonźdflez, R., Russell, R.D.: Precise computations of chemotactic collapse using moving mesh methods. J. Comput. Phys. 202(2), 463-487 (2005)
-
(2005)
J. Comput. Phys.
, vol.202
, Issue.2
, pp. 463-487
-
-
Budd, C.J.1
Carretero-Gonźdflez, R.2
Russell, R.D.3
-
10
-
-
33748418000
-
Free-flight responses of Drosophila melanogaster to attractive odors
-
Budick, S.A., Dickinson, M.H.: Free-flight responses of Drosophila melanogaster to attractive odors. J. Exp. Biol. 209(15), 3001-3017 (2006)
-
(2006)
J. Exp. Biol.
, vol.209
, Issue.15
, pp. 3001-3017
-
-
Budick, S.A.1
Dickinson, M.H.2
-
11
-
-
0026023209
-
Complex patterns formed by motile cells of Escherichia coli
-
Budrene, E.O., Berg, H.C.: Complex patterns formed by motile cells of Escherichia coli. Nature 349(6310), 630-633 (1991)
-
(1991)
Nature
, vol.349
, Issue.6310
, pp. 630-633
-
-
Budrene, E.O.1
Berg, H.C.2
-
12
-
-
0029023398
-
Dynamics of formation of symmetrical patterns by chemotactic bacteria
-
Budrene, E.O., Berg, H.C.: Dynamics of formation of symmetrical patterns by chemotactic bacteria. Nature 376(6535), 49-53 (1995)
-
(1995)
Nature
, vol.376
, Issue.6535
, pp. 49-53
-
-
Budrene, E.O.1
Berg, H.C.2
-
13
-
-
84863538590
-
The Keller-Segel model for chemotaxis: Linear vs. nonlinear diffusion
-
(to appear)
-
Burger, M., Di Francesco, M., Dolak-Struss, Y.: The Keller-Segel model for chemotaxis: linear vs. nonlinear diffusion. SIAM J. Math. Anal. (2008) (to appear)
-
(2008)
SIAM J. Math. Anal.
-
-
Burger, M.1
Di Francesco, M.2
Dolak-Struss, Y.3
-
14
-
-
0031694810
-
The effect of chemotaxis and chemokinesis on leukocyte locomotion: A new interpretation of experimental results
-
Byrne, H.M., Cave, G., McElwain, D.L.: The effect of chemotaxis and chemokinesis on leukocyte locomotion: a new interpretation of experimental results. IMA J. Math. Appl. Med. Biol. 15(3), 235-256 (1998)
-
(1998)
IMA J. Math. Appl. Med. Biol.
, vol.15
, Issue.3
, pp. 235-256
-
-
Byrne, H.M.1
Cave, G.2
McElwain, D.L.3
-
15
-
-
11144223026
-
A new interpretation of the Keller-Segel model based on multiphase modelling
-
Byrne, H.M., Owen, M.R.: A new interpretation of the Keller-Segel model based on multiphase modelling. J. Math. Biol. 49, 604-626 (2004)
-
(2004)
J. Math. Biol.
, vol.49
, pp. 604-626
-
-
Byrne, H.M.1
Owen, M.R.2
-
16
-
-
0034470377
-
Mathematical modelling of angiogenesis
-
Chaplain, M.A.: Mathematical modelling of angiogenesis. J. Neurooncol. 50(1-2), 37-51 (2000)
-
(2000)
J. Neurooncol.
, vol.50
, Issue.1-2
, pp. 37-51
-
-
Chaplain, M.A.1
-
17
-
-
77957176863
-
A model mechanism for the chemotactic response of endothelial cells to tumor angiogenesis factor
-
Chaplain, M.A.J., Stuart, A.M.: A model mechanism for the chemotactic response of endothelial cells to tumor angiogenesis factor. IMA J. Math. Appl. Med. Biol. 10, 149-168 (1993)
-
(1993)
IMA J. Math. Appl. Med. Biol.
, vol.10
, pp. 149-168
-
-
Chaplain, M.A.J.1
Stuart, A.M.2
-
18
-
-
0019784884
-
Nonlinear aspects of chemotaxis
-
Childress, S., Percus, J.K.: Nonlinear aspects of chemotaxis. Math. Biosci. 56, 217-237 (1981)
-
(1981)
Math. Biosci.
, vol.56
, pp. 217-237
-
-
Childress, S.1
Percus, J.K.2
-
19
-
-
28444472417
-
The great escape: When cancer cells hijack the genes for chemotaxis and motility
-
Condeelis, J., Singer, R.H., Segall, J.E.: The great escape: when cancer cells hijack the genes for chemotaxis and motility. Annu. Rev. Cell Dev. Biol. 21, 695-718 (2005)
-
(2005)
Annu. Rev. Cell Dev. Biol.
, vol.21
, pp. 695-718
-
-
Condeelis, J.1
Singer, R.H.2
Segall, J.E.3
-
20
-
-
26844499863
-
Global solutions of some chemotaxis and angiogenesis systems in high space dimensions
-
Corrias, L., Perthame, B., Zaag, H.: Global solutions of some chemotaxis and angiogenesis systems in high space dimensions. Milan J. Math. 72, 1-28 (2004)
-
(2004)
Milan J. Math.
