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Volumn 19, Issue 12, 2009, Pages 4055-4096

An atlas of robust, stable, high-dimensional limit cycles

Author keywords

Homoclinic bifurcation; Hopf bifurcation; Hypercube; Inverse problem; Piecewise linear equations

Indexed keywords

BIFURCATION (MATHEMATICS); DELTA SIGMA MODULATION; DIFFERENTIAL EQUATIONS; DIRECTED GRAPHS; DYNAMICAL SYSTEMS; FEEDBACK; GEOMETRY; GRAPH THEORY; INVERSE PROBLEMS; PIECEWISE LINEAR TECHNIQUES;

EID: 77950355238     PISSN: 02181274     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0218127409025225     Document Type: Article
Times cited : (10)

References (48)
  • 1
    • 0141811692 scopus 로고    scopus 로고
    • Boolean dynamics with random couplings
    • eds. Kaplan, E., Marsden, J. E. & Sreenivasan, K. R. (Springer, NY)
    • Aldana, M., Coppersmith, S. & Kadanoff, L. P. [2003] "Boolean dynamics with random couplings," in Perspectives and Problems in Nonlinear Science, eds. Kaplan, E., Marsden, J. E. & Sreenivasan, K. R. (Springer, NY), pp. 23-89.
    • (2003) Perspectives and Problems in Nonlinear Science , pp. 23-89
    • Aldana, M.1    Coppersmith, S.2    Kadanoff, L.P.3
  • 2
    • 33746059733 scopus 로고    scopus 로고
    • Diagonal stability of a class of cyclic systems and its connection with the secant criterion
    • Arcak, M. & Sontag, E. D. [2006] "Diagonal stability of a class of cyclic systems and its connection with the secant criterion," Automatica 42, 1531-1537.
    • (2006) Automatica , vol.42 , pp. 1531-1537
    • Arcak, M.1    Sontag, E.D.2
  • 4
    • 45249130262 scopus 로고
    • A 3(2) pair of Runge-Kutta formulas
    • Bogacki, L. & Shampine, L. F. [1989] "A 3(2) pair of Runge-Kutta formulas," Appl. Math. Lett. 2, 1-9.
    • (1989) Appl. Math. Lett. , vol.2 , pp. 1-9
    • Bogacki, L.1    Shampine, L.F.2
  • 6
    • 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, 67-103.
    • (2002) J. Comput. Biol. , vol.9 , pp. 67-103
    • De Jong, H.1
  • 8
    • 0034404253 scopus 로고    scopus 로고
    • Combinatorial explosion in model gene networks
    • Edwards, R. & Glass, L. [2000] "Combinatorial explosion in model gene networks," Chaos 10, 691-704.
    • (2000) Chaos , vol.10 , pp. 691-704
    • Edwards, R.1    Glass, L.2
  • 9
    • 29044447767 scopus 로고    scopus 로고
    • A calculus for relating the dynamics and structure of complex biological networks
    • eds. Berry, R. S. & Jortner, J. (John Wiley, NJ)
    • Edwards, R. & Glass, L. [2006] "A calculus for relating the dynamics and structure of complex biological networks," in Adventures in Chemical Physics, A Special Volume of Advances in Chemical Physics, Vol.132, eds. Berry, R. S. & Jortner, J. (John Wiley, NJ), pp. 151-178.
    • (2006) Adventures in Chemical Physics, A Special Volume of Advances in Chemical Physics , vol.132 , pp. 151-178
    • Edwards, R.1    Glass, L.2
  • 10
    • 0034688173 scopus 로고    scopus 로고
    • A synthetic oscillatory network of transcriptional regulators
    • Elowitz, M. B. & 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
  • 11
    • 0034688174 scopus 로고    scopus 로고
    • Construction of a genetic toggle switch in Escherichia coli
    • Gardner, T. S., Cantor, C. R. & Collins, J. J. [2000] "Construction of a genetic toggle switch in Escherichia coli," Nature 403, 339-342.
    • (2000) Nature , vol.403 , pp. 339-342
    • Gardner, T.S.1    Cantor, C.R.2    Collins, J.J.3
  • 12
    • 0032110391 scopus 로고    scopus 로고
    • Cyclic feedback systems
    • Gedeon, T. [1998] "Cyclic feedback systems," Mem. Amer. Math. Soc. 134, 1-73.
    • (1998) Mem. Amer. Math. Soc. , vol.134 , pp. 1-73
    • Gedeon, T.1
  • 13
    • 0015609281 scopus 로고
    • The logical analysis of continuous, non-linear biochemical control networks
    • Glass, L. & Kauffman, S. A. [1973] "The logical analysis of continuous, non-linear biochemical control networks," J. Theor. Biol. 39, 103-129.
    • (1973) J. Theor. Biol. , vol.39 , pp. 103-129
    • Glass, L.1    Kauffman, S.A.2
  • 14
    • 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
  • 16
    • 0008689406 scopus 로고
