TY - CHAP AU - Izhikevich, E. M. PY - 2007 DA - 2007// TI - Computational Neuroscience BT - Dynamical Systems in Neuroscience: The Geometry of Excitability and Bursting PB - MIT Press CY - Cambridge ID - Izhikevich2007 ER - TY - BOOK AU - Ermentrout, B. AU - Terman, D. PY - 2010 DA - 2010// TI - Mathematical Foundations of Neuroscience PB - Springer CY - New York UR - https://doi.org/10.1007/978-0-387-87708-2 DO - 10.1007/978-0-387-87708-2 ID - Ermentrout2010 ER - TY - CHAP AU - Schultheiss, N. W. AU - Prinz, A. A. AU - Butera, R. J. PY - 2012 DA - 2012// TI - Springer Series in Computational Neuroscience 6 BT - Phase Response Curves in Neuroscience Theory, Experiment, and Analysis PB - Springer CY - Berlin UR - https://doi.org/10.1007/978-1-4614-0739-3 DO - 10.1007/978-1-4614-0739-3 ID - Schultheiss2012 ER - TY - JOUR AU - Gutkin, B. S. AU - Ermentrout, G. B. AU - Reyes, A. D. PY - 2005 DA - 2005// TI - Phase-response curves give the responses of neurons to transient inputs JO - J Neurophysiol VL - 94 UR - https://doi.org/10.1152/jn.00359.2004 DO - 10.1152/jn.00359.2004 ID - Gutkin2005 ER - TY - JOUR AU - Ermentrout, G. B. AU - Beverlin, B. AU - Troyer, T. AU - Netoff, T. I. PY - 2011 DA - 2011// TI - The variance of phase-resetting curves JO - J Comput Neurosci VL - 31 UR - https://doi.org/10.1007/s10827-010-0305-9 DO - 10.1007/s10827-010-0305-9 ID - Ermentrout2011 ER - TY - JOUR AU - Oh, M. AU - Matveev, V. PY - 2011 DA - 2011// TI - Non-weak inhibition and phase resetting at negative values of phase in cells with fast-slow dynamics at hyperpolarized potentials JO - J Comput Neurosci VL - 31 UR - https://doi.org/10.1007/s10827-010-0292-x DO - 10.1007/s10827-010-0292-x ID - Oh2011 ER - TY - JOUR AU - Winfree, A. T. PY - 1974/1975 DA - 1974/1975// TI - Patterns of phase compromise in biological cycles JO - J Math Biol VL - 1 UR - https://doi.org/10.1007/BF02339491 DO - 10.1007/BF02339491 ID - Winfree1974/1975 ER - TY - JOUR AU - Guillamon, A. AU - Huguet, G. PY - 2009 DA - 2009// TI - A computational and geometric approach to phase resetting curves and surfaces JO - SIAM J Appl Dyn Syst VL - 8 UR - https://doi.org/10.1137/080737666 DO - 10.1137/080737666 ID - Guillamon2009 ER - TY - STD TI - Huguet G, de la Llave R: Computation of limit cycles and their isochrons: fast algorithms and their convergence. SIAM J Appl Dyn Syst 2013, in press. Huguet G, de la Llave R: Computation of limit cycles and their isochrons: fast algorithms and their convergence. SIAM J Appl Dyn Syst 2013, in press. ID - ref9 ER - TY - JOUR AU - Osinga, H. M. AU - Moehlis, J. PY - 2010 DA - 2010// TI - Continuation-based computation of global isochrons JO - SIAM J Appl Dyn Syst VL - 9 UR - https://doi.org/10.1137/090777244 DO - 10.1137/090777244 ID - Osinga2010 ER - TY - JOUR AU - Sherwood, W. E. AU - Guckenheimer, J. PY - 2010 DA - 2010// TI - Dissecting the phase response of a model bursting neuron JO - SIAM J Appl Dyn Syst VL - 9 UR - https://doi.org/10.1137/090773519 DO - 10.1137/090773519 ID - Sherwood2010 ER - TY - CHAP AU - Mauroy, A. AU - Mezić, I. PY - 2012 DA - 2012// TI - On the use of Fourier averages to compute the global isochrons of (quasi)periodic dynamics BT - Chaos ID - Mauroy2012 ER - TY - JOUR AU - Ermentrout, G. B. AU - Kopell, N. PY - 1991 DA - 1991// TI - Multiple pulse interactions and averaging