, vol.72
, pp. 1-28
-
-
Corrias, L.1
Perthame, B.2
Zaag, H.3
-
21
-
-
0015528241
-
Quantitative analysis of bacterial migration in chemotaxis
-
Dahlquist, F.W., Lovely, P., Koshland, D.E.: Quantitative analysis of bacterial migration in chemotaxis. Nat. New Biol. 236, 120-123 (1972)
-
(1972)
Nat. New Biol.
, vol.236
, pp. 120-123
-
-
Dahlquist, F.W.1
Lovely, P.2
Koshland, D.E.3
-
22
-
-
0031589922
-
A discrete cell model with adaptive signalling for aggregation of dictyostelium discoideum
-
Dallon, J.C., Othmer, H.G.: A discrete cell model with adaptive signalling for aggregation of dictyostelium discoideum. Philos. Trans. R. Soc. B 352, 391-417 (1997)
-
(1997)
Philos. Trans. R. Soc. B
, vol.352
, pp. 391-417
-
-
Dallon, J.C.1
Othmer, H.G.2
-
23
-
-
67749112512
-
Singular limit of a degenerate chemotaxis-fisher equation
-
Dkhil, F.: Singular limit of a degenerate chemotaxis-fisher equation. HiroshimaMath. J. 34, 101-115 (2004)
-
(2004)
HiroshimaMath. J.
, vol.34
, pp. 101-115
-
-
Dkhil, F.1
-
24
-
-
0141723483
-
Cattaneo models for chemotaxis, numerical solution and pattern formation
-
Dolak, Y., Hillen, T.: Cattaneo models for chemotaxis, numerical solution and pattern formation. J. Math. Biol. 46(2), 153-170 (2003)
-
(2003)
J. Math. Biol.
, vol.46
, Issue.2
, pp. 153-170
-
-
Dolak, Y.1
Hillen, T.2
-
25
-
-
33644610345
-
The Keller-Segel model with logistic sensitivity function and small diffusivity
-
Dolak, Y., Schmeiser, C.: The Keller-Segel model with logistic sensitivity function and small diffusivity. SIAM J. Appl. Math. 66, 286-308 (2005)
-
(2005)
SIAM J. Appl. Math.
, vol.66
, pp. 286-308
-
-
Dolak, Y.1
Schmeiser, C.2
-
26
-
-
33745600126
-
Chemotactic cell movement during Dictyostelium development and gastrulation
-
Dormann, D., Weijer, C.J.: Chemotactic cell movement during Dictyostelium development and gastrulation. Curr. Opin. Genet. Dev. 16(4), 367-373 (2006)
-
(2006)
Curr. Opin. Genet. Dev.
, vol.16
, Issue.4
, pp. 367-373
-
-
Dormann, D.1
Weijer, C.J.2
-
27
-
-
0035738988
-
A new deterministic spatio-temporal continuum model for biofilm development
-
Eberl, H.J., Parker, D.F., Loosdrecht, M.C.M. van.: A new deterministic spatio-temporal continuum model for biofilm development. J. Theor. Med. 3(3), 161-175 (2001)
-
(2001)
J. Theor. Med.
, vol.3
, Issue.3
, pp. 161-175
-
-
Eberl, H.J.1
Parker, D.F.2
van Loosdrecht, M.C.M.3
-
28
-
-
3843116761
-
-
Imperial College Press, London
-
Eisenbach, M.: Chemotaxis. Imperial College Press, London (2004)
-
(2004)
Chemotaxis
-
-
Eisenbach, M.1
-
29
-
-
0026133844
-
Measurement of bacterial random motility and chemotaxis coefficients: II. application of single cell based mathematical model
-
Ford, R.M., Lauffenburger, D.A.: Measurement of bacterial random motility and chemotaxis coefficients: II. application of single cell based mathematical model. Biotechnol. Bioeng. 37, 661-672 (1991)
-
(1991)
Biotechnol. Bioeng.
, vol.37
, pp. 661-672
-
-
Ford, R.M.1
Lauffenburger, D.A.2
-
30
-
-
0032445844
-
Global behavior of a reaction-diffusion system modelling chemotaxis
-
Gajewski, H., Zacharias, K.: Global behavior of a reaction-diffusion system modelling chemotaxis. Math. Nachr. 159, 77-114 (1998)
-
(1998)
Math. Nachr.
, vol.159
, pp. 77-114
-
-
Gajewski, H.1
Zacharias, K.2
-
31
-
-
0024355866
-
A model of herd grazing as a travelling wave, chemotaxis and stability
-
Gueron, S., Liron, N.: A model of herd grazing as a travelling wave, chemotaxis and stability. J. Math. Biol. 27(5), 595-608 (1989)
-
(1989)
J. Math. Biol.
, vol.27
, Issue.5
, pp. 595-608
-
-
Gueron, S.1
Liron, N.2
-
32
-
-
0003370729
-
Convergence to a viscocity solution for an advectionreaction-diffusion equation arising from a chemotaxis-growth model
-
Henry, M., Hilhorst, D., Schätzle, R.: Convergence to a viscocity solution for an advectionreaction-diffusion equation arising from a chemotaxis-growth model. Hiroshima Math. J. 29, 591-630 (1999)
-
(1999)
Hiroshima Math. J.
, vol.29
, pp. 591-630
-
-
Henry, M.1
Hilhorst, D.2
Schätzle, R.3
-
34
-
-
33847682685
-
A classification of spikes and plateaus
-
Hillen, T.: A classification of spikes and plateaus. SIAM Rev. 49(1), 35-51 (2007)
-
(2007)
SIAM Rev.
