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Volumn 57, Issue 4, 1997, Pages 1044-1081

Aggregation, blowup, and collapse: The ABC'S of taxis in reinforced random walks

Author keywords

Aggregation; Blowup; Chemotaxis equations; Collapse; Diffusion approximation; Reinforced random walk

Indexed keywords

BACTERIA; MICROORGANISMS; PARTIAL DIFFERENTIAL EQUATIONS; PROBABILITY DENSITY FUNCTION;

EID: 0031207030     PISSN: 00361399     EISSN: None     Source Type: Journal    
DOI: 10.1137/s0036139995288976     Document Type: Article
Times cited : (613)

References (29)
  • 1
    • 0002071824 scopus 로고
    • The role of diffusion in mathematical population biology: Skellam revisited
    • V. Capasso, E. Grosso, and S. L. Paveri-Fontana, eds., Springer-Verlag, New York
    • D. G. ARONSON, The role of diffusion in mathematical population biology: Skellam revisited, in Mathematics in Biology and Medicine, V. Capasso, E. Grosso, and S. L. Paveri-Fontana, eds., Springer-Verlag, New York, 1985, pp. 2-6.
    • (1985) Mathematics in Biology and Medicine , pp. 2-6
    • Aronson, D.G.1
  • 2
    • 0019784884 scopus 로고
    • Nonlinear aspects of chemotaxis
    • S. CHILDRESS AND J. K. PERCUS, Nonlinear aspects of chemotaxis, Math. Biosci., 56 (1981), pp. 217-237.
    • (1981) Math. Biosci. , vol.56 , pp. 217-237
    • Childress, S.1    Percus, J.K.2
  • 6
    • 0003299218 scopus 로고
    • Mathematical Aspects of Reacting and Diffusing Systems
    • Springer-Verlag, New York
    • P. C. FIFE, Mathematical Aspects of Reacting and Diffusing Systems, Lecture Notes in Biomath. 28, Springer-Verlag, New York, 1979.
    • (1979) Lecture Notes in Biomath. , vol.28
    • Fife, P.C.1
  • 7
    • 0002148022 scopus 로고
    • Asymptotic integration of linear differential equations
    • P. HARTMAN AND A. WINTNER, Asymptotic integration of linear differential equations, Amer. J. Math., 77 (1955), pp. 45-86.
    • (1955) Amer. J. Math. , vol.77 , pp. 45-86
    • Hartman, P.1    Wintner, A.2
  • 8
    • 0030334089 scopus 로고    scopus 로고
    • Chemotactic collapse for the Keller-Segel model
    • to appear
    • M. HERRERO AND J. VELÁZQUEZ, Chemotactic collapse for the Keller-Segel model, J. Math. Biol., to appear.
    • J. Math. Biol.
    • Herrero, M.1    Velázquez, J.2
  • 9
    • 0039712703 scopus 로고    scopus 로고
    • Singularity patterns in a chemotaxis model
    • M. HERRERO AND J. VELÁZQUEZ, Singularity patterns in a chemotaxis model, Math. Ann., 306 (1996), pp. 583-623.
    • (1996) Math. Ann. , vol.306 , pp. 583-623
    • Herrero, M.1    Velázquez, J.2
  • 11
    • 84966208077 scopus 로고
    • On explosions of solutions to a system of partial differential equations modelling chemotaxis
    • W. JÄGER AND S. LUCKHAUS, On explosions of solutions to a system of partial differential equations modelling chemotaxis, Trans. Amer. Math. Soc., 329 (1992), pp. 819-824.
    • (1992) Trans. Amer. Math. Soc. , vol.329 , pp. 819-824
    • Jäger, W.1    Luckhaus, S.2
  • 13
    • 0019212496 scopus 로고
    • "Pseudochemotaxis" by micro-organisms in an attractant gradient
    • I. R. LAPIDUS, "Pseudochemotaxis" by micro-organisms in an attractant gradient, J. Theor. Biol., 86 (1980), pp. 91-103.
    • (1980) J. Theor. Biol. , vol.86 , pp. 91-103
    • Lapidus, I.R.1
  • 14
    • 0031162898 scopus 로고    scopus 로고
    • A system, of reaction diffusion equations arising in the theory of reinforced random walks
    • H. A. LEVINE AND B. D. SLEEMAN, A system, of reaction diffusion equations arising in the theory of reinforced random walks, SIAM J. Appl. Math., 57 (1997), pp. 683-730.
    • (1997) SIAM J. Appl. Math. , vol.57 , pp. 683-730
    • Levine, H.A.1    Sleeman, B.D.2
