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Volumn 57, Issue 4, 2009, Pages 429-455

Periodic solutions of piecewise affine gene network models with non uniform decay rates: The case of a negative feedback loop

Author keywords

Monotone, concave maps; Negative feedback loop systems; Periodic trajectories; Piecewise linear dynamical systems

Indexed keywords

FEEDBACK MECHANISM; GENE; GENETICS; GEOMETRY; MAP;

EID: 77949885161     PISSN: 00015342     EISSN: None     Source Type: Journal    
DOI: 10.1007/s10441-009-9086-9     Document Type: Article
Times cited : (30)

References (16)
  • 1
    • 29244452623 scopus 로고    scopus 로고
    • Piecewise-linear models of genetic regulatory networks: Equilibria and their stability
    • Casey R, de Jong H, Gouzé JL (2006) Piecewise-linear models of genetic regulatory networks: equilibria and their stability. J Math Biol 52(1): 27-56.
    • (2006) J Math Biol , vol.52 , Issue.1 , pp. 27-56
    • Casey, R.1    de Jong, H.2    Gouzé, J.L.3
  • 2
    • 0036207347 scopus 로고    scopus 로고
    • Modeling and simulation of genetic regulatory systems: A literature review
    • de Jong H (2002) Modeling and simulation of genetic regulatory systems: a literature review. J Comput Biol 9(1): 67-103.
    • (2002) J Comput Biol , vol.9 , Issue.1 , pp. 67-103
    • de Jong, H.1
  • 3
    • 1242333310 scopus 로고    scopus 로고
    • Qualitative simulation of genetic regulatory networks using piecewise-linear models
    • de Jong H, Gouzé JL, Hernandez C, Page M, Sari T, Geiselmann J (2004) Qualitative simulation of genetic regulatory networks using piecewise-linear models. Bull Math Biol 66(2): 301-340.
    • (2004) Bull Math Biol , vol.66 , Issue.2 , pp. 301-340
    • de Jong, H.1    Gouzé, J.L.2    Hernandez, C.3    Page, M.4    Sari, T.5    Geiselmann, J.6
  • 4
    • 0034315476 scopus 로고    scopus 로고
    • Analysis of continuous-time switching networks
    • Edwards R (2000) Analysis of continuous-time switching networks. Phys D 146: 165-199.
    • (2000) Phys D , vol.146 , pp. 165-199
    • Edwards, R.1
  • 5
    • 0034688173 scopus 로고    scopus 로고
    • A synthetic oscillatory network of transcriptional regulators
    • Elowitz MB, Leibler S (2000) A synthetic oscillatory network of transcriptional regulators. Nature 403: 335-338.
    • (2000) Nature , vol.403 , pp. 335-338
    • Elowitz, M.B.1    Leibler, S.2
  • 6
    • 32544456601 scopus 로고    scopus 로고
    • Geometric properties of piecewise affine biological network models
    • Farcot E (2006) Geometric properties of piecewise affine biological network models. J Math Biol 52(3): 373-418.
    • (2006) J Math Biol , vol.52 , Issue.3 , pp. 373-418
    • Farcot, E.1
  • 7
    • 0000852386 scopus 로고
    • Structure of the global attractor of cyclic feedback systems
    • Gedeon T, Mischaikow K (1995) Structure of the global attractor of cyclic feedback systems. J Dyn Differ Equ 7(1): 141-190.
    • (1995) J Dyn Differ Equ , vol.7 , Issue.1 , pp. 141-190
    • Gedeon, T.1    Mischaikow, K.2
  • 8
    • 33749553474 scopus 로고
    • Combinatorial and topological methods in nonlinear chemical kinetics
    • Glass L (1975) Combinatorial and topological methods in nonlinear chemical kinetics. J Chem Phys 63: 1325-1335.
    • (1975) J Chem Phys , vol.63 , pp. 1325-1335
    • Glass, L.1
  • 9
    • 0017834347 scopus 로고
    • Prediction of limit cycles in mathematical models of biological oscillations
    • Glass L, Pasternack JS (1978a) Prediction of limit cycles in mathematical models of biological oscillations. Bull Math Biol 40: 27-44.
    • (1978) Bull Math Biol , vol.40 , pp. 27-44
    • Glass, L.1    Pasternack, J.S.2
  • 10
    • 0018168876 scopus 로고
    • Stable oscillations in mathematical models of biological control systems
    • Glass L, Pasternack JS (1978b) Stable oscillations in mathematical models of biological control systems. J Math Biol 6: 207-223.
    • (1978) J Math Biol , vol.6 , pp. 207-223
    • Glass, L.1    Pasternack, J.S.2
  • 11
    • 0036938728 scopus 로고    scopus 로고
    • A class of piecewise linear differential equations arising in biological models
    • Gouzé JL, Sari T (2003) A class of piecewise linear differential equations arising in biological models. Dyn Syst 17: 299-316.
    • (2003) Dyn Syst , vol.17 , pp. 299-316
    • Gouzé, J.L.1    Sari, T.2
  • 13
    • 0001051330 scopus 로고
    • The Poincaré-Bendixson Theorem for monotone cyclic feedback systems
    • Mallet-Paret J, Smith H (1990) The Poincaré-Bendixson Theorem for monotone cyclic feedback systems. J Dyn Differ Equ 2: 367-421.
    • (1990) J Dyn Differ Equ , vol.2 , pp. 367-421
    • Mallet-Paret, J.1    Smith, H.2
  • 14
    • 0001511149 scopus 로고
    • Periodic solutions of piecewise-linear differential equations
    • Mestl T, Plahte E, Omholt SW (1995) Periodic solutions of piecewise-linear differential equations. Dyn Stab Syst 10(2): 179-193.
    • (1995) Dyn Stab Syst , vol.10 , Issue.2 , pp. 179-193
    • Mestl, T.1    Plahte, E.2    Omholt, S.W.3
  • 15
    • 0007452641 scopus 로고
    • Cooperative systems of differential equations with concave nonlinearities
    • Smith H (1986) Cooperative systems of differential equations with concave nonlinearities. Nonlinear Anal 10: 1037-1052.
    • (1986) Nonlinear Anal , vol.10 , pp. 1037-1052
    • Smith, H.1
  • 16
    • 0024916497 scopus 로고
    • Qualitative dynamics of piecewise-linear differential equations: A discrete mapping approach
    • Snoussi EH (1989) Qualitative dynamics of piecewise-linear differential equations: a discrete mapping approach. Dyn Stab Syst 4(3-4): 189-207.
    • (1989) Dyn Stab Syst , vol.4 , Issue.3-4 , pp. 189-207
    • Snoussi, E.H.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.