    • Global analysis of nonlinear chemical kinetics
    • ed. Berne, B. (Plenum, NY)
    • Glass, L. [1977b] "Global analysis of nonlinear chemical kinetics," in Statistical Mechanics, Part B: Time Dependent Processes, ed. Berne, B. (Plenum, NY), pp. 311-349.
    • (1977) Statistical Mechanics, Part B: Time Dependent Processes , pp. 311-349
    • Glass, L.1
  • 17
    • 0017834347 scopus 로고
    • Prediction of limit cycles in mathematical models of biological oscillations
    • Glass, L. & Pasternack, J. S. [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
  • 18
    • 0018168876 scopus 로고
    • Stable oscillations in mathematical models of biological control systems
    • Glass, L. & Pasternack, J. S. [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
  • 19
    • 0018604323 scopus 로고
    • Structure and dynamics of neural network oscillators
    • Glass, L. & Young, R. E. [1979] "Structure and dynamics of neural network oscillators," Brain Res. 179, 207-218.
    • (1979) Brain Res. , vol.179 , pp. 207-218
    • Glass, L.1    Young, R.E.2
  • 22
    • 0022937687 scopus 로고
    • A survey of the theory of hypercube graphs
    • Harary, F., Hayes, J. P. & Wu, H. J. [1988] "A survey of the theory of hypercube graphs," Comput. Math. Appl. 15, 277-289.
    • (1988) Comput. Math. Appl. , vol.15 , pp. 277-289
    • Harary, F.1    Hayes, J.P.2    Wu, H.J.3
  • 24
    • 0002703577 scopus 로고
    • Existence of periodic solutions for negative feedback equations
    • Hastings, S., Tyson, J. J. & Webster, D. [1977] "Existence of periodic solutions for negative feedback equations," J. Diff. Eqs. 25, 39-64.
    • (1977) J. Diff. Eqs. , vol.25 , pp. 39-64
    • Hastings, S.1    Tyson, J.J.2    Webster, D.3
  • 25
    • 0035319006 scopus 로고    scopus 로고
    • Computational studies of gene regulatory networks: In numero molecular biology
    • Hasty, J., McMillen, D., Isaacs, F. & Collins, J. J. [2001] "Computational studies of gene regulatory networks: In numero molecular biology," Nat. Rev. Genet. 2, 268-279.
    • (2001) Nat. Rev. Genet. , vol.2 , pp. 268-279
    • Hasty, J.1    McMillen, D.2    Isaacs, F.3    Collins, J.J.4
  • 28
    • 0014489272 scopus 로고
    • Metabolic stability and epigenesis in randomly constructed genetic nets
    • Kauffman, S. A. [1969] "Metabolic stability and epigenesis in randomly constructed genetic nets," J. Theor. Biol. 22, 437-467.
    • (1969) J. Theor. Biol. , vol.22 , pp. 437-467
    • Kauffman, S.A.1
  • 30
    • 0014334125 scopus 로고
    • Simulation of rhythmic nervous activities
    • Kling, U. & Sźekely, G. [1968] "Simulation of rhythmic nervous activities," Biol. Cybern. 5, 89-103.
    • (1968) Biol. Cybern. , vol.5 , pp. 89-103
    • Kling, U.1    Sźekely, G.2
  • 31
    • 77950348201 scopus 로고    scopus 로고
    • Structural principles for periodic orbits in glass networks
    • to appear
    • Lu, L. & Edwards, R. [2010] "Structural principles for periodic orbits in glass networks," J. Math. Biol., to appear.
    • (2010) J. Math. Biol.
    • Lu, L.1    Edwards, R.2
  • 32
    • 0001051330 scopus 로고
    • The Poincaŕe- Bendixson theorem for monotone cyclic feedback systems
    • Mallet-Paret, J. & Smith, H. L. [1990] "The Poincaŕe- Bendixson theorem for monotone cyclic feedback systems," J. Dyn. Diff. Eqs. 2, 367-421.
    • (1990) J. Dyn. Diff. Eqs. , vol.2 , pp. 367-421
    • Mallet-Paret, J.1    Smith, H.L.2
  • 33
    • 0142027814 scopus 로고    scopus 로고
    • Structure and function of the feed-forward loop network motif
    • Mangan, S. & Alon, U. [2003] "Structure and function of the feed-forward loop network motif," Proc. Nat. Acad. Sci. U.S.A. 100, 11980-11985.
    • (2003) Proc. Nat. Acad. Sci. U.S.A. , vol.100 , pp. 11980-11985
    • Mangan, S.1    Alon, U.2
  • 34
    • 7244219911 scopus 로고    scopus 로고
    • Evolving complex dynamics in electronic models of genetic networks
    • Mason, J., Linsay, P. S., Collins, J. J. & Glass, L. [2004] "Evolving complex dynamics in electronic models of genetic networks," Chaos 14, 707-715.
    • (2004) Chaos , vol.14 , pp. 707-715
    • Mason, J.1    Linsay, P.S.2    Collins, J.J.3    Glass, L.4
  • 35
