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Volumn 26, Issue 1, 2011, Pages 54-60

Microscopic, mesoscopic and macroscopic descriptions of complex systems

Author keywords

DNA denaturation; Integro differential equations; LotkaVolterra equation; Markov jump processes; Microscopic models; Verhulst equation

Indexed keywords

DNA DENATURATION; LOTKA-VOLTERRA EQUATIONS; MARKOV JUMP PROCESS; MICROSCOPIC MODELS; VERHULST;

EID: 77957755467     PISSN: 02668920     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.probengmech.2010.06.007     Document Type: Article
Times cited : (28)

References (32)
  • 3
    • 33746069282 scopus 로고    scopus 로고
    • Looking for new paradigms towards a biological-mathematical theory of complex multicellular systems
    • N. Bellomo, and G. Forni Looking for new paradigms towards a biological-mathematical theory of complex multicellular systems Math Models Methods Appl Sci 16 2006 1001 1029
    • (2006) Math Models Methods Appl Sci , vol.16 , pp. 1001-1029
    • Bellomo, N.1    Forni, G.2
  • 4
    • 44349107599 scopus 로고    scopus 로고
    • On the foundations of cancer modelling: Selected topics, speculations and perspectives
    • N. Bellomo, Ph.K. Maini, and N.L. Martin On the foundations of cancer modelling: selected topics, speculations and perspectives Math Models Methods Appl Sci 18 2008 593 646
    • (2008) Math Models Methods Appl Sci , vol.18 , pp. 593-646
    • Bellomo, N.1    Maini ., P.K.2    Martin, N.L.3
  • 5
    • 35949030757 scopus 로고
    • On the Volterra and other nonlinear models of interacting populations
    • N.S. Goel, S.C. Maitra, and E.W. Montroll On the Volterra and other nonlinear models of interacting populations Rev Modern Phys 43 1971 231 276
    • (1971) Rev Modern Phys , vol.43 , pp. 231-276
    • Goel, N.S.1    Maitra, S.C.2    Montroll, E.W.3
  • 7
    • 78650821008 scopus 로고    scopus 로고
    • M. Lachowicz, J. Miekisz, World Sci. New Jersey
    • M. Lachowicz, J. Miekisz, From genetics to mathematics 2009 World Sci. New Jersey
    • (2009) From Genetics to Mathematics
  • 8
    • 18944378830 scopus 로고
    • Vlasov equations for Volterra dynamical systems
    • I.P. Pavlotsky Vlasov equations for Volterra dynamical systems Dokl AN SSSR 285 1985 331 339
    • (1985) Dokl AN SSSR , vol.285 , pp. 331-339
    • Pavlotsky, I.P.1
  • 9
    • 1642365792 scopus 로고    scopus 로고
    • Nonlinear dynamics and statistical physics of DNA
    • N. Peyrard Nonlinear dynamics and statistical physics of DNA Nonlinearity 17 2004 R1 R40
    • (2004) Nonlinearity , vol.17
    • Peyrard, N.1
  • 10
    • 44949083455 scopus 로고    scopus 로고
    • Modelling DNA at the mesoscale: A challenge for nonlinear science?
    • M. Peyrard, S. Cuesta-Lpez, and G. James Modelling DNA at the mesoscale: a challenge for nonlinear science? Nonlinearity 21 2008 T91 T100
    • (2008) Nonlinearity , vol.21
    • Peyrard, M.1    Cuesta-Lpez, S.2    James, G.3
  • 12
    • 6244221564 scopus 로고
    • Solutions of the NavierStokes equations in the case of evaporation
    • M. Lachowicz, and T. Ytrehus Solutions of the NavierStokes equations in the case of evaporation Bull Pol Acad Sci Tech 37 712 1989 453 458
    • (1989) Bull Pol Acad Sci Tech , vol.37 , Issue.712 , pp. 453-458
    • Lachowicz, M.1    Ytrehus, T.2
  • 14
    • 18944388598 scopus 로고    scopus 로고
    • General population systems. Macroscopic limit of a class of stochastic semigroups
    • M. Lachowicz General population systems. Macroscopic limit of a class of stochastic semigroups J Math Anal Appl 307 2005 585 605
    • (2005) J Math Anal Appl , vol.307 , pp. 585-605
    • Lachowicz, M.1
  • 15
    • 27644503155 scopus 로고    scopus 로고
    • Micro and meso scales of description corresponding to a model of tissue invasion by solid tumours
    • M. Lachowicz Micro and meso scales of description corresponding to a model of tissue invasion by solid tumours Math Models Methods Appl Sci 15 2005 1667 1683
    • (2005) Math Models Methods Appl Sci , vol.15 , pp. 1667-1683
    • Lachowicz, M.1
  • 17
    • 13844298300 scopus 로고    scopus 로고
    • An interacting particle system modelling aggregation behaviour: From individuals to populations
    • D. Morale, V. Capasso, and K. Oelschlger An interacting particle system modelling aggregation behaviour: from individuals to populations J Math Biol 50 2005 49 66
