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## Touboul, Jonathan David

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 Author ID: touboul.jonathan-david Published as: Touboul, J.; Touboul, Jonathan; Touboul, Jonathan D.; Touboul, Jonathan David
 Documents Indexed: 39 Publications since 2008, including 1 Book
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#### Co-Authors

 1 single-authored 4 Quiñinao, Cristobal 3 Cabana, Tanguy 2 Krupa, Maciej 2 Rubin, Jonathan E. 2 Signerska-Rynkowska, Justyna 2 Vidal, Alexandre 1 Bard Ermentrout, G. 1 Desroches, Mathieu 1 Faugeras, Olivier D. 1 Krupa, Martin 1 Levin, Simon Asher 1 Mischler, Stéphane 1 Perthame, Benoît 1 Staver, Ann Carla
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#### Serials

 3 Discrete and Continuous Dynamical Systems. Series B 2 Advances in Applied Probability 2 Journal of Computational Neuroscience 1 Communications in Mathematical Physics 1 Journal of Statistical Physics 1 Acta Applicandae Mathematicae 1 M$$^3$$AS. Mathematical Models & Methods in Applied Sciences 1 Proceedings of the National Academy of Sciences of the United States of America 1 SIAM Journal on Applied Mathematics 1 Journal of Dynamics and Differential Equations 1 Journal of Nonlinear Science 1 SIAM Journal on Applied Dynamical Systems
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#### Fields

 11 Biology and other natural sciences (92-XX) 6 Dynamical systems and ergodic theory (37-XX) 6 Statistical mechanics, structure of matter (82-XX) 5 Ordinary differential equations (34-XX) 5 Probability theory and stochastic processes (60-XX) 3 Partial differential equations (35-XX)

