S. H. Abrams and . Strogatz, or the prediction of a MackeyGlass equation [Dong 2016], only to name two examples. Future research in this topic will surely bring many surprises in the years to come, Physical Review Letters, vol.93, issue.17, p.174102, 2004.

D. M. Abrams, R. Mirollo, S. H. Strogatz, and D. A. Wiley, Solvable Model for Chimera States of Coupled Oscillators, Physical Review Letters, vol.101, issue.8, 2008.
DOI : 10.1103/physrevlett.101.084103

URL : http://arxiv.org/pdf/0806.0594

J. A. Acebrón, L. L. Bonilla, C. J. Vicente, F. Ritort, and R. Spigler, The Kuramoto model: A simple paradigm for synchronization phenomena, Reviews of Modern Physics, vol.77, issue.1, pp.137-185, 2005.

R. Adler, A Study of Locking Phenomena in Oscillators, Proceedings of the IRE, vol.34, issue.6, pp.351-357, 1946.

V. S. Afraimovich, S. V. Gonchenko, L. M. Lerman, A. L. Shilnikov, and D. V. Turaev, Scientific heritage of L, P. Shilnikov. Regular and Chaotic Dynamics, vol.19, issue.4, pp.435-460, 2014.

;. K. Al-naimee, F. Al-naimee, M. Marino, R. Ciszak, F. T. Meucci et al., Chaotic spiking and incomplete homoclinic scenarios in semiconductor lasers with optoelectronic feedback, New Journal of Physics, vol.11, issue.7, p.73022, 2009.
DOI : 10.1088/1367-2630/11/7/073022

URL : http://iopscience.iop.org/article/10.1088/1367-2630/11/7/073022/pdf

;. K. Al-naimee, F. Al-naimee, M. Marino, S. F. Ciszak, R. Abdalah et al., Excitability in optically injected microdisk lasers with phase controlled excitatory and inhibitory response, The European Physical Journal D, vol.58, issue.2, p.862888039, 2010.

P. M. Alsing, V. Kovanis, A. Gavrielides, and T. Erneux, Lang and Kobayashi phase equation, Physical Review A, vol.53, issue.6, pp.4429-4434, 1996.
DOI : 10.1103/physreva.53.4429

S. K. S.-i.-amari-;-r.-ananthanarayanan, H. D. Esser, D. S. Simon, and . Modha, The Cat is out of the Bag: Cortical Simulations with 109 Neurons, 1013 Synapses, Proceedings of the Conference on High Performance Computing Networking, Storage and Analysis, SC '09, vol.27, pp.1-63, 1977.

V. V. Antyukhov, A. F. Glova, O. R. Kachurin, F. V. Lebedev, V. V. Likhanskii et al., Automatic synchronization of triode oscillators, Proc. Cambridge Phil. Soc, vol.44, p.231, 1922.

I. S. Aranson and L. Kramer, The world of the complex Ginzburg-Landau equation, Reviews of Modern Physics, vol.74, issue.1, pp.99-143, 2002.

F. Arecchi and R. Bonifacio, Theory of optical maser amplifiers, IEEE Journal of Quantum Electronics, vol.1, issue.4, pp.169-178, 1965.
DOI : 10.1109/jqe.1965.1072212

F. T. Arecchi, G. L. Lippi, G. P. Puccioni, and J. R. Tredicce, Deterministic chaos in laser with injected signal, Optics Communications, vol.51, issue.5, pp.308-314, 1984.
DOI : 10.1016/0030-4018(84)90016-6

A. Arenas, A. Díaz-guilera, J. Kurths, Y. Moreno, and C. Zhou, Synchronization in complex networks, Physics Reports, vol.469, issue.3, pp.93-153, 2008.

P. Ashwin, S. Coombes, and R. Nicks, Mathematical Frameworks for Oscillatory Network Dynamics in Neuroscience, The Journal of Mathematical Neuroscience, vol.6, issue.1, 2016.

S. Barland, O. Piro, M. Giudici, J. R. Tredicce, S. Balle et al., Experimental evidence of van der Pol-Fitzhugh-Nagumo dynamics in semiconductor optical amplifiers, IEEE Journal of Quantum Electronics, vol.68, issue.3, pp.1549-1551, 1989.
URL : https://hal.archives-ouvertes.fr/hal-00016764

B. P. Belousov, Periodicheski deistvuyushchaya reaktsia i ee mekhanism [Periodically acting reaction and its mechanism, Sbornik referatov po radiotsionnoi meditsine, 1958.

E. Beno??tbeno??t, J. L. Callot, F. Diener, M. M. Diener, ;. Berglund et al., Noise-Induced Phenomena in Slow-Fast Dynamical Systems: A Sample-Paths Approach. Probability and Its Applications, vol.32, pp.978-979, 1981.

C. Bick, M. Timme, D. Paulikat, D. Rathlev, and P. Ashwin, Chaos in Symmetric Phase Oscillator Networks, Physical Review Letters, vol.107, issue.24, p.244101, 2011.
DOI : 10.1103/physrevlett.107.244101

URL : https://ore.exeter.ac.uk/repository/bitstream/10036/4437/22/Chaos%20in%20Symmetric%20Phase%20Oscillator%20Networks.pdf

B. H. Bland, L. V. Colom, J. Konopacki, and S. H. Roth, Intracellular records of carbachol-induced theta rhythm in hippocampal slices, Brain Research, vol.447, issue.2, pp.364-368, 1988.