, vol.49
, Issue.1
, pp. 35-51
-
-
Hillen, T.1
-
35
-
-
0034917420
-
The diffusion limit of transport equations derived from velocity jump processes
-
Hillen, T., Othmer, H.G.: The diffusion limit of transport equations derived from velocity jump processes. SIAM J. Appl. Math. 61(3), 751-775 (2000)
-
(2000)
SIAM J. Appl. Math.
, vol.61
, Issue.3
, pp. 751-775
-
-
Hillen, T.1
Othmer, H.G.2
-
36
-
-
0001404830
-
Global existence for a parabolic chemotaxis model with prevention of overcrowding
-
Hillen, T., Painter, K.: Global existence for a parabolic chemotaxis model with prevention of overcrowding. Adv. Appl. Math. 26, 280-301 (2001)
-
(2001)
Adv. Appl. Math.
, vol.26
, pp. 280-301
-
-
Hillen, T.1
Painter, K.2
-
37
-
-
33847657245
-
Global existence for chemotaxis with finite sampling radius
-
Hillen, T., Painter, K., Schmeiser, C.: Global existence for chemotaxis with finite sampling radius. Discr. Cont. Dyn. Syst. B 7(1), 125-144 (2007)
-
(2007)
Discr. Cont. Dyn. Syst. B
, vol.7
, Issue.1
, pp. 125-144
-
-
Hillen, T.1
Painter, K.2
Schmeiser, C.3
-
38
-
-
0028987613
-
Dictyostelium discoideum: Cellular self-organisation in an excitable biological medium
-
Höfer, T., Sherratt, J.A., Maini, P.K.: Dictyostelium discoideum: cellular self-organisation in an excitable biological medium. Proc. R. Soc. Lond. B. 259, 249-257 (1995)
-
(1995)
Proc. R. Soc. Lond. B.
, vol.259
, pp. 249-257
-
-
Höfer, T.1
Sherratt, J.A.2
Maini, P.K.3
-
39
-
-
0005525774
-
Lyapunov functions and L p-estimates for a class of reaction-diffusion systems
-
Horstmann, D.: Lyapunov functions and L p-estimates for a class of reaction-diffusion systems. Coll. Math. 87, 113-127 (2001)
-
(2001)
Coll. Math.
, vol.87
, pp. 113-127
-
-
Horstmann, D.1
-
40
-
-
4744373150
-
From 1970 until present: The Keller-Segel model in chemotaxis and its consequences I
-
Horstmann, D.: From 1970 until present: the Keller-Segel model in chemotaxis and its consequences I. Jahresberichte DMV 105(3), 103-165 (2003)
-
(2003)
Jahresberichte DMV
, vol.105
, Issue.3
, pp. 103-165
-
-
Horstmann, D.1
-
41
-
-
84867943821
-
A constructive approach to traveling waves in chemotaxis
-
Horstmann, D., Stevens, A.: A constructive approach to traveling waves in chemotaxis. J. Nonlin. Sci. 14(1), 1-25 (2004)
-
(2004)
J. Nonlin. Sci.
, vol.14
, Issue.1
, pp. 1-25
-
-
Horstmann, D.1
Stevens, A.2
-
42
-
-
18044364211
-
Chemotaxis and random motility in unsteady chemoattractant fields: A computational study
-
Jabbarzadeh, E., Abrams, C.F.: Chemotaxis and random motility in unsteady chemoattractant fields: a computational study. J. Theor. Biol. 235(2), 221-232 (2005)
-
(2005)
J. Theor. Biol.
, vol.235
, Issue.2
, pp. 221-232
-
-
Jabbarzadeh, E.1
Abrams, C.F.2
-
43
-
-
0023504111
-
Swarms of predators exhibit 'prey-taxis' if individual predators use arearestricted search
-
Kareiva, P., Odell, G.: Swarms of predators exhibit 'prey-taxis' if individual predators use arearestricted search. Am. Nat. 130(2), 233-270 (1987)
-
(1987)
Am. Nat.
, vol.130
, Issue.2
, pp. 233-270
-
-
Kareiva, P.1
Odell, G.2
-
44
-
-
0014748565
-
Initiation of slime mold aggregation viewed as an instability
-
Keller, E.F., Segel, L.A.: Initiation of slime mold aggregation viewed as an instability. J. Theor. Biol. 26, 399-415 (1970)
-
(1970)
J. Theor. Biol.
, vol.26
, pp. 399-415
-
-
Keller, E.F.1
Segel, L.A.2
-
46
-
-
0015010990
-
Traveling bands of chemotactic bacteria: A theoretical analysis
-
Keller, E.F., Segel, L.A.: Traveling bands of chemotactic bacteria: a theoretical analysis. J. Theor. Biol. 30, 377-380 (1971)
-
(1971)
J. Theor. Biol.
, vol.30
, pp. 377-380
-
-
Keller, E.F.1
Segel, L.A.2
-
47
-
-
0016190439
-
Pheromone-regulated anemotaxis in flying moths
-
Kennedy, J.S., Marsh, D.: Pheromone-regulated anemotaxis in flying moths. Science 184, 999-1001 (1974)
-
(1974)
Science
, vol.184
, pp. 999-1001
-
-
Kennedy, J.S.1
Marsh, D.2
-
48
-
-
0035501627
-
Limits of chemotaxis growth model
-
Kim, I.C.: Limits of chemotaxis growth model. Nonlinear Anal. 46, 817-834 (2001)
-
(2001)
Nonlinear Anal.
