Balanced Dynamics in Strongly Coupled Networks, Cristobal Quiñinao and Jonathan Touboul. Accepted for publication in SIAM Journal on Dynamical Systems (2025) 

On a kinetic Fizhugh-Nagumo model of neuronal network (with Stéphane Mischler and Cristóbal Quiñinao), Communications in Mathematical Physics 342 (3) pp 1001–1042 (2016) [HAL].

The propagation of chaos in neural fields. Annals of Applied Probability 24 (3), 1298-1328 (2014) – [arXiv]

Large deviations for randomly connected neural networks: I. Spatially extended systems (with T. Cabana); Advances in Applied Probability 50 (3), pp. 944-982 (2018) &
Large deviations for randomly connected neural networks: II. State-Dependent interactions, Advances in Applied Probability 50 (3), pp. 983-1004 .

Probabilistic foundations of spatial mean-field models in ecology and applications (Denis D. Patterson, Simon A. Levin, A. Carla Staver & Jonathan D. Touboul), SIAM Journal on Applied Dynamical Systems Vol. 19, No. 4, pp. 2682-2719 (2020).

Clamping and Synchronization in the strongly coupled FitzHugh-Nagumo model (with Cristobal Quiñinao) – SIAM Journal on Applied Dynamical Systems Vol. 19, No. 2, pp. 788-827 (2020) [arXiv preprint]

The hipster effect: when anticonformists all look the same – Discrete and Continuous Dynamical Systems series B 24(8): 4379-4415 (2019) [arXiv preprint].

Noise-induced synchronization and anti-resonance in interacting excitable systems; Applications to Deep Brain Stimulation in Parkinson’s Disease (J. Touboul, C. Piette, L. Venance, G. Bard Ermentrout) – Physical Review X 10, 011073 (2020).

The real Ginibre ensemble with k=O(n) real eigenvalues (with L.C. García del Molino, K.Pakdaman and G. Wainrib). Journal of Statistical Physics 163 (2) pp 303-323 (2016) [arXiv preprint]

The heterogeneous gas with singular interaction: Generalized circular law and heterogeneous renormalized energy (with Luis-Carlos Garcia del Molino & Khashayar Pakdaman) Journal of Physics A: Mathematical and Theoretical 48 (4) 045208 (2015) [arXiv preprint]

Index Distribution of the Ginibre Ensemble (with Romain Allez & Gilles Wainrib) Journal of Physics A: Mathematical and Theoretical; Fast Track Communication, Vol. 27 4, 042001 (2014) [arXiv preprint].

Spatially extended networks with singular multi-scale connectivity patterns Journal of Statistical Physics 56 (3), p. 546-573 (2014) [arXiv preprint].

Topological and Dynamical Complexity of Random Neural Networks (with G. Wainrib) Physical Review Letters 110 (118101) [arXiv preprint]
(Editors’ Selection, 2013)

 Heterogeneous connections induce oscillations in large scale networks (with G. Hermann) Physical Review Letters 109 (1), 018702 (2012) [arXiv preprint]

Limits and dynamics of stochastic neuronal networks with random delays Journal of Statistical Physics vol. 149, issue 4, pp. 569-597 (2012) [Udpated arXiv]

Mean-Field equations for stochastic firing-rate neural fields with delays: derivation and noise-induced transitions Physica D, Volume 241, Issue 15, pp 1223–1244 (2012) [arXiv preprint].

Topological and Dynamical Complexity of Random Neural Networks (with G. Wainrib) Physical Review Letters 110 (118101) [arXiv preprint]
(Editors’ Selection, 2013)

 Heterogeneous connections induce oscillations in large scale networks (with G. Hermann) Physical Review Letters 109 (1), 018702 (2012) [arXiv preprint]

Limits and dynamics of stochastic neuronal networks with random delays Journal of Statistical Physics vol. 149, issue 4, pp. 569-597 (2012) [Udpated arXiv]

Mean-Field equations for stochastic firing-rate neural fields with delays: derivation and noise-induced transitions Physica D, Volume 241, Issue 15, pp 1223–1244 (2012) [arXiv preprint].