#### Citations contained in zbMATH

32 Publications have been cited 241 times in 164 Documents Cited by Year
Mean-field description and propagation of chaos in networks of Hodgkin-Huxley and FitzHugh-Nagumo neurons. Zbl 1322.60205
Baladron, Javier; Fasoli, Diego; Faugeras, Olivier; Touboul, Jonathan
2012
Noise-induced behaviors in neural mean field dynamics. Zbl 1235.92016
Touboul, Jonathan; Hermann, Geoffroy; Faugeras, Olivier
2012
Propagation of chaos in neural fields. Zbl 1305.60107
Touboul, Jonathan
2014
Spiking dynamics of bidimensional integrate-and-fire neurons. Zbl 1204.37019
Touboul, Jonathan; Brette, Romain
2009
On a kinetic FitzHugh-Nagumo model of neuronal network. Zbl 1338.35001
Mischler, S.; Quiñinao, C.; Touboul, J.
2016
Dynamics and bifurcations of the adaptive exponential integrate-and-fire model. Zbl 1161.92016
Touboul, Jonathan; Brette, Romain
2008
On the dynamics of random neuronal networks. Zbl 1360.82071
Robert, Philippe; Touboul, Jonathan
2016
Importance of the cutoff value in the quadratic adaptive integrate-and-fire model. Zbl 1167.92008
Touboul, Jonathan
2009
Complex oscillations in the delayed Fitzhugh-Nagumo equation. Zbl 1337.34079
Krupa, Maciej; Touboul, Jonathan D.
2016
Mean-field equations for stochastic firing-rate neural fields with delays: derivation and noise-induced transitions. Zbl 1317.92021
Touboul, Jonathan
2012
Index distribution of the Ginibre ensemble. Zbl 1290.82024
Allez, Romain; Touboul, Jonathan; Wainrib, Gilles
2014
A characterization of the first hitting time of double integral processes to curved boundaries. Zbl 1147.60027
Touboul, Jonathan; Faugeras, Olivier
2008
Spatially extended networks with singular multi-scale connectivity patterns. Zbl 1310.82036
Touboul, Jonathan
2014
Large deviations, dynamics and phase transitions in large stochastic and disordered neural networks. Zbl 1291.82099
Cabana, Tanguy; Touboul, Jonathan
2013
Wild oscillations in a nonlinear neuron model with resets. II: Mixed-mode oscillations. Zbl 1375.34075
Rubin, Jonathan E.; Signerska-Rynkowska, Justyna; Touboul, Jonathan D.; Vidal, Alexandre
2017
Canard explosion in delay differential equations. Zbl 1350.34059
Krupa, Maciej; Touboul, Jonathan D.
2016
Dynamics and absorption properties of stochastic equations with Hölder diffusion coefficients. Zbl 1364.60076
Touboul, Jonathan; Wainrib, Gilles
2015
Limits and dynamics of randomly connected neuronal networks. Zbl 1328.82033
Quiñinao, Cristobal; Touboul, Jonathan
2015
The hipster effect: when anti-conformists all look the same. Zbl 1427.82026
Touboul, Jonathan D.
2019
On the complex dynamics of savanna landscapes. Zbl 1416.92185
Touboul, Jonathan David; Staver, Ann Carla; Levin, Simon Asher
2018
Erratum: “Propagation of chaos in neural fields”. Zbl 1434.60304
Touboul, Jonathan
2018
Wild oscillations in a nonlinear neuron model with resets. I: Bursting, spike-adding and chaos. Zbl 1371.37032
Rubin, Jonathan E.; Signerska-Rynkowska, Justyna; Touboul, Jonathan D.; Vidal, Alexandre
2017
The real Ginibre ensemble with $$k=O(n)$$ real eigenvalues. Zbl 1343.15024
del Molino, Luis Carlos García; Pakdaman, Khashayar; Touboul, Jonathan; Wainrib, Gilles
2016
The heterogeneous gas with singular interaction: generalized circular law and heterogeneous renormalized energy. Zbl 1311.82044
del Molino, Luis Carlos García; Pakdaman, Khashayar; Touboul, Jonathan
2015
On the simulation of nonlinear bidimensional spiking neuron models. Zbl 1218.92024
Touboul, Jonathan
2011
Clamping and synchronization in the strongly coupled FitzHugh-Nagumo model. Zbl 1447.35335
Quininao, Cristobal; Touboul, Jonathan D.
2020
Large deviations for randomly connected neural networks. II: State-dependent interactions. Zbl 1431.60030
Cabana, Tanguy; Touboul, Jonathan D.
2018
Large deviations for randomly connected neural networks. I: Spatially extended systems. Zbl 1442.60036
Cabana, Tanguy; Touboul, Jonathan D.
2018
Competition and boundary formation in heterogeneous media: application to neuronal differentiation. Zbl 1325.35237
Perthame, Benoît; Quiñinao, Cristóbal; Touboul, Jonathan
2015
Pulsatile localized dynamics in delayed neural field equations in arbitrary dimension. Zbl 1345.92039
Faye, Grégory; Touboul, Jonathan
2014
Controllability of the heat and wave equations and their finite difference approximations by the shape of the domain. Zbl 1262.35207
Touboul, Jonathan
2012
Nonlinear and stochastic models in neuroscience. Zbl 1185.92027