, vol.46
, pp. 817-834
-
-
Kim, I.C.1
-
49
-
-
31144461544
-
Mesa-type patterns in the one-dimensional Brusselator and their stability
-
Kolokolnikov, T., Erneux, T., Wei, J.: Mesa-type patterns in the one-dimensional Brusselator and their stability. Physica D 214, 63-77 (2006)
-
(2006)
Physica D
, vol.214
, pp. 63-77
-
-
Kolokolnikov, T.1
Erneux, T.2
Wei, J.3
-
50
-
-
15844396394
-
Preventing blow-up in a chemotaxis model
-
Kowalczyk, R.: Preventing blow-up in a chemotaxis model. J. Math. Anal. Appl. 305, 566-588 (2005)
-
(2005)
J. Math. Anal. Appl.
, vol.305
, pp. 566-588
-
-
Kowalczyk, R.1
-
51
-
-
33846882488
-
A priori bounds and global existence for a strongly coupled quasilinear parabolic system modelling chemotaxis
-
Kuiper, H.: A priori bounds and global existence for a strongly coupled quasilinear parabolic system modelling chemotaxis. Electron. J. Differ. Equ. 52, 1-18 (2001)
-
(2001)
Electron. J. Differ. Equ.
, vol.52
, pp. 1-18
-
-
Kuiper, H.1
-
52
-
-
39349116728
-
Global attractors for cross-diffusion systems on domains of arbitrary dimensions
-
Kuiper, H., Dung, L.: Global attractors for cross-diffusion systems on domains of arbitrary dimensions. Rocky Mountain J. Math. 37(5), 1645-1668 (2007)
-
(2007)
Rocky Mountain J. Math.
, vol.37
, Issue.5
, pp. 1645-1668
-
-
Kuiper, H.1
Dung, L.2
-
53
-
-
0344896624
-
Chemotactic cellular migration: Smooth and discontinuous travelling wave solutions
-
Landman, K.A., Pettet, G.J., Newgreen, D.F.: Chemotactic cellular migration: smooth and discontinuous travelling wave solutions. SIAM J. Appl. Math. 63(5), 1666-1681 (2003)
-
(2003)
SIAM J. Appl. Math.
, vol.63
, Issue.5
, pp. 1666-1681
-
-
Landman, K.A.1
Pettet, G.J.2
Newgreen, D.F.3
-
54
-
-
0037340207
-
Mathematical models of cell colonization of uniformly growing domains
-
Landman, K.A., Pettet, G.J., Newgreen, D.F.: Mathematical models of cell colonization of uniformly growing domains. Bull. Math. Biol. 65(2), 235-262 (2003)
-
(2003)
Bull. Math. Biol.
, vol.65
, Issue.2
, pp. 235-262
-
-
Landman, K.A.1
Pettet, G.J.2
Newgreen, D.F.3
-
55
-
-
0017117005
-
Model for the chemotactic response of a bacterial population
-
Lapidus, I.R., Schiller, R.: Model for the chemotactic response of a bacterial population. Biophys. J 16(7), 779-789 (1976)
-
(1976)
Biophys. J
, vol.16
, Issue.7
, pp. 779-789
-
-
Lapidus, I.R.1
Schiller, R.2
-
56
-
-
0034181948
-
Signaling pathways induced by vascular endothelial growth factor (review)
-
Larrivee, B., Karsan, A.: Signaling pathways induced by vascular endothelial growth factor (review). Int. J. Mol. Med. 5(5), 447-456 (2000)
-
(2000)
Int. J. Mol. Med.
, vol.5
, Issue.5
, pp. 447-456
-
-
Larrivee, B.1
Karsan, A.2
-
57
-
-
0020695978
-
Localized bacterial infection in a distributed model for tissue inflammation
-
Lauffenburger, D.A., Kennedy, C.R.: Localized bacterial infection in a distributed model for tissue inflammation. J. Math. Biol. 16(2), 141-163 (1983)
-
(1983)
J. Math. Biol.
, vol.16
, Issue.2
, pp. 141-163
-
-
Lauffenburger, D.A.1
Kennedy, C.R.2
-
59
-
-
0031162898
-
A system of reaction diffusion equations arising in the theory of reinforced random walks
-
Levine, H.A., Sleeman, B.D.: A system of reaction diffusion equations arising in the theory of reinforced random walks. SIAM J. Appl. Math. 57, 683-730 (1997)
-
(1997)
SIAM J. Appl. Math.
, vol.57
, pp. 683-730
-
-
Levine, H.A.1
Sleeman, B.D.2
-
60
-
-
0032100234
-
Model analysis of spatial patterns in Mountain Pine Beetle outbreaks
-
Logan, J.A., White, B.J., Bentz, P., Powell, J.A.: Model analysis of spatial patterns in Mountain Pine Beetle outbreaks. Theor. Popul. Biol. 53(3), 236-255 (1998)
-
(1998)
Theor. Popul. Biol.
, vol.53
, Issue.3
, pp. 236-255
-
-
Logan, J.A.1
White, B.J.2
Bentz, P.3
Powell, J.A.4
-
61
-
-
0038645352
-
Chemotactic signaling, microglia, andAlzheimer's disease senile plaques: Is there a connection?