Multi-Resolution Schauder Approach To Multidimensional Gauss-Markov Processes (with T. Taillefumier)  International Journal of Stochastic Analysis Vol. 2011 (2011), Article ID 247329 [arXiv preprint]

Jonathan Touboul, Alain Destexhe Can power-law scaling and neuronal avalanches arise from stochastic dynamics? (2010) PLoS ONE 5(2): e8982. [arXiv preprint].

Olivier Faugeras, Jonathan Touboul, Bruno Cessac A constructive mean field analysis of multi population neural networks with random synaptic weights and stochastic inputs. (2009) Frontiers in Computational Neurosciences, vol. 3, number 1, doi:10.3389/neuro.10.001.2009. [pdf].

Jonathan Touboul, Geoffroy Hermann and Olivier Faugeras Noise-induced behaviors in neural mean field dynamics. SIAM Journal on Applied Dynamical Systems, vol. 11, number 1, pp. 49-81 (2012) [arXiv preprint].

Jonathan Touboul, Olivier Faugeras A Markovian event-based framework for stochastic spiking neural networks Journal of Computational Neuroscience vol.31, number 3, pp. 485-507 (2011) [arXiv preprint].

Jonathan Touboul, Olivier Faugeras First hitting times of Double Integral Process to curved boundaries. (2008) Advances in Applied Probability vol.40, number 2, pp. 501-528 [Preprint]

Jonathan Touboul, Olivier Faugeras The spikes trains probability distributions: A stochastic calculus approach (2007) Journal of Physiology, Paris vol. 101 number 1–3, pp. 78-98 [Preprint]

Striatal endocannabinoid-long-term potentiation mediates one-shot learning, Charlotte Piette, Arnaud Hubert, Sylvie Perez, Hugues Berry*, Jonathan Touboul*, Laurent Venance*. In revision. 

Deep Brain Stimulation enables the restoration of information processing in Parkinsonian cortical networks, Charlotte Piette, Sophie Ng Wing Tin, Astrid De Liège, Coralie Block-Queyrat, Bertrand Degos, Laurent Venance and Jonathan Touboul. In revision. 

Anti-Hebbian Learning drives sequence learning in striatum, Gaëtan Vignoud, Laurent Venance and Jonatha Touboul. Nature Communications Biology 7, Article number: 555 (2024).

The use of AI in legal systems: determining independent contractor vs. employee status, MC Cohen, Samuel Dahan, W Khern-Am-Nuai, H Shimao, Jonathan Touboul. Artificial intelligence and law (8) 1-30, 2023

Striatum expresses region-specific plasticity consistent with distinct memory abilities Sylvie PEREZ, Yihui CUI, Gaëtan VIGNOUD, Elodie PERRIN, Alexandre MENDES, Zhiwei ZHENG, Jonathan TOUBOUL* and Laurent VENANCE*. Cell Report 38 (11) 2022, 110521.

Is there sufficient evidence for criticality in cortical systems? (with A. Destexhe). eNeuro 8 (2) ENEURO.0551-20.2021. Preprint and Code.

Engrams of fast learning (Charlotte Piette, Jonathan Touboul, Laurent Venance), Frontiers in Cellular Neuroscience 14 (342) (2020).

Predicting Employment Notice Period with Machine Learning: Promises and Limitations (with S. Dahan, J. Lam and D. Sfedj). McGill Law Journal (2020). Website: MyOpenCourt.org

Interplay of multiple pathways and activity-dependent rules in STDP (G. Vignoud, L. Venance*, J. Touboul*), Plos Comp. Biol. 14(8): e1006184 (2018).

Power-law statistics and universal scaling in the absence of criticality (J. Touboul, A. Destexhe) – Physical Review E 95, 012413 (2017).

Reliability and robustness of oscillations in some slow-fast chaotic systems, Jonathan Jaquette, S. Kedal, Evelyn Sander, Jonathan Touboul. Chaos 33(10):103135 (Oct 1st, 2023). Preprint.

