Synchronization of Bursting Neurons: What Matters in the Network Topology, Physical Review Letters, vol.49, issue.18, p.188101, 2005. ,
DOI : 10.1109/81.974874
Symbolic computations of nonlinear observability, Physical Review E, vol.91, issue.6, p.62912, 2015. ,
DOI : 10.1098/rspb.1995.0153
URL : https://hal.archives-ouvertes.fr/hal-01612374
Extracting qualitative dynamics from experimental data, Physica D: Nonlinear Phenomena, vol.20, issue.2-3, pp.217-236, 1986. ,
DOI : 10.1016/0167-2789(86)90031-X
The tale of the neuroscientists and the computer: why mechanistic theory matters, Frontiers in Neuroscience, vol.146, p.349, 2014. ,
DOI : 10.1126/science.146.3642.347
Impulses and Physiological States in Theoretical Models of Nerve Membrane, Biophysical Journal, vol.1, issue.6, pp.445-466, 1961. ,
DOI : 10.1016/S0006-3495(61)86902-6
Controllability Index Based on Conditioning Number, Journal of Dynamic Systems, Measurement, and Control, vol.97, issue.4, pp.444-445, 1975. ,
DOI : 10.1115/1.3426963
Influence of the singular manifold of nonobservable states in reconstructing chaotic attractors, Physical Review E, vol.22, issue.2, p.26205, 2012. ,
DOI : 10.1111/j.1749-6632.1980.tb29710.x
A brief history of excitable map-based neurons and neural networks, Journal of Neuroscience Methods, vol.220, issue.2, pp.116-130, 2013. ,
DOI : 10.1016/j.jneumeth.2013.07.014
Monte Carlo Singular Spectrum Analysis (SSA) Revisited: Detecting Oscillator Clusters in Multivariate Datasets, Journal of Climate, vol.28, issue.19, pp.7873-7893, 2015. ,
DOI : 10.1175/JCLI-D-15-0100.1
URL : https://cloudfront.escholarship.org/dist/prd/content/qt11r3w74z/qt11r3w74z.pdf
Multivariate singular spectrum analysis and the road to phase synchronization, Physical Review E, vol.84, issue.3, p.36206, 2011. ,
DOI : 10.1103/PhysRevLett.47.179
Advanced spectral methods for climate time series, Rev. Geophys, vol.40, issue.1, 2002. ,
Nonlinear controllability and observability, IEEE Transactions on Automatic Control, vol.22, issue.5, pp.728-740, 1977. ,
DOI : 10.1109/TAC.1977.1101601
A Model of Neuronal Bursting Using Three Coupled First Order Differential Equations, Proceedings of the Royal Society B: Biological Sciences, vol.221, issue.1222, pp.87-102, 1984. ,
DOI : 10.1098/rspb.1984.0024
A quantitative description of membrane current and its application to conduction and excitation in nerve, The Journal of Physiology, vol.117, issue.4, pp.500-544, 1952. ,
DOI : 10.1113/jphysiol.1952.sp004764
Simple model of spiking neurons, IEEE Transactions on Neural Networks, vol.14, issue.6, pp.1569-1572, 2003. ,
DOI : 10.1109/TNN.2003.820440
URL : http://www.nsi.edu/users/izhikevich/publications/spikes.pdf
Which Model to Use for Cortical Spiking Neurons?, IEEE Transactions on Neural Networks, vol.15, issue.5, pp.1063-1070, 2004. ,
DOI : 10.1109/TNN.2004.832719
Large-scale model of mammalian thalamocortical systems, Proceedings of the National Academy of Sciences, vol.451, issue.7174, pp.3593-3598, 2008. ,
DOI : 10.1038/nature06447
On the general theory of control systems, Proceedings of the First IFAC Congress Automatic Control, pp.481-492, 1960. ,
DOI : 10.1109/TAC.1959.1104873
Coupling-induced population synchronization in an excitatory population of subthreshold Izhikevich neurons, Cognitive Neurodynamics, vol.73, issue.6, pp.495-503, 2013. ,
DOI : 10.1016/j.neucom.2010.05.001
Time-resolved and time-scale adaptive measures of spike train synchrony, Journal of Neuroscience Methods, vol.195, issue.1, pp.92-106, 2011. ,