in systems of coupled neural oscillators JO - J Math Biol VL - 29 UR - https://doi.org/10.1007/BF00160535 DO - 10.1007/BF00160535 ID - Ermentrout1991 ER - TY - JOUR AU - Brown, E. AU - Holmes, P. AU - Moehlis, J. PY - 2004 DA - 2004// TI - On the phase reduction and response dynamics of neural oscillator populations JO - Neural Comput VL - 16 UR - https://doi.org/10.1162/089976604322860668 DO - 10.1162/089976604322860668 ID - Brown2004 ER - TY - JOUR AU - Oprisan, S. A. AU - Canavier, C. PY - 2001 DA - 2001// TI - Stability analysis of rings of pulse-coupled oscillators: the effect of phase resetting in the second cycle after the pulse is important at synchrony and for long pulses JO - Differ Equ Dyn Syst VL - 9 ID - Oprisan2001 ER - TY - JOUR AU - Oprisan, S. A. AU - Prinz, A. A. AU - Canavier, C. C. PY - 2004 DA - 2004// TI - Phase resetting and phase locking in hybrid circuits of one model and one biological neuron JO - Biophys J VL - 87 UR - https://doi.org/10.1529/biophysj.104.046193 DO - 10.1529/biophysj.104.046193 ID - Oprisan2004 ER - TY - JOUR AU - Maran, S. AU - Canavier, C. PY - 2008 DA - 2008// TI - Using phase resetting to predict 1:1 and 2:2 locking in two neuron networks in which firing order is not always preserved JO - J Comput Neurosci VL - 24 UR - https://doi.org/10.1007/s10827-007-0040-z DO - 10.1007/s10827-007-0040-z ID - Maran2008 ER - TY - JOUR AU - Lin, K. K. AU - Wedgwood, K. C. A. AU - Coombes, S. AU - Young, L. S. PY - 2013 DA - 2013// TI - Limitations of perturbative techniques in the analysis of rhythms and oscillations JO - J Math Biol VL - 66 UR - https://doi.org/10.1007/s00285-012-0506-0 DO - 10.1007/s00285-012-0506-0 ID - Lin2013 ER - TY - JOUR AU - Ermentrout, G. B. PY - 1996 DA - 1996// TI - Type I membranes, phase resetting curves, and synchrony JO - Neural Comput VL - 8 UR - https://doi.org/10.1162/neco.1996.8.5.979 DO - 10.1162/neco.1996.8.5.979 ID - Ermentrout1996 ER - TY - JOUR AU - Guckenheimer, J. PY - 1974/1975 DA - 1974/1975// TI - Isochrons and phaseless sets JO - J Math Biol VL - 1 UR - https://doi.org/10.1007/BF01273747 DO - 10.1007/BF01273747 ID - Guckenheimer1974/1975 ER - TY - JOUR AU - Cabré, X. AU - Fontich, E. AU - de la Llave, R. PY - 2005 DA - 2005// TI - The parameterization method for invariant manifolds. III. Overview and applications JO - J Differ Equ VL - 218 UR - https://doi.org/10.1016/j.jde.2004.12.003 DO - 10.1016/j.jde.2004.12.003 ID - Cabré2005 ER - TY - JOUR AU - Rabinovitch, A. AU - Friedman, M. PY - 2006 DA - 2006// TI - Fixed points of two-dimensional maps obtained under rapid stimulations JO - Phys Lett A VL - 355 UR - https://doi.org/10.1016/j.physleta.2006.02.059 DO - 10.1016/j.physleta.2006.02.059 ID - Rabinovitch2006 ER - TY - JOUR AU - Takeshita, D. AU - Feres, R. PY - 2010 DA - 2010// TI - Higher order approximation of isochrons JO - Nonlinearity VL - 23 UR - https://doi.org/10.1088/0951-7715/23/6/004 DO - 10.1088/0951-7715/23/6/004 ID - Takeshita2010 ER - TY - JOUR AU - Suvak, O. AU - Demir, A. PY - 2010 DA - 2010// TI - Quadratic approximations for the isochrons of oscillators: a general theory, advanced numerical methods and accurate phase computations JO - IEEE Trans Comput-Aided Des Integr Circuits Syst VL - 29 UR - https://doi.org/10.1109/TCAD.2010.2049056 DO - 10.1109/TCAD.2010.2049056 ID - Suvak2010 ER -