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Volumn 29, Issue 8, 2010, Pages 1215-1228

Quadratic approximations for the isochrons of oscillators: A general theory, advanced numerical methods, and accurate phase computations

Author keywords

Isochrons; oscillators; phase of an oscillator

Indexed keywords

EXACT CALCULATIONS; EXPONENTIAL COMPLEXITY; FORCE METHOD; GENERAL THEORY; GENERALIZED PHASE; HARD PROBLEMS; ISOCHRONS; LARGE DIMENSIONS; LOCAL LINEAR APPROXIMATION; MACRO-MODELS; MATHEMATICAL BIOLOGY; NUMERICAL TECHNIQUES; PERTURBATION ANALYSIS; QUADRATIC APPROXIMATION; SECOND ORDERS;

EID: 77954872218     PISSN: 02780070     EISSN: None     Source Type: Journal    
DOI: 10.1109/TCAD.2010.2049056     Document Type: Article
Times cited : (29)

References (29)
  • 5
    • 0004202803 scopus 로고
    • Berlin, Germany: Springer-Verlag
    • M. Farkas, Periodic Motions. Berlin, Germany: Springer-Verlag, 1994.
    • (1994) Periodic Motions
    • Farkas, M.1
  • 6
    • 33947725581 scopus 로고    scopus 로고
    • Fully nonlinear oscillator noise analysis: An oscillator with no asymptotic phase
    • Mar.-Apr
    • A. Demir, "Fully nonlinear oscillator noise analysis: An oscillator with no asymptotic phase," Int. J. Circuit Theory Applicat., vol.32, no.2, pp. 175-203, Mar.-Apr. 2007.
    • (2007) Int. J. Circuit Theory Applicat. , vol.32 , Issue.2 , pp. 175-203
    • Demir, A.1
  • 8
    • 0025491739 scopus 로고
    • Analysis of white and f-a noise in oscillators
    • F. X. Kaertner, "Analysis of white and f-a noise in oscillators," Int. J. Circuits Theory Applicat., vol.18, no.5, pp. 485-519, 1990.
    • (1990) Int. J. Circuits Theory Applicat. , vol.18 , Issue.5 , pp. 485-519
    • Kaertner, F.X.1
  • 10
    • 0033700459 scopus 로고    scopus 로고
    • Phase noise in oscillators: A unifying theory and numerical methods for characterization
    • May
    • A. Demir, A. Mehrotra, and J. Roychowdhury, "Phase noise in oscillators: A unifying theory and numerical methods for characterization," IEEE Trans. Circuits Syst. I: Fundam. Theory Applicat., vol.47, no.5, pp. 655-674, May 2000.
    • (2000) IEEE Trans. Circuits Syst. I: Fundam. Theory Applicat. , vol.47 , Issue.5 , pp. 655-674
    • Demir, A.1    Mehrotra, A.2    Roychowdhury, J.3
  • 11
    • 18144404189 scopus 로고    scopus 로고
    • Computation of period sensitivity functions for the simulation of phase noise in oscillators
    • Apr
    • A. Brambilla, P. Maffezzoni, and G. Storti-Gajani, "Computation of period sensitivity functions for the simulation of phase noise in oscillators," IEEE Trans. Circuits Syst. I, Reg. Papers, vol.52, no.4, pp. 681-694, Apr. 2005.
    • (2005) IEEE Trans. Circuits Syst. I, Reg. Papers , vol.52 , Issue.4 , pp. 681-694
    • Brambilla, A.1    Maffezzoni, P.2    Storti-Gajani, G.3
  • 13
    • 77949358878 scopus 로고    scopus 로고
    • Synchronization analysis of two weakly coupled oscillators through a PPV macromodel
    • Mar. 2010
    • P. Maffezzoni, "Synchronization analysis of two weakly coupled oscillators through a PPV macromodel," IEEE Trans. Circuits Syst. I: Reg. Papers, vol.57, no.3, pp. 654-663, Mar. 2010.
    • IEEE Trans. Circuits Syst. I: Reg. Papers , vol.57 , Issue.3 , pp. 654-663
    • Maffezzoni, P.1
  • 14
    • 70349744596 scopus 로고    scopus 로고
    • Evaluating pulling effects in oscillators due to small-signal injection
    • Jan
    • P. Maffezzoni and D. D'Amore, "Evaluating pulling effects in oscillators due to small-signal injection," IEEE Trans. Comput.-Aided Design Integr. Circuits Syst., vol.28, no.1, pp. 22-31, Jan. 2009.
    • (2009) IEEE Trans. Comput.-Aided Design Integr. Circuits Syst. , vol.28 , Issue.1 , pp. 22-31
    • Maffezzoni, P.1    D'Amore, D.2
  • 15
    • 77949356564 scopus 로고    scopus 로고
    • The spectrum of a noisy free-running oscillator explained by random frequency pulling
    • Mar. 2010
    • A. Mirzaei and A. Abidi, "The spectrum of a noisy free-running oscillator explained by random frequency pulling," IEEE Trans. Circuits Syst. I: Reg. Papers, vol.57, no.3, pp. 642-653, Mar. 2010.
    • IEEE Trans. Circuits Syst. I: Reg. Papers , vol.57 , Issue.3 , pp. 642-653
    • Mirzaei, A.1    Abidi, A.2
  • 16
    • 0034474750 scopus 로고    scopus 로고
    • Computing phase noise eigenfunctions directly from steady-state Jacobian matrices
    • Nov
    • A. Demir, D. Long, and J. Roychowdhury, "Computing phase noise eigenfunctions directly from steady-state Jacobian matrices," in Proc. ICCAD, Nov. 2000, pp. 283-288.