    • (2005) J Math Biol , vol.50 , pp. 49-66
    • Morale, D.1    Capasso, V.2    Oelschlger, K.3
  • 18
    • 0034455986 scopus 로고    scopus 로고
    • The derivation of chemotaxis equations as limit dynamics of moderately interacting stochastic many-particle systems
    • A. Stevens The derivation of chemotaxis equations as limit dynamics of moderately interacting stochastic many-particle systems SIAM J Appl Math 61 2000 183 212
    • (2000) SIAM J Appl Math , vol.61 , pp. 183-212
    • Stevens, A.1
  • 21
    • 0344211073 scopus 로고    scopus 로고
    • An integro differential model for orientational distribution of F-actin in cells
    • E. Geigant, K. Ladizhansky, and A. Mogilner An integro differential model for orientational distribution of F-actin in cells SIAM J Appl Math 59 1998 787 809
    • (1998) SIAM J Appl Math , vol.59 , pp. 787-809
    • Geigant, E.1    Ladizhansky, K.2    Mogilner, A.3
  • 22
    • 0026932946 scopus 로고
    • On the distribution of dominance in a population of interacting anonymous organisms
    • E. Jger, and L. Segel On the distribution of dominance in a population of interacting anonymous organisms SIAM J Appl Math 52 1992 1442 1468
    • (1992) SIAM J Appl Math , vol.52 , pp. 1442-1468
    • Jger, E.1    Segel, L.2
  • 23
    • 0347081772 scopus 로고    scopus 로고
    • Nonlocal bilinear equations. Equilibrium solutions and diffusive limit
    • M. Lachowicz, and D. Wrzosek Nonlocal bilinear equations. Equilibrium solutions and diffusive limit Math Models Methods Appl Sci 11 2001 1375 1390
    • (2001) Math Models Methods Appl Sci , vol.11 , pp. 1375-1390
    • Lachowicz, M.1    Wrzosek, D.2
  • 26
    • 44449099134 scopus 로고    scopus 로고
    • A kinetic-based sigmoidal model for the polymerase chain reaction and its applications to high-capacity absolute quantitative real-time PCR
    • R.G. Rutledge, and D. Steward A kinetic-based sigmoidal model for the polymerase chain reaction and its applications to high-capacity absolute quantitative real-time PCR BMC Mol Biol 8 2008 47 75
    • (2008) BMC Mol Biol , vol.8 , pp. 47-75
    • Rutledge, R.G.1    Steward, D.2
  • 27
    • 58149197860 scopus 로고    scopus 로고
    • Critical evaluation of methods used to determine amplification efficiency refutes the exponential character of real-time PCR
    • R.G. Rutledge, and D. Steward Critical evaluation of methods used to determine amplification efficiency refutes the exponential character of real-time PCR BMC Mol Biol 9 2008 96 108
    • (2008) BMC Mol Biol , vol.9 , pp. 96-108
    • Rutledge, R.G.1    Steward, D.2
  • 28
    • 37649032816 scopus 로고    scopus 로고
    • LotkaVolterra system in a random environment
    • 036204
    • M.F. Dimentberg LotkaVolterra system in a random environment Phys Rev E 65 036204 2002
    • (2002) Phys Rev e , vol.65
    • Dimentberg, M.F.1
  • 29
    • 50249169347 scopus 로고    scopus 로고
    • LotkaVolterra systems in environments with randomly disordered temporal periodicity
    • A. Naess, M.F. Dimentberg, and O. Gaidai LotkaVolterra systems in environments with randomly disordered temporal periodicity Phys Rev E 78 2008 021126-1 021126-9
    • (2008) Phys Rev e , vol.78 , pp. 0211261-0211269
    • Naess, A.1    Dimentberg, M.F.2    Gaidai, O.3
  • 30
    • 0035413567 scopus 로고    scopus 로고
    • Long term behaviour of solutions of the LotkaVolterra system under small random perturbations
    • R.Z. Khasminskii, and F.C. Klebaner Long term behaviour of solutions of the LotkaVolterra system under small random perturbations Ann Appl Probab 11 2001 952 963
    • (2001) Ann Appl Probab , vol.11 , pp. 952-963
    • Khasminskii, R.Z.1    Klebaner, F.C.2
  • 31
    • 0141799906 scopus 로고    scopus 로고
    • Long-time behaviour of a stochastic preypredator model
    • R. Rudnicki Long-time behaviour of a stochastic preypredator model Stoch Process Appl 108 2003 93 107
    • (2003) Stoch Process Appl , vol.108 , pp. 93-107
    • Rudnicki, R.1
  • 32
    • 33847295610 scopus 로고    scopus 로고
    • Influence of stochastic perturbation on preypredator systems
    • R. Rudnicki, and K. Pichr Influence of stochastic perturbation on preypredator systems Math Biosci 206 2007 108 119
    • (2007) Math Biosci , vol.206 , pp. 108-119
    • Rudnicki, R.1    Pichr, K.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.