Pattern Formation in Mesic Savannas, Denis Patterson, Simon Levin, A. Carla Staver, Jonathan Touboul. Bulletin of Mathematical Biology (2023). Preprint

Spatial Dynamics with Heterogeneity, Denis Patterson, A. Carla Staver, Simon Levin, Jonathan Touboul SIAM journal on applied mathematics, S225-S248, 2023.

Pattern formation in a four-ring reaction-diffusion network with heterogeneity (Ian Hunter, Michael M. Norton, Bolun Chen, Chris Simonetti, Maria Eleni Moustaka, Jonathan Touboul, Seth Fraden) Physical Review E 105, 024310 (2022) [arXiv]

Type III Responses to Transient Inputs in Hybrid Nonlinear Neuron Models (with Jonathan Rubin and Justyna Signerska), SIAM J. on Applied Dynamical Systems  20(2), 953–980 (2021) Preprint.

Development of inhibitory synaptic delay drives maturation of thalamocortical network dynamics (Alberto Romagnoni, Matthew Colonnese, Jonathan Touboul*, Boris Gutkin*) – Journal of Neurophysiogy 123 (5) 1583-1599(2020) – biorxiv preprint.

Noise-induced synchronization and anti-resonance in interacting excitable systems; Applications to Deep Brain Stimulation in Parkinson’s Disease (J. Touboul, C. Piette, L. Venance, G. Bard Ermentrout) – Physical Review X 10, 011073 (2020).

On the complex dynamics of savanna landscapes (J. Touboul, A.C. Staver, S.A. Levin), Proceedings of the National Academy of Science, USA (PNAS Plus) – 115 (7) E1336-E1345 (2018) 

Wild oscillations in a nonlinear neuron model with resets: (I) Bursting, spike adding and chaos (with Jonathan Rubin, Justyna Signerska and Alexandre Vidal) DCDS-B 22(10): 3967-4002, and (II) Mixed Mode Oscillations,  pp4003-4039, December 2017.

Canard explosion in delayed equations with multiple timescales (with Maciej Krupa), Journal of Dynamics and Differential Equations 28 (2), pp 471-491 (2016) [arXiv preprint]

 Complex oscillations in the delayed van der Pol equation (with Maciej Krupa) Journal of Nonlinear Science 26 (1), pp 43-81 (2016) [arXiv preprint]

Jonathan Touboul, Martin Krupa, Mathieu Desroches Noise-induced canard and mixed-mode oscillations in large stochastic networks with multiple timescales SIAM Journal on Applied Mathematics 75 (5), pp. 2024–2049 (2016) [arXiv preprint].

 Competition and boundary formation in heterogeneous media: Application to neuronal differentiation (with Cristobal Quiñinao and B Pretame) Mathematical Models and Methods in Applied Science 25 (13) 2477–2502 (2015) [arXiv preprint]

Pulsatile localized dynamics in delayed neural-field equations in arbitrary dimension (with Grégory Faye) SIAM J. on Applied Mathematics 74 (5), pp.  1657-1690 (2014) [arXiv preprint].

Jonathan Touboul, Fabrice Wendling, Patrick Chauvel, Olivier Faugeras Neural Mass Activity, Bifurcations, and Epilepsy Neural Computation vol.23, number 12, pp. 3232-3286 (2011) [preprint].

Jonathan Touboul, Bard Ermentrout Finite-size and correlation-induced effects in Mean-field Dynamics Journal of Computational Neuroscience vol.31, number 3, pp. 453-484 (2011) [arXiv preprint].

Controllability of the heat and wave equations and their finite difference approximations by the shape of the domain, Mathematical Control and Related Fields 2012, 2(4): 429-455. Erratum.

Jonathan Touboul On the simulation of nonlinear bidimensional spiking neuron models Neural Computation vol. 23, No 7, pages 1704-1742 (2011) [arXiv preprint]

Jonathan Touboul, Romain Brette Spiking dynamics of bidimensional integrate-and-fire neurons (2009) SIAM Journal on Applied Dynamical Systems, vol. 8, pages 1462-1506 [Preprint].