Touboul, Jonathan
2008
Clamping and synchronization in the strongly coupled FitzHugh-Nagumo model. Zbl 1447.35335
Quininao, Cristobal; Touboul, Jonathan D.
2020
The hipster effect: when anti-conformists all look the same. Zbl 1427.82026
Touboul, Jonathan D.
2019
On the complex dynamics of savanna landscapes. Zbl 1416.92185
Touboul, Jonathan David; Staver, Ann Carla; Levin, Simon Asher
2018
Erratum: “Propagation of chaos in neural fields”. Zbl 1434.60304
Touboul, Jonathan
2018
Large deviations for randomly connected neural networks. II: State-dependent interactions. Zbl 1431.60030
Cabana, Tanguy; Touboul, Jonathan D.
2018
Large deviations for randomly connected neural networks. I: Spatially extended systems. Zbl 1442.60036
Cabana, Tanguy; Touboul, Jonathan D.
2018
Wild oscillations in a nonlinear neuron model with resets. II: Mixed-mode oscillations. Zbl 1375.34075
Rubin, Jonathan E.; Signerska-Rynkowska, Justyna; Touboul, Jonathan D.; Vidal, Alexandre
2017
Wild oscillations in a nonlinear neuron model with resets. I: Bursting, spike-adding and chaos. Zbl 1371.37032
Rubin, Jonathan E.; Signerska-Rynkowska, Justyna; Touboul, Jonathan D.; Vidal, Alexandre
2017
On a kinetic FitzHugh-Nagumo model of neuronal network. Zbl 1338.35001
Mischler, S.; Quiñinao, C.; Touboul, J.
2016
On the dynamics of random neuronal networks. Zbl 1360.82071
Robert, Philippe; Touboul, Jonathan
2016
Complex oscillations in the delayed Fitzhugh-Nagumo equation. Zbl 1337.34079
Krupa, Maciej; Touboul, Jonathan D.
2016
Canard explosion in delay differential equations. Zbl 1350.34059
Krupa, Maciej; Touboul, Jonathan D.
2016
The real Ginibre ensemble with $$k=O(n)$$ real eigenvalues. Zbl 1343.15024
del Molino, Luis Carlos García; Pakdaman, Khashayar; Touboul, Jonathan; Wainrib, Gilles
2016
Dynamics and absorption properties of stochastic equations with Hölder diffusion coefficients. Zbl 1364.60076
Touboul, Jonathan; Wainrib, Gilles
2015
Limits and dynamics of randomly connected neuronal networks. Zbl 1328.82033
Quiñinao, Cristobal; Touboul, Jonathan
2015
The heterogeneous gas with singular interaction: generalized circular law and heterogeneous renormalized energy. Zbl 1311.82044
del Molino, Luis Carlos García; Pakdaman, Khashayar; Touboul, Jonathan
2015
Competition and boundary formation in heterogeneous media: application to neuronal differentiation. Zbl 1325.35237
Perthame, Benoît; Quiñinao, Cristóbal; Touboul, Jonathan
2015
Propagation of chaos in neural fields. Zbl 1305.60107
Touboul, Jonathan
2014
Index distribution of the Ginibre ensemble. Zbl 1290.82024
Allez, Romain; Touboul, Jonathan; Wainrib, Gilles
2014
Spatially extended networks with singular multi-scale connectivity patterns. Zbl 1310.82036
Touboul, Jonathan
2014
Pulsatile localized dynamics in delayed neural field equations in arbitrary dimension. Zbl 1345.92039
Faye, Grégory; Touboul, Jonathan
2014
Large deviations, dynamics and phase transitions in large stochastic and disordered neural networks. Zbl 1291.82099
Cabana, Tanguy; Touboul, Jonathan
2013
Mean-field description and propagation of chaos in networks of Hodgkin-Huxley and FitzHugh-Nagumo neurons. Zbl 1322.60205
Baladron, Javier; Fasoli, Diego; Faugeras, Olivier; Touboul, Jonathan
2012
Noise-induced behaviors in neural mean field dynamics. Zbl 1235.92016
Touboul, Jonathan; Hermann, Geoffroy; Faugeras, Olivier
2012
Mean-field equations for stochastic firing-rate neural fields with delays: derivation and noise-induced transitions. Zbl 1317.92021
Touboul, Jonathan
2012
Controllability of the heat and wave equations and their finite difference approximations by the shape of the domain. Zbl 1262.35207
Touboul, Jonathan
2012
On the simulation of nonlinear bidimensional spiking neuron models. Zbl 1218.92024
Touboul, Jonathan
2011
Spiking dynamics of bidimensional integrate-and-fire neurons. Zbl 1204.37019
Touboul, Jonathan; Brette, Romain
2009
Importance of the cutoff value in the quadratic adaptive integrate-and-fire model. Zbl 1167.92008
Touboul, Jonathan
2009
Dynamics and bifurcations of the adaptive exponential integrate-and-fire model. Zbl 1161.92016
Touboul, Jonathan; Brette, Romain
2008
A characterization of the first hitting time of double integral processes to curved boundaries. Zbl 1147.60027
Touboul, Jonathan; Faugeras, Olivier
2008
Nonlinear and stochastic models in neuroscience. Zbl 1185.92027
Touboul, Jonathan
2008
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#### Cited by 296 Authors