    • 0001511149 scopus 로고
    • Periodic solutions in systems of piecewise-linear differential equations
    • Mestl, T., Plahte, E. & Omholt, S. W. [1995] "Periodic solutions in systems of piecewise-linear differential equations," Dyn. Stab. Syst. 10, 179-193.
    • (1995) Dyn. Stab. Syst. , vol.10 , pp. 179-193
    • Mestl, T.1    Plahte, E.2    Omholt, S.W.3
  • 36
    • 56749160113 scopus 로고    scopus 로고
    • Design principles of biochemical oscillators
    • Nov́ak, B. & Tyson, J. J. [2008] "Design principles of biochemical oscillators," Nat. Rev. Mol. Cell Biol. 9, 981-991.
    • (2008) Nat. Rev. Mol. Cell Biol. , vol.9 , pp. 981-991
    • Nov́ak, B.1    Tyson, J.J.2
  • 37
    • 4143051643 scopus 로고    scopus 로고
    • Inferring models of gene expression dynamics
    • Perkins, T. J., Hallett, M. & Glass, L. [2004] "Inferring models of gene expression dynamics," J. Theor. Biol. 230, 289-300.
    • (2004) J. Theor. Biol. , vol.230 , pp. 289-300
    • Perkins, T.J.1    Hallett, M.2    Glass, L.3
  • 38
    • 0032020122 scopus 로고    scopus 로고
    • A methodological basis for description and analysis of systems with complex switch-like interactions
    • Plahte, E.,Mestl, T. & Omholt, S.W. [1998] "A methodological basis for description and analysis of systems with complex switch-like interactions," J. Math. Biol. 36, 321-348.
    • (1998) J. Math. Biol. , vol.36 , pp. 321-348
    • Plahte, E.1    Mestl, T.2    Omholt, S.W.3
  • 39
    • 13244279645 scopus 로고    scopus 로고
    • Analysis and generic properties of gene regulatory networks with graded response functions
    • Plahte, E. & Kjoglum, S. [2005] "Analysis and generic properties of gene regulatory networks with graded response functions," Physica D 201, 150-176.
    • (2005) Physica D , vol.201 , pp. 150-176
    • Plahte, E.1    Kjoglum, S.2
  • 40
    • 0001037786 scopus 로고
    • Introduction to a general theory of elementary propositions
    • Post, E. L. [1921] "Introduction to a general theory of elementary propositions," Am. J. Math. 43, 163-185.
    • (1921) Am. J. Math. , vol.43 , pp. 163-185
    • Post, E.L.1
  • 42
    • 0001723411 scopus 로고
    • Logical identification of all steady states: The concept of feedback loop characteristic states
    • Snoussi, E. H. & Thomas, R. [1993] "Logical identification of all steady states: The concept of feedback loop characteristic states," Bull. Math. Biol. 55, 973-991.
    • (1993) Bull. Math. Biol. , vol.55 , pp. 973-991
    • Snoussi, E.H.1    Thomas, R.2
  • 43
    • 0000481503 scopus 로고
    • Logical network for controlling limb movements in Urodela
    • Sźekely, G. [1965] "Logical network for controlling limb movements in Urodela," Acta Physiologica Acad. Sci. Hung. 27, 285-289.
    • (1965) Acta Physiologica Acad. Sci. Hung. , vol.27 , pp. 285-289
    • Sźekely, G.1
  • 45
    • 27244462819 scopus 로고
    • The secant condition for instability in biochemical feedback control I. The role of cooperativity and saturability
    • Thron, C. D. [1991] "The secant condition for instability in biochemical feedback control I. The role of cooperativity and saturability," Bull. Math. Biol. 53, 383-401.
    • (1991) Bull. Math. Biol. , vol.53 , pp. 383-401
    • Thron, C.D.1
  • 46
    • 0002275384 scopus 로고
    • The dynamics of feedback control circuits in biochemical pathways
    • Tyson, J. J. & Othmer, H. G. [1978] "The dynamics of feedback control circuits in biochemical pathways," Progress in Theoretical Biology, pp. 1-62.
    • (1978) Progress in Theoretical Biology , pp. 1-62
    • Tyson, J.J.1    Othmer, H.G.2
  • 48
    • 38149086858 scopus 로고    scopus 로고
    • An algebraic algorithm for the identification of glass networks with periodic orbits along cyclic attractors
    • Zinovik, I., Kroening, D. & Chebiryak, Y. [2007] "An algebraic algorithm for the identification of glass networks with periodic orbits along cyclic attractors," Lecture Notes in Computer Science 4545, 140-154.
    • (2007) Lecture Notes in Computer Science , vol.4545 , pp. 140-154
    • Zinovik, I.1    Kroening, D.2    Chebiryak, Y.3


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.