Importance of the Cutoff Value in the Quadratic Adaptive Integrate-and-Fire Model (2009), Neural Computation vol. 21, number 2 [Preprint]

Jonathan Touboul, Romain Brette Dynamics and bifurcations of the adaptive exponential integrate-and-fire model. (2008) Biological Cybernetics, vol. 99, number 4-5, pp. 319-334. [Preprint], Brian python scripts for the figures here.
Correction on plateau condition.

Bifurcation analysis of a general class of non-linear integrate and fire neurons. SIAM Journal on Applied Mathematics, 2008, vol.68, number 4, pp.1045-1079 [Preprint].

COUP-TFI specifies the medial entorhinal cortex identity and induces differential cell adhesion to determine the integrity of its boundary with neocortex. (Feng, J., Hsu, W.H., Patterson, D., Tseng, C.S., Hsing, H.W., Zhuang, Z.H., Huang, Y.T., Faedo, A., Rubenstein, J.L., Touboul, J. and Chou, S.J.,)  2021. Science Advances, 7(27), p.eabf6808.

In vitro characterization of the human segmentation clock (Margarete Diaz-Cuadros, Daniel E. Wagner, Christoph Budjan, Alexis Hubaud, Oscar A. Tarazona, Sophia Donelly, Arthur Michaut, Ziad Al Tanoury, Kumiko Yoshioka-Kobayashi, Yusuke Niino, Ryoichiro Kageyama, Atsushi Miyawaki, Jonathan Touboul & Olivier Pourquié) Nature 580, 113–118 (2020).
Press coverage: Eurekalert, MedicalXpress, ScienceDaily. 

Deep brain stimulation-guided optogenetic rescue of parkinsonian symptoms (Marie Vandecasteele, Sebastien Valverde, Charlotte Piette, Giuseppe Gangarossa, Willy Derousseaux, Asier Aristieta Arbelaiz, Jonathan Touboul*, Bertrand Degos*, Laurent Venance*), Nature Communications 11, 2388 (2020).

A “Numerical Evo-Devo” Synthesis for the Identification of Pattern-Forming Factors (Richard Bailleul, Marie Manceau, Jonathan Touboul), Cells 9 (8), 1840 (2020).

Symmetry breaking in the embryonic skin triggers a directional and sequential front of competence during plumage patterning. PLoS Biology Bailleul, R., Desmarquet-Trin-Dinh, C., Hidalgo, M., Curantz, C., Touboul, J.*, and Manceau, M.* (2019), doi.org/10.1371/journal.pbio.3000448
Press coverage: The Node, preLights

The hemodynamic signal as a first-order low-pass temporal filter: Evidence and implications for neuroimaging studies (A. Sauvage, G. Hubert, J. Touboul *, J. Ribot*), NeuroImage 155, pp. 394-405 (2017) [biorXiv preprint]

Enhanced abventricular proliferation compensates cell death in the embryonic cerebral cortex (B Freret-Hodara, Y Cui, A Griveau, L Vigier, Y Arai, J Touboul and A Pierani), Cerebral Cortex 27(10):4701-4718 (2017).

Pinwheel-Dipole configuration in cat visual cortex (J. Ribot*, A. Romagnoni*, C. Milleret, D. Bennequin+, J. Touboul+) – NeuroImage 128,  63–73 (2016) [bioRxiv preprint]

Lhx2 regulates the timing of β-catenin-dependent cortical neurogenesis (CL Hsu, S Nam, Y Cui, CP Chang, CF Wang, PS Hou, HC Kuo, J Touboul and SJ Chou) Proceedings of the National Academy of Science 112 (39), pp. 12199–12204 (2015)

Parsimony, exhaustivity and balanced detection in neocortex (A. Romagnoni*, J. Ribot*, D. Bennequin+, J. Touboul+) – PLoS Comp. Biol. 11(11):e1004623 (2015). [arXiv preprint]

 Competition and boundary formation in heterogeneous media: Application to neuronal differentiation (with Cristobal Quiñinao and B Pretame) Mathematical Models and Methods in Applied Science 25 (13) 2477–2502 (2015) [arXiv preprint]

C. Quiñinao, A. Prochiantz, J. Touboul, Local homeoprotein diffusion can stabilize boundaries generated by graded positional cues,  Development 142 (10), 1860-1868