 23 Touboul, Jonathan David 5 Cáceres, María-José 5 Mischler, Stéphane 5 Quiñinao, Cristobal 4 Dai Pra, Paolo 4 Signerska-Rynkowska, Justyna 4 Tang, Sanyi 4 Wainrib, Gilles 3 Budhiraja, Amarjit S. 3 Cabana, Tanguy 3 Collet, Francesca 3 Cunden, Fabio Deelan 3 Faugeras, Olivier Paul 3 Formentin, Marco 3 Galves, Antonio 3 Krupa, Maciej 3 Löcherbach, Eva 3 Luçon, Eric 3 Ost, Guilherme 3 Perthame, Benoît 3 Schneider, Ricarda 3 Stannat, Wilhelm 3 Tang, Biao 3 Touboul, Jonathan 3 Vivo, Pierpaolo 3 Weng, Qilong 3 Wu, Ruoyu 2 Andreis, Luisa 2 Bossy, Mireille 2 Bressloff, Paul C. 2 Crevat, Joachim 2 del Molino, Luis Carlos García 2 Desroches, Mathieu 2 Drogoul, Audric 2 Duarte, Aline 2 Facchi, Paolo 2 Fasoli, Diego 2 Gerstner, Wulfram 2 Giacomin, Giambattista 2 Granados, Albert 2 Gu, Huaguang 2 Laing, Carlo R. 2 Ligabò, Marilena 2 MacLaurin, James N. 2 Majumdar, Satya N. 2 Mao, Xiaochen 2 Nguyen Huu Du 2 Nguyen, Son Luu 2 Oliveira, Roberto Imbuzeiro 2 Pakdaman, Khashayar 2 Panzeri, Stefano 2 Poquet, Christophe 2 Reis, Guilherme H. 2 Rubin, Jonathan E. 2 Salort, Delphine 2 Shiau, LieJune 2 Shlizerman, Eli 2 Taillefumier, Thibaud 2 Veltz, Romain 2 Vidal, Alexandre 2 Xiao, Yanni 2 Zhang, Qianqian 1 Adhikari, Kartick 1 Agram, Nacira 1 Aihara, Kazuyuki 1 Alsedà, Lluís 1 Ascione, Giacomo 1 Avitable, Daniele 1 Baccelli, François Louis 1 Bačić, Iva 1 Baptista, Murilo S. 1 Bard Ermentrout, G. 1 Barranca, Victor J. 1 Barreiro, Andrea K. 1 Batista, Antonio Marcos 1 Bhamidi, Shankar 1 Bonetti, R. C. 1 Borges, Fernando S. 1 Borgo, Martina Dal 1 Brette, Romain 1 Cai, David 1 Caldas, Iberê L. 1 Cang, Shijian 1 Cao, Junfei 1 Cao, Zhengran 1 Carrillo de la Plata, José Antonio 1 Cattani, Anna 1 Chartrand, Thomas 1 Cheke, Robert A. 1 Chen, Ling 1 Chen, Shuang 1 Chen, Zengqiang 1 Cheng, Tianyu 1 Cherry, Elizabeth M. 1 Chevallier, Julien 1 Chong, Carsten 1 Clopath, Claudia 1 Conti, Federica 1 Coombes, Stephen 1 De Masi, Anna ...and 196 more Authors
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#### Cited in 69 Serials