    • (2000) Proc. ICCAD , pp. 283-288
    • Demir, A.1    Long, D.2    Roychowdhury, J.3
  • 17
    • 0037320460 scopus 로고    scopus 로고
    • A reliable and efficient procedure for oscillator PPV computation, with phase noise macromodeling applications
    • Feb
    • A. Demir and J. Roychowdhury, "A reliable and efficient procedure for oscillator PPV computation, with phase noise macromodeling applications," IEEE Trans. Comput.-Aided Design Integr. Circuits Syst., vol.22, no.2, pp. 188-197, Feb. 2003.
    • (2003) IEEE Trans. Comput.-Aided Design Integr. Circuits Syst. , vol.22 , Issue.2 , pp. 188-197
    • Demir, A.1    Roychowdhury, J.2
  • 19
    • 1542351229 scopus 로고    scopus 로고
    • On the phase reduction and response dynamics of neural oscillator populations
    • Apr
    • E. Brown, J. Moehlis, and P. Holmes, "On the phase reduction and response dynamics of neural oscillator populations," Neural Comput., vol.16, no.4, pp. 673-715, Apr. 2004.
    • (2004) Neural Comput. , vol.16 , Issue.4 , pp. 673-715
    • Brown, E.1    Moehlis, J.2    Holmes, P.3
  • 20
    • 33645722312 scopus 로고    scopus 로고
    • Computation of the phase response curve: A direct numerical approach
    • Apr
    • W. Govaerts and B. Sautois, "Computation of the phase response curve: A direct numerical approach," Neural Comput., vol.18, no.4, pp. 817-847, Apr. 2006.
    • (2006) Neural Comput. , vol.18 , Issue.4 , pp. 817-847
    • Govaerts, W.1    Sautois, B.2
  • 21
    • 76349106404 scopus 로고    scopus 로고
    • Computing quadratic approximations for the isochrons of oscillators: A general theory and advanced numerical methods
    • O. Suvak and A. Demir, "Computing quadratic approximations for the isochrons of oscillators: A general theory and advanced numerical methods," in Proc. IEEE/ACM Int. Conf. Comput.-Aided Design, 2009, pp. 397-402.
    • (2009) Proc. IEEE/ACM Int. Conf. Comput.-Aided Design , pp. 397-402
    • Suvak, O.1    Demir, A.2
  • 23
    • 0032342953 scopus 로고    scopus 로고
    • Numerical solution of generalized Lyapunov equations
    • T. Penzl, "Numerical solution of generalized Lyapunov equations," Adv. Comput. Math., vol.8, no.1, pp. 33-48, 1998.
    • (1998) Adv. Comput. Math. , vol.8 , Issue.1 , pp. 33-48
    • Penzl, T.1
  • 25
    • 55749097248 scopus 로고    scopus 로고
    • Numerical solution of large-scale Lyapunov equations, Riccati equations, and linear-quadratic optimal control problems
    • P. Benner, J. R. Li, and T. Penzl, "Numerical solution of large-scale Lyapunov equations, Riccati equations, and linear-quadratic optimal control problems," Numer. Linear Algebra Applicat., vol.15, no.9, pp. 755-777, 2008.
    • (2008) Numer. Linear Algebra Applicat. , vol.15 , Issue.9 , pp. 755-777
    • Benner, P.1    Li, J.R.2    Penzl, T.3
  • 26
    • 77954871283 scopus 로고    scopus 로고
    • The Control and Systems Library SLICOT [Online]. Available
    • The Control and Systems Library SLICOT [Online]. Available: http://www.slicot.org/
  • 27
    • 39849102205 scopus 로고    scopus 로고
    • Sensitivity measures for oscillating systems: Application to mammalian circadian gene network
    • Jan
    • S. R. Taylor, R. Gunawan, L. R. Petzold, and F. J. Doyle, III, "Sensitivity measures for oscillating systems: Application to mammalian circadian gene network," IEEE Trans. Automat. Contr., vol.53. pp. 177-188, Jan. 2008.
    • (2008) IEEE Trans. Automat. Contr. , vol.53 , pp. 177-188
    • Taylor, S.R.1    Gunawan, R.2    Petzold, L.R.3    Doyle III, F.J.4
  • 28
    • 2142811057 scopus 로고    scopus 로고
    • Simulation of Drosophila circadian oscillations, mutations, and light responses by a model with VRI, PDP-1, and CLK
    • May
    • P. Smolen, P. E. Hardin, B. S. Lo, D. A. Baxte, and J. H. Byrne, "Simulation of Drosophila circadian oscillations, mutations, and light responses by a model with VRI, PDP-1, and CLK," Biophys. J., vol.86, pp. 2786-2802, May 2004.
    • (2004) Biophys. J. , vol.86 , pp. 2786-2802
    • Smolen, P.1    Hardin, P.E.2    Lo, B.S.3    Baxte, D.A.4    Byrne, J.H.5
  • 29
    • 0034688173 scopus 로고    scopus 로고
    • A synthetic oscillatory network of transcriptional regulators
    • Jan
    • M. B. Elowitz and S. Leibler, "A synthetic oscillatory network of transcriptional regulators," Nature, vol.403, no.6767, pp. 335-338, Jan. 2000.
    • (2000) Nature , vol.403 , Issue.6767 , pp. 335-338
    • Elowitz, M.B.1    Leibler, S.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.