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Volumn 71, Issue 12, 2009, Pages

Turing instability conditions for growing domains with divergence free mesh velocity

Author keywords

Advection reaction diffusion systems; Autonomous; Diffusion driven instability; Growing domains; Non autonomous system of partial differential equations; Pattern formation; Schnakenberg model; Turing instability

Indexed keywords

ADVECTION-REACTION-DIFFUSION SYSTEM; DIFFUSION-DRIVEN INSTABILITY; GROWING DOMAINS; NON-AUTONOMOUS SYSTEM; PATTERN FORMATION; TURING INSTABILITY;

EID: 72149120586     PISSN: 0362546X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.na.2009.05.027     Document Type: Article
Times cited : (17)

References (36)
  • 2
  • 3
    • 5544250703 scopus 로고
    • Experimental evidence of a sustained Turing-type equilibrium chemical pattern
    • Castets V., Dulos E., Boissonade J., and De Kepper P. Experimental evidence of a sustained Turing-type equilibrium chemical pattern. Phys. Rev. Lett. 64 3 (1990) 2953-2956
    • (1990) Phys. Rev. Lett. , vol.64 , Issue.3 , pp. 2953-2956
    • Castets, V.1    Dulos, E.2    Boissonade, J.3    De Kepper, P.4
  • 4
    • 34047187677 scopus 로고
    • Transition from a uniform state to hexagonal and striped Turing patterns
    • Ouyang Q., and Swinney H.L. Transition from a uniform state to hexagonal and striped Turing patterns. Nature 352 (1991) 610-612
    • (1991) Nature , vol.352 , pp. 610-612
    • Ouyang, Q.1    Swinney, H.L.2
  • 5
    • 33845301220 scopus 로고    scopus 로고
    • WNT and DKK determine hair follicle spacing through a reaction-diffusion mechanism
    • Sick S., Reinker S., Timmer J., and Schlake T. WNT and DKK determine hair follicle spacing through a reaction-diffusion mechanism. Science 314 (2006) 1447-1450
    • (2006) Science , vol.314 , pp. 1447-1450
    • Sick, S.1    Reinker, S.2    Timmer, J.3    Schlake, T.4
  • 6
    • 33845326442 scopus 로고    scopus 로고
    • The Turing model comes of molecular age (Invited Perspective)
    • Maini P.K., Baker R.E., and Chong C.M. The Turing model comes of molecular age (Invited Perspective). Science 314 (2006) 1397-1398
    • (2006) Science , vol.314 , pp. 1397-1398
    • Maini, P.K.1    Baker, R.E.2    Chong, C.M.3
  • 7
    • 0029163545 scopus 로고
    • A reaction-diffusion wave on the skin of the marine angelfish Pomacanthus
    • Kondo S., and Asai R. A reaction-diffusion wave on the skin of the marine angelfish Pomacanthus. Nature 376 (1995) 765-768
    • (1995) Nature , vol.376 , pp. 765-768
    • Kondo, S.1    Asai, R.2
  • 9
    • 0000763323 scopus 로고    scopus 로고
    • Confined Turing patterns in growing systems
    • Varea C., Aragón J.L., and Barrio R.A. Confined Turing patterns in growing systems. Phys. Rev. E. 36 (1997) 1250-1253
    • (1997) Phys. Rev. E. , vol.36 , pp. 1250-1253
    • Varea, C.1    Aragón, J.L.2    Barrio, R.A.3
  • 10
    • 0035348998 scopus 로고    scopus 로고
    • Spatio-temporal pattern formation on spherical surfaces: Numerical simulation and application to solid tumor growth
    • Chaplain M.A.J., Gnesh M., and Graham I.G. Spatio-temporal pattern formation on spherical surfaces: Numerical simulation and application to solid tumor growth. J. Math. Biol. 42 (2001) 387-423
    • (2001) J. Math. Biol. , vol.42 , pp. 387-423
    • Chaplain, M.A.J.1    Gnesh, M.2    Graham, I.G.3
  • 11
    • 0035474955 scopus 로고    scopus 로고
    • Turing model patterns of lady beetles
    • Liaw S.S., Yang C.C., and Liu R.T. Turing model patterns of lady beetles. Phys. Rev. E. 64 (2001) 041909
    • (2001) Phys. Rev. E. , vol.64 , pp. 041909
    • Liaw, S.S.1    Yang, C.C.2    Liu, R.T.3
  • 12
    • 0033545988 scopus 로고    scopus 로고
    • Stripe formation in juvenile Pomacanthus explained by a generalised Turing mechanism with chemotaxis
