Macroscopic models for networks of coupled biological oscillators
Tóm tắt
Từ khóa
Tài liệu tham khảo
S. Strogatz Sync (Hyperion 2003).
G. B. Ermentrout, N. Kopell, Parabolic bursting in an excitable system coupled with a slow oscillation. SIAM J. Appl. Math. 46, 233–253 (1986).
N. Schultheiss A. Prinz R. Butera Phase Response Curves in Neuroscience: Theory Experiment and Analysis (Springer Science Business Media LLC 2011).
J. H. Abel, K. Meeker, D. Granados-Fuentes, P. C. S. John, T. J. Wang, B. B. Bales, F. J. Doyle III, E. D. Herzog, L. R. Petzold, Functional network inference of the suprachiasmatic nucleus. Proc. Natl. Acad. Sci. U.S.A. 113, 4512–4517 (2016).
A. Pikovsky, M. Rosenblum, Dynamics of globally coupled oscillators: Progress and perspectives. Chaos 25, 097616 (2015).
T. B. Luke, E. Barreto, P. So, Complete classification of the macroscopic behavior of a heterogeneous network of theta neurons. Neural Comput. 25, 3207–3234 (2013).
K. M. Hannay, V. Booth, D. B. Forger, Collective phase response curves for heterogeneous coupled oscillators. Phys. Rev. E 92, 022923 (2015).
E. Montbrió, D. Pazó, A. Roxin, Macroscopic description for networks of spiking neurons. Phys. Rev. X 5, 021028 (2015).
Z. Lu, K. Klein-Cardeña, S. Lee, T. M. Antonsen, M. Girvan, E. Ott, Resynchronization of circadian oscillators and the east-west asymmetry of jet-lag. Chaos 26, 094811 (2016).
S. A. Marvel, R. E. Mirollo, S. H. Strogatz, Identical phase oscillators with global sinusoidal coupling evolve by Möbius group action. Chaos 19, 043104 (2009).
B. Sonnenschein, L. Schimansky-Geier, Approximate solution to the stochastic Kuramoto model. Phys. Rev. E 88, 052111 (2013).
D. Hansel, G. Mato, C. Meunier, Phase dynamics for weakly coupled Hodgkin-Huxley neurons. Europhys. Lett. 23, 367 (1993).
M. Breakspear, S. Heitmann, A. Daffertshofer, Generative models of cortical oscillations: Neurobiological implications of the Kuramoto model. Front. Hum. Neurosci. 4, 190 (2010).
H. Daido, Order function and macroscopic mutual entrainment in uniformly coupled limit-cycle oscillators. Progr. Theor. Phys. 88, 1213–1218 (1992).
H. Daido, Critical conditions of macroscopic mutual entrainment in uniformly coupled limit-cycle oscillators. Progr. Theor. Phys. 89, 929–934 (1993).
P. S. Skardal, E. Ott, J. G. Restrepo, Cluster synchrony in systems of coupled phase oscillators with higher-order coupling. Phys. Rev. E 84, 036208 (2011).
Y. M. Lai, M. A. Porter, Noise-induced synchronization, desynchronization, and clustering in globally coupled nonidentical oscillators. Phys. Rev. E Stat. Nonlinear Soft Matter Phys. 88, 012905 (2013).
M. A. Zaks, A. B. Neiman, S. Feistel, L. Schimansky-Geier, Noise-controlled oscillations and their bifurcations in coupled phase oscillators. Phys. Rev. E 68, 066206 (2003).
P. S. Skardal, D. Taylor, J. Sun, Optimal synchronization of directed complex networks. Phys. Rev. Lett. 113, 144101 (2014).
D. J. Watts, S. H. Strogatz, Collective dynamics of ’small-world’ networks. Nature 393, 440–442 (1998).
J. Guckenheimer P. J. Holmes Nonlinear Oscillations Dynamical Systems and Bifurcations of Vector Fields (Springer Science & Business Media 2013).
M. E. Jewett, R. E. Kronauer, Refinement of a limit cycle oscillator model of the effects of light on the human circadian pacemaker. J. Theor. Biol. 192, 455–465 (1998).
M. E. Jewett, D. W. Rimmer, J. F. Duffy, E. B. Klerman, R. E. Kronauer, C. A. Czeisler, Human circadian pacemaker is sensitive to light throughout subjective day without evidence of transients. Am. J. Physiol. 273, R1800–R1809 (1997).
P. Indic, D. B. Forger, M. A. S. Hilaire, D. A. Dean II, E. N. Brown, R. E. Kronauer, E. B. Klerman, M. E. Jewett, Comparison of amplitude recovery dynamics of two limit cycle oscillator models of the human circadian pacemaker. Chronobiol. Int. 22, 613–629 (2005).
S. A. Brown, F. Fleury-Olela, E. Nagoshi, C. Hauser, C. Juge, C. A. Meier, R. Chicheportiche, J.-M. Dayer, U. Albrecht, U. Schibler, The period length of fibroblast circadian gene expression varies widely among human individuals. PLOS Biol. 3, e338 (2005).
J. Myung, S. Hong, D. DeWoskin, E. De Schutter, D. B. Forger, T. Takumi, GABA-mediated repulsive coupling between circadian clock neurons in the SCN encodes seasonal time. Proc. Natl. Acad. Sci. U.S.A. 112, E3920–E3929 (2015).
J. Myung, S. Hong, F. Hatanaka, Y. Nakajima, E. De Schutter, T. Takumi, Period coding of Bmal1 oscillators in the suprachiasmatic nucleus. J. Neurosci. 32, 8900–8918 (2012).
M. Small Applied Nonlinear Time Series Analysis (World Scientific Publishing Co. 2005).
B. Kralemann, L. Cimponeriu, M. Rosenblum, A. Pikovsky, R. Mrowka, Uncovering interaction of coupled oscillators from data. Phys. Rev. E Stat. Nonlinear Soft Matter Phys. 76, 055201 (2007).
B. Kralemann, L. Cimponeriu, M. Rosenblum, A. Pikovsky, R. Mrowka, Phase dynamics of coupled oscillators reconstructed from data. Phys. Rev. E 77, 066205 (2008).
C. Morris, H. Lecar, Voltage oscillations in the barnacle giant muscle fiber. Biophys. J. 35, 193–213 (1981).
J. Rinzel, G. B. Ermentrout, Analysis of neural excitability and oscillations. Methods Neuronal Modeling 2, 251–292 (1998).
A. Wachter, L. T. Biegler, On the implementation of a primal-dual interior point filter line search algorithm for large-scale nonlinear programming. Math. Program. 106, 25–47 (2006).
J. Andersson “A General Purpose Software Framework for Dynamic Optimization ” thesis Arenberg Doctoral School KU Leuven (2013).