-
Luca, M., Chavez-Ross, A., Edelstein-Keshet, L., Mogilner, A.: Chemotactic signaling, microglia, andAlzheimer's disease senile plaques: is there a connection? Bull. Math. Biol. 65(4), 693-730 (2003)
-
(2003)
Bull. Math. Biol.
, vol.65
, Issue.4
, pp. 693-730
-
-
Luca, M.1
Chavez-Ross, A.2
Edelstein-Keshet, L.3
Mogilner, A.4
-
62
-
-
0025986583
-
Bifurcating spatially heterogeneous solutions in a chemotaxis model for biological pattern generation
-
Maini, P.K., Myerscough, M.R., Winters, K.H., Murray, J.D.: Bifurcating spatially heterogeneous solutions in a chemotaxis model for biological pattern generation. Bull. Math. Biol. 53(5), 701-719 (1991)
-
(1991)
Bull. Math. Biol.
, vol.53
, Issue.5
, pp. 701-719
-
-
Maini, P.K.1
Myerscough, M.R.2
Winters, K.H.3
Murray, J.D.4
-
63
-
-
16644400591
-
Mathematical modeling of tumor-induced angiogenesis
-
Mantzaris, N.V., Webb, S., Othmer, H.G.: Mathematical modeling of tumor-induced angiogenesis. J. Math. Biol. 49(2), 111-187 (2004)
-
(2004)
J. Math. Biol.
, vol.49
, Issue.2
, pp. 111-187
-
-
Mantzaris, N.V.1
Webb, S.2
Othmer, H.G.3
-
64
-
-
0035957392
-
How amoeboids self-organize into a fruiting body: Multicellular coordination in Dictyostelium discoideum
-
Maree, A.F., Hogeweg, P.: How amoeboids self-organize into a fruiting body: multicellular coordination in Dictyostelium discoideum. Proc. Natl. Acad. Sci. USA 98(7), 3879-3883 (2001)
-
(2001)
Proc. Natl. Acad. Sci. USA
, vol.98
, Issue.7
, pp. 3879-3883
-
-
Maree, A.F.1
Hogeweg, P.2
-
65
-
-
0030243891
-
Aggregation pattern dynamics in a chemotaxis model including growth
-
Mimura, M., Tsujikawa, T.: Aggregation pattern dynamics in a chemotaxis model including growth. Physica A 230, 499-543 (1996)
-
(1996)
Physica A
, vol.230
, pp. 499-543
-
-
Mimura, M.1
Tsujikawa, T.2
-
66
-
-
0344392719
-
Motility of Escherichia coli cells in clusters formed by chemotactic aggregation
-
Mittal, N., Budrene, E.O., Brenner, M.P., Van Oudenaarden, A.: Motility of Escherichia coli cells in clusters formed by chemotactic aggregation. Proc. Natl. Acad. Sci. USA 100(23), 13259-13263 (2003)
-
(2003)
Proc. Natl. Acad. Sci. USA
, vol.100
, Issue.23
, pp. 13259-13263
-
-
Mittal, N.1
Budrene, E.O.2
Brenner, M.P.3
van Oudenaarden, A.4
-
67
-
-
0031436781
-
Molecular neurogenetics of chemotaxis and thermotaxis in the nematode Caenorhabditis elegans
-
Mori, I., Ohshima, Y.: Molecular neurogenetics of chemotaxis and thermotaxis in the nematode Caenorhabditis elegans. Bioessays 19(12), 1055-1064 (1997)
-
(1997)
Bioessays
, vol.19
, Issue.12
, pp. 1055-1064
-
-
Mori, I.1
Ohshima, Y.2
-
69
-
-
0025919498
-
Pigmentation pattern formation on snakes
-
Murray, J.D., Myerscough, M.R.: Pigmentation pattern formation on snakes. J. Theor. Biol. 149(3), 339-360 (1991)
-
(1991)
J. Theor. Biol.
, vol.149
, Issue.3
, pp. 339-360
-
-
Murray, J.D.1
Myerscough, M.R.2
-
70
-
-
0031904305
-
Pattern formation in a generalized chemotactic model
-
Myerscough, M.R., Maini, P.K., Painter, K.J.: Pattern formation in a generalized chemotactic model. Bull. Math. Biol. 60(1), 1-26 (1998)
-
(1998)
Bull. Math. Biol.
, vol.60
, Issue.1
, pp. 1-26
-
-
Myerscough, M.R.1
Maini, P.K.2
Painter, K.J.3
-
71
-
-
0001205112
-
Application of the Trudinger-Moser inequality to a parabolic system of chemotaxis
-
Nagai, T., Senba, T., Yoshida, K.: Application of the Trudinger-Moser inequality to a parabolic system of chemotaxis. Funkcial. Ekvac. 40(3), 411-433 (1997)
-
(1997)
Funkcial. Ekvac.