  • 15
    • 0002542873 scopus 로고
    • Large amplitude stationary solutions to a chemotaxis system
    • C.-S. LIN, W.-M. NI, AND I. TAKAGI, Large amplitude stationary solutions to a chemotaxis system, J. Differential Equations, 72 (1988), pp. 1-27.
    • (1988) J. Differential Equations , vol.72 , pp. 1-27
    • Lin, C.-S.1    Ni, W.-M.2    Takagi, I.3
  • 17
    • 0000729412 scopus 로고
    • Dynamics of aggregating patterns in a chemotaxis-diffusion-growth model equation
    • M. MIMURA, T. TSUJIKAWA, R. KOBAYASHI, AND D. UEYAMA, Dynamics of aggregating patterns in a chemotaxis-diffusion-growth model equation, Forma, 8 (1993), pp. 179-195.
    • (1993) Forma , vol.8 , pp. 179-195
    • Mimura, M.1    Tsujikawa, T.2    Kobayashi, R.3    Ueyama, D.4
  • 18
    • 0000911252 scopus 로고
    • Blow-up of radially symmetric solutions to a chemotaxis system
    • T. NAGAI, Blow-up of radially symmetric solutions to a chemotaxis system, Adv. Math. Sci. Appl., 5 (1995), pp. 581-601.
    • (1995) Adv. Math. Sci. Appl. , vol.5 , pp. 581-601
    • Nagai, T.1
  • 19
    • 0015757937 scopus 로고
    • Chemotaxis, signal relaying and aggregation morphology
    • V. NANJUNDIAH, Chemotaxis, signal relaying and aggregation morphology, J. Theor. Biol., 42 (1973), pp. 63-105.
    • (1973) J. Theor. Biol. , vol.42 , pp. 63-105
    • Nanjundiah, V.1
  • 20
    • 0010182615 scopus 로고
    • A fluctuation theorem for moderately interacting diffusion processes
    • K. OELSCHLÄGER, A fluctuation theorem for moderately interacting diffusion processes, Probab. Theory Related Fields, 74 (1987), pp. 591-616.
    • (1987) Probab. Theory Related Fields , vol.74 , pp. 591-616
    • Oelschläger, K.1
  • 22
    • 0023746235 scopus 로고
    • Models of dispersal in biological systems
    • H. G. OTHMER, S. R. DUNBAR, AND W. ALT, Models of dispersal in biological systems., J. Math. Biol., 26 (1988), pp. 263-298.
    • (1988) J. Math. Biol. , vol.26 , pp. 263-298
    • Othmer, H.G.1    Dunbar, S.R.2    Alt, W.3
  • 23
    • 51249193541 scopus 로고
    • Random walk with persistence and external bias
    • C. S. PATLAK, Random walk with persistence and external bias, Bull. of Math. Biophys., 15 (1953), pp. 311-338.
    • (1953) Bull. of Math. Biophys. , vol.15 , pp. 311-338
    • Patlak, C.S.1
  • 24
    • 0029192972 scopus 로고
    • Finite time blow-up in some models of chemotaxis
    • M. RASCLE AND C. ZITI, Finite time blow-up in some models of chemotaxis, J. Math. Biol., 33 (1995), pp. 388-414.
    • (1995) J. Math. Biol. , vol.33 , pp. 388-414
    • Rascle, M.1    Ziti, C.2
  • 25
    • 0001373727 scopus 로고
    • Stationary solutions of chemotaxis equations
    • R. SCHAAF, Stationary solutions of chemotaxis equations, Trans. Amer. Math. Soc., 292 (1985), pp. 531-556.
    • (1985) Trans. Amer. Math. Soc. , vol.292 , pp. 531-556
    • Schaaf, R.1
  • 27
    • 0000389227 scopus 로고
    • A model for gliding and aggregation of myxobacteria
    • A. Holden, M. Markus, and H. G. Othmer, eds., Plenum Press, New York
    • A. STEVENS, A model for gliding and aggregation of myxobacteria, in Proc. Conf. on Nonlinear Wave Processes in Excitable Media, A. Holden, M. Markus, and H. G. Othmer, eds., Plenum Press, New York, 1991, pp. 269-276.
    • (1991) Proc. Conf. on Nonlinear Wave Processes in Excitable Media , pp. 269-276
    • Stevens, A.1
  • 29
    • 0001408135 scopus 로고
    • Trail following and aggregation of myxobacteria
    • A. STEVENS, Trail following and aggregation of myxobacteria, J. Biol. Sys., 3 (1995), pp. 1059-1068.
    • (1995) J. Biol. Sys. , vol.3 , pp. 1059-1068
    • Stevens, A.1


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