Computing quadratic approximations for the isochrons of oscillators: A general theory and advanced numerical methods

IEEE/ACM International Conference on Computer-Aided Design, Digest of Technical Papers, ICCAD

Volumn , Issue , 2009, Pages 397-402

  Şuvak, Önder ^a   Demir, Alper ^a  

^a KOÇ UNIVERSITY   (Turkey)

Author keywords

[No Author keywords available]

Indexed keywords

BIOLOGICAL OSCILLATIONS; EXACT CALCULATIONS; GENERAL THEORY; GENERALIZED PHASE; ISOCHRONS; LARGE DIMENSIONS; LINEAR APPROXIMATIONS; MATHEMATICAL BIOLOGY; NUMERICAL TECHNIQUES; PERTURBATION ANALYSIS; QUADRATIC APPROXIMATION;

BIOLOGY; COMPUTER AIDED DESIGN; NONLINEAR CONTROL SYSTEMS; NUMBER THEORY; OSCILLATORS (ELECTRONIC);

NUMERICAL METHODS;

EID: 76349106404     PISSN: 10923152     EISSN: None     Source Type: Conference Proceeding    
DOI: None     Document Type: Conference Paper

References (18)

1. E.M. Izhikevich. Dynamical Systems in Neuroscience: The Geometry of Excitability and Bursting. Chapter 10. MIT Press, 2007.
2. Arthur T. Winfree. The Geometry of Biological Time. Springer, 2001.
3. A. Goldbeter. Biochemical Oscillations and Cellular Rythms. Cambridge Univ Press, 1996.
4. K. Josic, E. T. Shea-Brown, and J. Moehlis. Isochron. Scholarpedia, 1(8):1361, 2006.
5. M. Farkas. Periodic Motions. Springer-Verlag, 1994.
6. A. Demir. Fully nonlinear oscillator noise analysis: An oscillator with no asymptotic phase. International Journal of Circuit Theory and Applications, pages 175-203, March-April 2007.
7. J. Guckenheimer and P. Holmes. Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields. Springer, 1983.
8. A. Demir, A. Mehrotra, and J. Roychowdhury. Phase noise in oscillators: A unifying theory and numerical methods for characterisation. IEEE Transactions on Circuits and Systems-I: Fundamental Theory and Applications, 47(5):655-674, May 2000.
9. A. Demir and J. Roychowdhury. A reliable and efficient procedure for oscillator PPV computation, with phase noise macromodelling applications. IEEE Tran. on CAD of ICs and Systems, 22(2):188-197, February 2003.
10. G.B. Ermentrout. Simulating, Analyzing, and Animating Dynamical Systems: A Guide to XPPAUT for Researchers and Students. SIAM, 2002.
11. Eric Brown, Jeff Moehlis, and Philip Holmes. On the phase reduction and response dynamics of neural oscillator populations. Neural Comput, 16(4):673-715, Apr 2004.
12. W. Govaerts and B. Sautois. Computation of the phase response curve: A direct numerical approach. Neural Comput, 18(4):817-847, Apr 2006.
13. Z. Gajic and M.T. Javed Qureshi. Lyapunov Matrix Equation in System Stability and Control. Academic Press, 1995.
14. Thilo Penzl. Numerical solution of generalized Lyapunov equations. Advances in Computational Mathematics, 8(1):33-48, 1998.
15. A. Demir and A. Sangiovanni-Vincentelli. Analysis and Simulation of Noise in Nonlinear Electronic Circuits and Systems. Kluwer Academic Publishers, 1998.
16. P. Benner, V. Mehrmann, V. Sima, S. Van Huffel, and A. Varga. SLICOTA subroutine library in systems and control theory. In B.N. Datta, editor, Applied and Computational Control, Signals, and Circuits, volume 1, chapter 10, pages 499-539. Boston, MA: Birkhuser, 1999.
17. 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., 153:177-188, 2008.
18. 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. Biophysical Journal, 86:2786-2802, May 2004.