, vol.40
, Issue.3
, pp. 411-433
-
-
Nagai, T.1
Senba, T.2
Yoshida, K.3
-
72
-
-
0015757937
-
Chemotaxis, signal relaying and aggregationmorphology
-
Nanjundiah, V.: Chemotaxis, signal relaying and aggregationmorphology. J. Theor. Biol. 42, 63-105 (1973)
-
(1973)
J. Theor. Biol.
, vol.42
, pp. 63-105
-
-
Nanjundiah, V.1
-
73
-
-
0017184096
-
Traveling bands of chemotactic bacteria revisited
-
Odell, G.M., Keller, E.F.: Traveling bands of chemotactic bacteria revisited. J. Theor. Biol. 56(1), 243-247 (1976)
-
(1976)
J. Theor. Biol.
, vol.56
, Issue.1
, pp. 243-247
-
-
Odell, G.M.1
Keller, E.F.2
-
74
-
-
0036778798
-
Exponential attractor for a chemotaxis-growth system of equations
-
Osaki, K., Tsujikawa, T., Yagi, A., Mimura, M.: Exponential attractor for a chemotaxis-growth system of equations. Nonlinear Anal. 51, 119-144 (2002)
-
(2002)
Nonlinear Anal.
, vol.51
, pp. 119-144
-
-
Osaki, K.1
Tsujikawa, T.2
Yagi, A.3
Mimura, M.4
-
75
-
-
0141644434
-
Finite dimensional attractor for one-dimensional Keller-Segel equations
-
Osaki, K., Yagi, A.: Finite dimensional attractor for one-dimensional Keller-Segel equations. Funkcial. Ekvac. 44, 441-469 (2001)
-
(2001)
Funkcial. Ekvac.
, vol.44
, pp. 441-469
-
-
Osaki, K.1
Yagi, A.2
-
76
-
-
0023746235
-
Models of dispersal in biological systems
-
Othmer, H.G., Dunbar, S.R., Alt, W.: Models of dispersal in biological systems. J. Math. Biol. 26, 263-298 (1988)
-
(1988)
J. Math. Biol.
, vol.26
, pp. 263-298
-
-
Othmer, H.G.1
Dunbar, S.R.2
Alt, W.3
-
77
-
-
0036553052
-
The diffusion limit of transport equations II: Chemotaxis equations
-
Othmer, H.G., Hillen, T.: The diffusion limit of transport equations II: chemotaxis equations. SIAM J. Appl. Math. 62(4), 1122-1250 (2002)
-
(2002)
SIAM J. Appl. Math.
, vol.62
, Issue.4
, pp. 1122-1250
-
-
Othmer, H.G.1
Hillen, T.2
-
78
-
-
0031207030
-
Aggregation, blowup and collapse: The ABC's of taxis in reinforced random walks
-
Othmer, H.G., Stevens, A.: Aggregation, blowup and collapse: The ABC's of taxis in reinforced random walks. SIAM J. Appl. Math. 57, 1044-1081 (1997)
-
(1997)
SIAM J. Appl. Math.
, vol.57
, pp. 1044-1081
-
-
Othmer, H.G.1
Stevens, A.2
-
79
-
-
0031558747
-
Pattern formation and spatiotemporal irregularity in a model for macrophage-tumour interactions
-
Owen, M.R., Sherratt, J.A.: Pattern formation and spatiotemporal irregularity in a model for macrophage-tumour interactions. J. Theor. Biol. 189(1), 63-80 (1997)
-
(1997)
J. Theor. Biol.
, vol.189
, Issue.1
, pp. 63-80
-
-
Owen, M.R.1
Sherratt, J.A.2
-
80
-
-
4944248574
-
Volume-filling and quorum-sensing in models for chemosensitive movement
-
Painter, K., Hillen, T.: Volume-filling and quorum-sensing in models for chemosensitive movement. Can. Appl. Math. Quart. 10(4), 501-543 (2002)
-
(2002)
Can. Appl. Math. Quart.
, vol.10
, Issue.4
, pp. 501-543
-
-
Painter, K.1
Hillen, T.2
-
81
-
-
0034304765
-
Complex spatial patterns in a hybrid chemotaxis reaction-diffusion model
-
Painter, K.J., Maini, P.K., Othmer, H.G.: Complex spatial patterns in a hybrid chemotaxis reaction-diffusion model. J. Math. Biol. 41(4), 285-314 (2000)
-
(2000)
J. Math. Biol.
, vol.41
, Issue.4
, pp. 285-314
-
-
Painter, K.J.1
Maini, P.K.2
Othmer, H.G.3
-
82
-
-
0034304765
-
Development and applications of a model for cellular response to multiple chemotactic cues
-
Painter, K.J., Maini, P.K., Othmer, H.G.: Development and applications of a model for cellular response to multiple chemotactic cues. J. Math. Biol. 41(4), 285-314 (2000)
-
(2000)