    • Painter K.J., Maini P.K., and Othmer H.G. Stripe formation in juvenile Pomacanthus explained by a generalised Turing mechanism with chemotaxis. Proc. Natl. Acad. Sci. USA 96 (1999) 5549-5554
    • (1999) Proc. Natl. Acad. Sci. USA , vol.96 , pp. 5549-5554
    • Painter, K.J.1    Maini, P.K.2    Othmer, H.G.3
  • 14
    • 0032701813 scopus 로고    scopus 로고
    • Reaction and diffusion on growing domains: Scenarios for robust pattern formation
    • Crampin E.J., Gaffney E.A., and Maini P.K. Reaction and diffusion on growing domains: Scenarios for robust pattern formation. Bull. Math. Biol. 61 (2002) 1093-1120
    • (2002) Bull. Math. Biol. , vol.61 , pp. 1093-1120
    • Crampin, E.J.1    Gaffney, E.A.2    Maini, P.K.3
  • 16
    • 0036562274 scopus 로고    scopus 로고
    • A numerical approach to the study of spatial pattern formation in the Ligaments of Arcoid Bivalves
    • Madzvamuse A., Thomas R.D.K., Maini P.K., and Wathen A.J. A numerical approach to the study of spatial pattern formation in the Ligaments of Arcoid Bivalves. Bull. Math. Biol. 64 (2002) 501-530
    • (2002) Bull. Math. Biol. , vol.64 , pp. 501-530
    • Madzvamuse, A.1    Thomas, R.D.K.2    Maini, P.K.3    Wathen, A.J.4
  • 17
    • 0141515669 scopus 로고    scopus 로고
    • A moving grid finite element method applied to a model biological pattern generator
    • Madzvamuse A., Maini P.K., and Wathen A.J. A moving grid finite element method applied to a model biological pattern generator. J. Comput. Phys. 190 (2003) 478-500
    • (2003) J. Comput. Phys. , vol.190 , pp. 478-500
    • Madzvamuse, A.1    Maini, P.K.2    Wathen, A.J.3
  • 19
    • 33644519990 scopus 로고    scopus 로고
    • Time-stepping schemes for moving grid finite elements applied to reaction-diffusion systems on fixed and growing domains
    • Madzvamuse A. Time-stepping schemes for moving grid finite elements applied to reaction-diffusion systems on fixed and growing domains. J. Comput. Phys. 214 (2006) 239-263
    • (2006) J. Comput. Phys. , vol.214 , pp. 239-263
    • Madzvamuse, A.1
  • 20
    • 34447283073 scopus 로고    scopus 로고
    • Velocity-induced numerical solutions of reaction-diffusion systems on fixed and growing domains
    • Madzvamuse A., and Maini P.K. Velocity-induced numerical solutions of reaction-diffusion systems on fixed and growing domains. J. Comput. Phys. 225 (2007) 100-119
    • (2007) J. Comput. Phys. , vol.225 , pp. 100-119
    • Madzvamuse, A.1    Maini, P.K.2
  • 22
    • 23944439965 scopus 로고    scopus 로고
    • A moving grid finite element method for the simulation of pattern generation by Turing models on growing domains
    • Madzvamuse A. A moving grid finite element method for the simulation of pattern generation by Turing models on growing domains. J. Sci. Comp. 24 2 (2005) 247-262
    • (2005) J. Sci. Comp. , vol.24 , Issue.2 , pp. 247-262
    • Madzvamuse, A.1
  • 23
    • 0015454185 scopus 로고
    • A theory of biological pattern formation
    • Gierer A., and Meinhardt H. A theory of biological pattern formation. Kybernetik. 12 (1972) 30-39
    • (1972) Kybernetik. , vol.12 , pp. 30-39
    • Gierer, A.1    Meinhardt, H.2
  • 24
    • 0018784247 scopus 로고
    • Simple chemical reaction systems with limit cycle behaviour
    • Schnakenberg J. Simple chemical reaction systems with limit cycle behaviour. J. Theoret. Biol. 81 (1979) 32101-32105
    • (1979) J. Theoret. Biol. , vol.81 , pp. 32101-32105
    • Schnakenberg, J.1
  • 25
    • 36849102494 scopus 로고
    • Symmetry breaking instabilities in dissipative systems. II
    • Prigogine I., and Lefever R. Symmetry breaking instabilities in dissipative systems. II. J. Chem. Phys. 48 (1968) 1695-1700
    • (1968) J. Chem. Phys. , vol.48 , pp. 1695-1700
    • Prigogine, I.1    Lefever, R.2
  • 26
    • 0034488635 scopus 로고    scopus 로고