DOI : 10.1016/j.jneumeth.2010.11.020
Monitoring spike train synchrony, Journal of Neurophysiology, vol.76, issue.5, pp.1457-1472, 2013. ,
DOI : 10.1162/089976601300014321
Investigating nonlinear dynamics from time series: The influence of symmetries and the choice of observables, Chaos: An Interdisciplinary Journal of Nonlinear Science, vol.6, issue.3, pp.549-558, 2002. ,
DOI : 10.1364/JOSAB.2.000018
Symbolic observability coefficients for univariate and multivariate analysis, Physical Review E, vol.4, issue.6, p.66210, 2009. ,
DOI : 10.1016/j.automatica.2007.02.010
Relation between observability and differential embeddings for nonlinear dynamics, Physical Review E, vol.170, issue.6, p.66213, 2005. ,
DOI : 10.1086/109234
On the non-equivalence of observables in phase-space reconstructions from recorded time series, Journal of Physics A: Mathematical and General, vol.31, issue.39, pp.7913-7927, 1998. ,
DOI : 10.1088/0305-4470/31/39/008
URL : https://hal.archives-ouvertes.fr/hal-01596843
A symbolic network-based nonlinear theory for dynamical systems observability, 2017. ,
Quantifying Neural Oscillatory Synchronization: A Comparison between Spectral Coherence and Phase-Locking Value Approaches, PLOS ONE, vol.80, issue.1, p.146443, 2016. ,
DOI : 10.1371/journal.pone.0146443.s001
URL : https://doi.org/10.1371/journal.pone.0146443
Topological analysis for designing a suspension of the H??non map, Physics Letters A, vol.379, issue.47-48, pp.3069-3074, 2015. ,
DOI : 10.1016/j.physleta.2015.10.016
An Active Pulse Transmission Line Simulating Nerve Axon, Proc. IRE, pp.2061-2070, 1962. ,
DOI : 10.1109/JRPROC.1962.288235
Enhancing multivariate singular spectrum analysis for phase synchronization: The role of observability, Chaos: An Interdisciplinary Journal of Nonlinear Science, vol.16, issue.9, p.93112, 2016. ,
DOI : 10.1007/BF02294840
Matrix formulation and singular-value decomposition algorithm for structured varimax rotation in multivariate singular spectrum analysis, Physical Review E, vol.16, issue.5, p.52216, 2016. ,
DOI : 10.1177/001316445901900314
Impact of the recorded variable on recurrence quantification analysis of flows, Physics Letters A, vol.378, issue.32-33, pp.32-33, 2014. ,
DOI : 10.1016/j.physleta.2014.06.014
Reconstructing Mammalian Sleep Dynamics with Data Assimilation, PLoS Computational Biology, vol.163, issue.11, p.1002788, 2012. ,
DOI : 10.1371/journal.pcbi.1002788.g008
URL : https://doi.org/10.1371/journal.pcbi.1002788
Observability coefficients for predicting the class of synchronizability from the algebraic structure of the local oscillators, Physical Review E, vol.94, issue.4, p.42205, 2016. ,
DOI : 10.1098/rspb.1984.0024
Multiscale modeling of brain dynamics: from single neurons and networks to mathematical tools, Wiley Interdisciplinary Reviews: Systems Biology and Medicine, vol.1, issue.Suppl 1, pp.438-458, 2016. ,
DOI : 10.3389/fncir.2016.00023
Analysis and application of neuronal network controllability and observability, Chaos: An Interdisciplinary Journal of Nonlinear Science, vol.27, issue.2, p.23103, 2017. ,
DOI : 10.1073/pnas.1500643112
Observability and Controllability of Nonlinear Networks: The Role of Symmetry, Physical Review X, vol.57, issue.1, p.11005, 2015. ,
DOI : 10.1090/S0273-0979-06-01108-6
NONLINEAR DYNAMICAL SYSTEM IDENTIFICATION FROM UNCERTAIN AND INDIRECT MEASUREMENTS, International Journal of Bifurcation and Chaos, vol.39, issue.06, pp.1905-1933, 2004. ,
DOI : 10.1007/978-3-642-82336-7