J. Math. Biol.
, vol.41
, Issue.4
, pp. 285-314
-
-
Painter, K.J.1
Maini, P.K.2
Othmer, H.G.3
-
83
-
-
0033545988
-
Stripe formation in juvenile pomacanthus via chemotactic response to a reaction-diffusion mechanism
-
Painter, K.J., Othmer, H.G., Maini, P.K.: Stripe formation in juvenile pomacanthus via chemotactic response to a reaction-diffusion mechanism. Proc. Natl. Acad. Sci. USA 96, 5549-5554 (1999)
-
(1999)
Proc. Natl. Acad. Sci. USA
, vol.96
, pp. 5549-5554
-
-
Painter, K.J.1
Othmer, H.G.2
Maini, P.K.3
-
84
-
-
0034641740
-
A model for individual and collective cell movement in Dictyostelium discoideum
-
Palsson, E., Othmer, H.G.: A model for individual and collective cell movement in Dictyostelium discoideum. Proc. Natl. Acad. Sci. USA 97(19), 10448-10453 (2000)
-
(2000)
Proc. Natl. Acad. Sci. USA
, vol.97
, Issue.19
, pp. 10448-10453
-
-
Palsson, E.1
Othmer, H.G.2
-
85
-
-
0036713578
-
Molecular control of neuronalmigration
-
Park, H.T., Wu, J., Rao, Y.: Molecular control of neuronalmigration. Bioessays 24(9), 821-827 (2002)
-
(2002)
Bioessays
, vol.24
, Issue.9
, pp. 821-827
-
-
Park, H.T.1
Wu, J.2
Rao, Y.3
-
86
-
-
51249193541
-
Random walk with persistence and external bias
-
Patlak, C.S.: Random walk with persistence and external bias. Bull. Math. Biophys. 15, 311-338 (1953)
-
(1953)
Bull. Math. Biophys.
, vol.15
, pp. 311-338
-
-
Patlak, C.S.1
-
88
-
-
0030407429
-
Biological inferences from a mathematical model for malignant invasion
-
Perumpanani, A.J., Sherratt, J.A., Norbury, J., Byrne, H.M.: Biological inferences from a mathematical model for malignant invasion. Invas. Metastas. 16(4-5), 209-221 (1996)
-
(1996)
Invas. Metastas.
, vol.16
, Issue.4-5
, pp. 209-221
-
-
Perumpanani, A.J.1
Sherratt, J.A.2
Norbury, J.3
Byrne, H.M.4
-
90
-
-
21244493212
-
Metastability in chemotaxis models
-
Potapov, A., Hillen, T.: Metastability in chemotaxis models. J. Dyn. Diff. Equ. 17, 293-330 (2005)
-
(2005)
J. Dyn. Diff. Equ.
, vol.17
, pp. 293-330
-
-
Potapov, A.1
Hillen, T.2
-
91
-
-
0029192972
-
Finite time blow up in some models of chemotaxis
-
Rascle, M., Ziti, C.: Finite time blow up in some models of chemotaxis. J. Math. Biol. 33, 388-414 (1995)
-
(1995)
J. Math. Biol.
, vol.33
, pp. 388-414
-
-
Rascle, M.1
Ziti, C.2
-
92
-
-
0024940626
-
Transport models for chemotactic cell populations based on individual cell behavior
-
Rivero, M.A., Tranquillo, R.T., Buettner, H.M., Lauffenburger, D.A.: Transport models for chemotactic cell populations based on individual cell behavior. Chem. Eng. Sci. 44, 1-17 (1989)
-
(1989)
Chem. Eng. Sci.
, vol.44
, pp. 1-17
-
-
Rivero, M.A.1
Tranquillo, R.T.2
Buettner, H.M.3
Lauffenburger, D.A.4
-
93
-
-
0017136101
-
Incorporation of receptor kinetics into a model for bacterial chemotaxis
-
Segel, L.A.: Incorporation of receptor kinetics into a model for bacterial chemotaxis. J. Theor. Biol. 57(1), 23-42 (1976)
-
(1976)
J. Theor. Biol.
, vol.57
, Issue.1
, pp. 23-42
-
-
Segel, L.A.1
-
94
-
-
0001595172
-
A theoretical study of receptor mechanisms in bacterial chemotaxis
-
Segel, L.A.: A theoretical study of receptor mechanisms in bacterial chemotaxis. SIAM J. Appl. Math. 32, 653-665 (1977)
-
(1977)
SIAM J. Appl. Math.
, vol.32
, pp. 653-665
-
-
Segel, L.A.1
-
95
-
-
0028003498
-
Chemotaxis and chemokinesis in eukaryotic cells: The Keller-Segel equations as an approximation to a detailed model
-
Sherratt, J.A.: Chemotaxis and chemokinesis in eukaryotic cells: the Keller-Segel equations as an approximation to a detailed model. Bull. Math. Biol. 56(1), 129-146 (1994)
-
(1994)
Bull. Math. Biol.
, vol.56
, Issue.1
, pp. 129-146
-
-
Sherratt, J.A.1
-
96
-
-
0027214763
-
Chemical control of eukaryotic cell movement: A newmodel
-
Sherratt, J.A., Sage, E.H., Murray, J.D.: Chemical control of eukaryotic cell movement: a newmodel. J. Theor. Biol. 162(1), 23-40 (1993)
-
(1993)
J. Theor. Biol.
, vol.162
, Issue.1
, pp. 23-40
-
-
Sherratt, J.A.1
Sage, E.H.2
Murray, J.D.3
-
97
-
-
0034455986
-
The derivation of chemotaxis-equations as limit dynamics of moderately interacting stochastic many particle systems
-
Stevens, A.: The derivation of chemotaxis-equations as limit dynamics of moderately interacting stochastic many particle systems. SIAM J. Appl. Math. 61(1), 183-212 (2000)
-
(2000)
SIAM J. Appl. Math.