    • Growth patterns of noetiid ligaments: implications of developmental models for the origin of an evolutionary novelty among arcoid bivalves
    • Harper E.M., Taylor J.D., and Crame J.A. (Eds), Geological Society Special Publication pp. 289-279
    • Thomas R.D.K., Madzvamuse A., Maini P.K., and Wathen A.J. Growth patterns of noetiid ligaments: implications of developmental models for the origin of an evolutionary novelty among arcoid bivalves. In: Harper E.M., Taylor J.D., and Crame J.A. (Eds). The Evolutionary Biology of the Bivalvia vol. 177 (2000), Geological Society Special Publication pp. 289-279
    • (2000) The Evolutionary Biology of the Bivalvia , vol.177
    • Thomas, R.D.K.1    Madzvamuse, A.2    Maini, P.K.3    Wathen, A.J.4
  • 28
    • 0003036489 scopus 로고
    • Phase differences in reaction-diffusion-advection systems and applications to morphogenesis
    • Perumpanani A.J., Sherratt A.J., and Maini P.K. Phase differences in reaction-diffusion-advection systems and applications to morphogenesis. IMA J. Appl. Math. 55 (1995) 19-33
    • (1995) IMA J. Appl. Math. , vol.55 , pp. 19-33
    • Perumpanani, A.J.1    Sherratt, A.J.2    Maini, P.K.3
  • 29
    • 0034225683 scopus 로고    scopus 로고
    • Non-Turing stationary patterns in flow-distributed oscillators with general diffusion and flow rates
    • Satnoianu R.A., and Menzinger M. Non-Turing stationary patterns in flow-distributed oscillators with general diffusion and flow rates. Phys. Rev. E. 62 1 (2000) 113-119
    • (2000) Phys. Rev. E. , vol.62 , Issue.1 , pp. 113-119
    • Satnoianu, R.A.1    Menzinger, M.2
  • 30
    • 0242579631 scopus 로고    scopus 로고
    • Coexistence of stationary and travelling waves in reaction-diffusion-advection systems
    • Satnoianu R.A. Coexistence of stationary and travelling waves in reaction-diffusion-advection systems. Phys. Rev. E. 68 3 (2003) 32101-32105
    • (2003) Phys. Rev. E. , vol.68 , Issue.3 , pp. 32101-32105
    • Satnoianu, R.A.1
  • 31
    • 0000122671 scopus 로고    scopus 로고
    • Nonlinear analysis of stationary patterns in convection-reaction-diffusion systems
    • Nekhamkina O.A., Nepomnyashchy A.A., Rubistein B.Y., and Sheintuch M. Nonlinear analysis of stationary patterns in convection-reaction-diffusion systems. Phys. Rev. E 61 3 (2000) 2436-2444
    • (2000) Phys. Rev. E , vol.61 , Issue.3 , pp. 2436-2444
    • Nekhamkina, O.A.1    Nepomnyashchy, A.A.2    Rubistein, B.Y.3    Sheintuch, M.4
  • 32
    • 0242579499 scopus 로고    scopus 로고
    • Asymptotic solutions of stationary patterns in convection-reaction-diffusion systems
    • Nekhamkina O., and Sheintuch M. Asymptotic solutions of stationary patterns in convection-reaction-diffusion systems. Phys. Rev. E 68 3 (2003) 36207-36217
    • (2003) Phys. Rev. E , vol.68 , Issue.3 , pp. 36207-36217
    • Nekhamkina, O.1    Sheintuch, M.2
  • 34
    • 60649118457 scopus 로고    scopus 로고
    • Stability analysis of reaction-diffusion systems with constant coefficients on growing domains
    • Madzvamuse A. Stability analysis of reaction-diffusion systems with constant coefficients on growing domains. Int. J. Dynam. Differential Equations 1 4 (2008) 250-262
    • (2008) Int. J. Dynam. Differential Equations , vol.1 , Issue.4 , pp. 250-262
    • Madzvamuse, A.1
  • 35
    • 77952292392 scopus 로고    scopus 로고
    • Stability analysis of non-autonomous reaction-diffusion systems: The effects of growing domains
    • submitted for publication
    • A. Madzvamuse, E.A. Gaffney, P.K. Maini, 2009, Stability analysis of non-autonomous reaction-diffusion systems: the effects of growing domains, J. Math. Biol. (submitted for publication)
    • (2009) J. Math. Biol
    • Madzvamuse, A.1    Gaffney, E.A.2    Maini, P.K.3


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.