My research interests lie in the area of nonlinear dynamical systems and their applications in mathematical neuroscience. In particular, I work on: Dynamics of neural systems, Piecewise linear dynamical systems, Nonlinear oscillations and bifurcations, Discrete nonlinear waves, Numerical schemes, Mathematical psychology.

Contact information

Email arnaud.tonnelier at
Phone (+33) 4 76 61 55 72
Office E117
Address INRIA Rhône-Alpes, 655 avenue de l'Europe, Montbonnot, 38334 St Ismier Cedex, France


A. Tonnelier, Threshold curve for the excitability of bidimensional spiking neurons, Phys. Rev. E 90, 2, 022701 (2014). [Preprint]
A. Tonnelier, Cyclic Negative Feedback Systems: What is the Chance of Oscillation?, Bulletin of Mathematical Biology 76, 5, pp. 1155-1193 (2014). [Preprint]
A. Tonnelier, S. Coecke and J.M. Zaldivar, Screening of chemicals for human bioaccumulative potential with a physiologically based toxicokinetics, Arch. Toxicol. 86, 3, pp. 393-403 (2012). [Preprint]
M.G. Kaabi, A. Tonnelier and D. Martinez, On the performance of voltage stepping for the simulation of adaptive, nonlinear integrate-and-fire neuronal networks, Neural Computation 23, 5, pp.1187-1204 (2011). [Preprint]
A. Tonnelier, Propagation of spike sequences in neural networks, SIAM J. Appl. Dyn. Syst. 9, 3, pp. 1090-1118 (2010). [Preprint]
G. Zheng, A. Tonnelier and D. Martinez, Voltage-stepping schemes for the simulation of spiking neural networks, Journal of Computational Neuroscience 26, 3, pp.409-423 (2009). [Preprint]
G. Zheng and A. Tonnelier, Chaotic solutions in the quadratic integrate-and-fire neuron with adaptation, Cognitive Neurodynamics 3, 3, pp. 197-204 (2009). [Preprint]
J. C. Sarrazin, A. Tonnelier, B. Berberian and M.D. Giraudo, Structuring process and closure principle in spatial and temporal reproduction tasks, Cognitive Neurodynamics 2, 3, pp. 273-282 (2008). [Preprint]
A. Tonnelier, H. Belmabrouk and D. Martinez, Event-driven simulations of nonlinear integrate-and-fire neurons, Neural Computation 19, 12, pp. 3226-3238 (2007). [Preprint]
A. Tonnelier, McKean model, Scholarpedia, 2(4):2795 (2007). [Link]
A. Tonnelier, Stabilization of pulse waves through inhibition in a feedforward neural network, Physica D 210, pp. 118-137 (2005). [Preprint]
J.C. Sarrazin, A. Tonnelier and F. Alexandre, A model of contextual effect on reproduced extents in recall tasks: The issue of the imputed motion hypothesis, Biol. Cybern. 92, 5, pp. 303-315 (2005). [Preprint]
A. Tonnelier, Categorization of neural excitability using threshold models, Neural Computation 17, 7, pp. 1447-1455 (2005). [Preprint]
A. Tonnelier, On the number of limit cycles in piecewise linear Liénard systems, Int. J. Bifurcation and Chaos 15, 4, pp. 1417-1422 (2005). [Preprint]
L. Badel and A. Tonnelier, Pulse propagation in discrete excitatory networks of integrate-and-fire neurons, Phys. Rev E 70, 1 (2004). [Preprint]
A. Tonnelier, Bifurcation properties of the average activity of interconnected neural populations, Biol. Cybern. 89, 3, pp. 179-189 (2003). [Preprint]
A. Tonnelier, McKean caricature of the FitzHugh-Nagumo model: Traveling pulses in a discrete diffusive medium, Phys. Rev. E 67, 036105 (2003). [Preprint]
A. Tonnelier and W. Gerstner, Piecewise linear differential equations and integrate-and-fire neurons : insights from two-dimensional membrane models, Phys. Rev. E 67, 021908 (2003). [Preprint]
A. Tonnelier, The McKean's caricature of the FitzHugh-Nagumo model I. The space-clamped system, SIAM Journal on Applied Mathematics 63, pp. 459-484 (2002). [Preprint]
A. Tonnelier, Wave propagation in discrete media, Journal of Mathematical Biology 44, pp. 87-105 (2002). [Preprint]
A. Tonnelier, S. Meignen, H. Bosch, J. Demongeot, Synchronization and desynchronization of neural oscillators, Neural Networks 12, pp. 1213-1228 (1999). [Preprint]