, vol.61
, Issue.1
, pp. 183-212
-
-
Stevens, A.1
-
99
-
-
0023881276
-
A stochastic model for leukocyte random motility and chemotaxis based on receptor binding fluctuations
-
Tranquillo, R.T., Lauffenburger, D.A., Zigmond, S.H.: A stochastic model for leukocyte random motility and chemotaxis based on receptor binding fluctuations. J. Cell Biol. 106(2), 303-309 (1988)
-
(1988)
J. Cell Biol.
, vol.106
, Issue.2
, pp. 303-309
-
-
Tranquillo, R.T.1
Lauffenburger, D.A.2
Zigmond, S.H.3
-
100
-
-
0033531342
-
A minimal mechanism for bacterial pattern formation
-
Tyson, R., Lubkin, S.R., Murray, J.D.: A minimal mechanism for bacterial pattern formation. Proc. R. Soc. Lond. B 266, 299-304 (1999)
-
(1999)
Proc. R. Soc. Lond. B
, vol.266
, pp. 299-304
-
-
Tyson, R.1
Lubkin, S.R.2
Murray, J.D.3
-
101
-
-
0033112265
-
Model and analysis of chemotactic bacterial patterns in a liquid medium
-
Tyson, R., Lubkin, S.R., Murray, J.D.: Model and analysis of chemotactic bacterial patterns in a liquid medium. J. Math. Biol. 38(4), 359-375 (1999)
-
(1999)
J. Math. Biol.
, vol.38
, Issue.4
, pp. 359-375
-
-
Tyson, R.1
Lubkin, S.R.2
Murray, J.D.3
-
102
-
-
4544331862
-
Point dynamics for a singular limit of the Keller-Segel model. I. motion of the concentration regions
-
Velazquez, J.J.L.: Point dynamics for a singular limit of the Keller-Segel model. I. motion of the concentration regions. SIAM J. Appl. Math. 64(4), 1198-1223 (2004)
-
(2004)
SIAM J. Appl. Math.
, vol.64
, Issue.4
, pp. 1198-1223
-
-
Velazquez, J.J.L.1
-
103
-
-
4544331862
-
Point dynamics for a singular limit of the Keller-Segel model. II. formation of the concentration regions
-
Velazquez, J.J.L.: Point dynamics for a singular limit of the Keller-Segel model. II. formation of the concentration regions. SIAM J. Appl. Math. 64(4), 1198-1223 (2004)
-
(2004)
SIAM J. Appl. Math.
, vol.64
, Issue.4
, pp. 1198-1223
-
-
Velazquez, J.J.L.1
-
104
-
-
0034376967
-
Qualitative behavior of solutions of chemotactic diffusion systems: Effects of motility and chemotaxis and dynamics
-
Wang, X.: Qualitative behavior of solutions of chemotactic diffusion systems: Effects of motility and chemotaxis and dynamics. SIAM J. Math. Ana. 31, 535-560 (2000)
-
(2000)
SIAM J. Math. Ana.
, vol.31
, pp. 535-560
-
-
Wang, X.1
-
105
-
-
34848920328
-
Classical solutions and pattern formation for a volume filling chemotaxis model
-
(037108)
-
Wang, Z.A., Hillen, T.: Classical solutions and pattern formation for a volume filling chemotaxis model. Chaos, 17(037108) (2007), 13 pp
-
(2007)
Chaos
, vol.17
, pp. 13
-
-
Wang, Z.A.1
Hillen, T.2
-
106
-
-
37049029658
-
Shock formation in a chemotaxis model
-
Wang, Z.A., Hillen, T.: Shock formation in a chemotaxis model. Math. Methods Appl. Sci. 31(1), 45-70 (2008)
-
(2008)
Math. Methods Appl. Sci.
, vol.31
, Issue.1
, pp. 45-70
-
-
Wang, Z.A.1
Hillen, T.2
-
108
-
-
0028907273
-
Spatiotemporal patterns generated by Salmonella typhimurium
-
Woodward, D.E., Tyson, R., Myerscough, M.R., Murray, J.D., Budrene, E.O., Berg, H.C.: Spatiotemporal patterns generated by Salmonella typhimurium. Biophys. J. 68(5), 2181-2189 (1995)
-
(1995)
Biophys. J.
, vol.68
, Issue.5
, pp. 2181-2189
-
-
Woodward, D.E.1
Tyson, R.2
Myerscough, M.R.3
Murray, J.D.4
Budrene, E.O.5
Berg, H.C.6
-
109
-
-
33646266962
-
Long time behaviour of solutions to a chemotaxis modelwith volume filling effect
-
Wrzosek, D.: Long time behaviour of solutions to a chemotaxis modelwith volume filling effect. Proc. Roy. Soc. Edinb. Sect. A 136, 431-444 (2006)
-
(2006)
Proc. Roy. Soc. Edinb. Sect. A
, vol.136
, pp. 431-444
-
-
Wrzosek, D.1
-
110
-
-
9244236567
-
Global attractor for a chemotaxis model with prevention of overcrowding
-
P2004
-
Wrzosek, D.: Global attractor for a chemotaxis model with prevention of overcrowding. Nonlin. Ana. 59, 1293-1310, P2004
-
Nonlin. Ana.
, vol.59
, pp. 1293-1310
-
-
Wrzosek, D.1
-
111
-
-
19644386779
-
Signaling mechanisms for regulation of chemotaxis
-
Wu, D.: Signaling mechanisms for regulation of chemotaxis. Cell Res. 15(1), 52-56 (2005)
-
(2005)
Cell Res.
, vol.15
, Issue.1
, pp. 52-56
-
-
Wu, D.1
|