 17 Journal of Statistical Physics 9 Stochastic Processes and their Applications 7 Neural Computation 7 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering 7 Journal of Computational Neuroscience 6 Chaos 6 The Journal of Mathematical Neuroscience 5 Biological Cybernetics 5 SIAM Journal on Applied Dynamical Systems 4 Journal of Mathematical Biology 4 The Annals of Applied Probability 4 Nonlinear Dynamics 4 Journal of Theoretical Biology 3 Advances in Applied Probability 3 Acta Applicandae Mathematicae 3 Physica D 3 Communications in Nonlinear Science and Numerical Simulation 3 Discrete and Continuous Dynamical Systems. Series B 2 Communications in Mathematical Physics 2 Journal of Differential Equations 2 Neural Networks 2 M$$^3$$AS. Mathematical Models & Methods in Applied Sciences 2 Communications in Partial Differential Equations 2 SIAM Journal on Applied Mathematics 2 SIAM Journal on Mathematical Analysis 2 Electronic Journal of Probability 2 Discrete and Continuous Dynamical Systems 2 Discrete Dynamics in Nature and Society 2 Journal of Physics A: Mathematical and Theoretical 2 Kinetic and Related Models 1 Journal of Mathematical Analysis and Applications 1 Mathematical Biosciences 1 Nonlinearity 1 Mathematics of Computation 1 Acta Mathematica Vietnamica 1 The Annals of Probability 1 Applied Mathematics and Computation 1 Journal of Functional Analysis 1 Journal of Multivariate Analysis 1 Stochastic Analysis and Applications 1 Probability Theory and Related Fields 1 Journal of Theoretical Probability 1 Annals of Operations Research 1 Applied Mathematical Modelling 1 European Journal of Operational Research 1 SIAM Review 1 Journal of Dynamics and Differential Equations 1 Journal of Nonlinear Science 1 NoDEA. Nonlinear Differential Equations and Applications 1 Complexity 1 Electronic Communications in Probability 1 Bernoulli 1 European Journal of Control 1 European Series in Applied and Industrial Mathematics (ESAIM): Probability and Statistics 1 Mathematical Physics, Analysis and Geometry 1 Philosophical Transactions of the Royal Society of London. Series A. Mathematical, Physical and Engineering Sciences 1 Brazilian Journal of Probability and Statistics 1 Journal of Evolution Equations 1 Differentsial’nye Uravneniya i Protsessy Upravleniya 1 Entropy 1 Comptes Rendus. Mathématique. Académie des Sciences, Paris 1 Stochastics and Dynamics 1 Journal of Statistical Mechanics: Theory and Experiment 1 Sibirskie Èlektronnye Matematicheskie Izvestiya 1 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis 1 International Journal of Stochastic Analysis 1 Afrika Matematika 1 Mathematical Control and Related Fields 1 Journal de l’École Polytechnique – Mathématiques
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#### Cited in 29 Fields

 97 Biology and other natural sciences (92-XX) 67 Probability theory and stochastic processes (60-XX) 38 Ordinary differential equations (34-XX) 36 Dynamical systems and ergodic theory (37-XX) 34 Statistical mechanics, structure of matter (82-XX) 33 Partial differential equations (35-XX) 13 Systems theory; control (93-XX) 9 Combinatorics (05-XX) 8 Linear and multilinear algebra; matrix theory (15-XX) 7 Numerical analysis (65-XX) 5 Statistics (62-XX) 4 Computer science (68-XX) 3 Special functions (33-XX) 3 Integral equations (45-XX) 3 Operator theory (47-XX) 3 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 2 Calculus of variations and optimal control; optimization (49-XX) 2 Optics, electromagnetic theory (78-XX) 2 Operations research, mathematical programming (90-XX) 1 Potential theory (31-XX) 1 Difference and functional equations (39-XX) 1 Harmonic analysis on Euclidean spaces (42-XX) 1 General topology (54-XX) 1 Algebraic topology (55-XX) 1 Mechanics of particles and systems (70-XX) 1 Mechanics of deformable solids (74-XX) 1 Fluid mechanics (76-XX) 1 Classical thermodynamics, heat transfer (80-XX) 1 Quantum theory (81-XX)