S. Boccaletti, V. Latora, Y. Moreno, M. Chavez, and D. U. Hwang, Complex networks: Structure and dynamics, vol.424, pp.175-308, 2006.

A. Borst and F. E. Theunissen, Information theory and neural coding, Nature Neuroscience, vol.2, p.947, 1994.

G. L. Bourdet, R. A. Muller, G. M. Mullot, and J. Y. Vinet, Active mode locking of a high pressure CW waveguide CO2 laser, Applied Physics B, vol.44, issue.2, pp.107-110, 1987.

P. A. Braza and T. Erneux, Constant phase, phase drift, and phase entrainment in lasers with an injected signal, Physical Review A, vol.41, issue.11, pp.6470-6479, 1990.

P. C. Bressloff, ;. Brøns, T. J. Kaper, and H. G. Rotstein, Introduction to Focus Issue: Mixed Mode Oscillations: Experiment, Computation, and Analysis, Spatiotemporal dynamics of continuum neural fields, vol.45, p.15101, 2008.

C. Brownlee, Carnivorous Plants: Trapping, Digesting and Absorbing All in One, Current Biology, vol.23, issue.17, pp.714-716, 2013.

E. Brun, B. Derighetti, D. Meier, R. Holzner, and M. Ravani, Observation of order and chaos in a nuclear spin-flip laser, JOSA B, vol.2, issue.1, pp.156-167, 1985.

N. Brunel, Dynamics of Sparsely Connected Networks of Excitatory and Inhibitory Spiking Neurons, Journal of Computational Neuroscience, vol.8, issue.3, pp.183-208, 2000.

D. Brunner, M. C. Soriano, C. R. Mirasso, and I. Fischer, Parallel photonic information processing at gigabyte per second data rates using transient states, Nature Communications, vol.4, issue.1, 2013.

D. Brunner and I. Fischer, Reconfigurable semiconductor laser networks based on diffractive coupling, Optics Letters, vol.40, issue.16, p.3854, 2015.

M. Brunstein, A. M. Yacomotti, I. Sagnes, F. Raineri, L. Bigot et al., Electrically pumped InP-based microdisk lasers integrated with a nanophotonic silicon-on-insulator waveguide circuit, SemiconductorLaser Physics, vol.85, pp.978-981, 1988.

]. C. Chow, Phase-locking in weakly heterogeneous neuronal networks, Physica D: Nonlinear Phenomena, vol.118, issue.3, pp.343-370, 1998.

J. A. Connor, D. Walter, R. Mckown, and ;. S. Coombes, Neural repetitive firing: modifications of the Hodgkin-Huxley axon suggested by experimental results from crustacean axons, Physica D: Nonlinear Phenomena, vol.18, issue.1, pp.173-188, 1977.

F. Corinto, M. Bonnin, and M. Gilli, Weakly connected oscillatory network models for associative and dynamic memories, International Journal of Bifurcation and Chaos, vol.17, issue.12, pp.4365-4379, 2007.

P. Coullet, L. Gil, and F. Rocca, Optical vortices, Optics Communications, vol.73, issue.5, pp.403-408, 1989.

P. Coullet, D. Daboussy, and J. R. Tredicce, Optical excitable waves, Physical Review E, vol.58, issue.5, pp.5347-5350, 1998.

P. Coullet, J. M. Gilli, M. Monticelli, and N. Vandenberghe, A damped pendulum forced with a constant torque, American Journal of Physics, vol.73, issue.12, pp.1122-1128, 2005.
URL : https://hal.archives-ouvertes.fr/hal-00016283

S. Crook, G. Ermentrout, M. Vanier, and J. Bower, The Role of Axonal Delay in the Synchronization of Networks of Coupled Cortical Oscillators, Journal of Computational Neuroscience, vol.4, issue.2, pp.161-172, 1997.

;. P. De-maesschalck, M. De-maesschalck, and . Wechselberger, Neural Excitability and Singular Bifurcations, The Journal of Mathematical Neuroscience (JMN), vol.5, issue.1, 2015.

M. Desroches, J. Guckenheimer, B. Krauskopf, C. Kuehn, H. Osinga et al., Stable propagation of synchronous spiking in cortical neural networks, Time Scales. SIAM Review, vol.54, issue.2, p.529, 1999.

A. Dolcemascolo-;-a.-dolcemascolo, B. Garbin, B. Peyce, R. Veltz, and S. Barland, Resonator neuron and triggering multipulse excitability in laser with injected signal, Physical Review E, vol.98, p.62211, 2015.

A. Dolcemascolo, R. Veltz, F. Marino, and S. Barland, Mean field dimensionality reduction of coupled lasers (title subject to change). To be submitted, 2019.

J. Dong, S. Gigan, F. Krzakala, and G. Wainrib, Scaling up EchoState Networks with multiple light scattering, 2016.

F. Dörfler, M. Chertkov, and F. Bullo, Synchronization in complex oscillator networks and smart grids, Proceedings of the National Academy of Sciences, vol.110, issue.6, 2005.

F. Dörfler, F. N. Bullo-;-s, A. V. Dorogovtsev, J. F. Goltsev, and . Mendes, Critical phenomena in complex networks, Synchronization in complex networks of phase oscillators: A survey. Automatica, vol.50, pp.325-338, 1999.

R. W. Dunn, S. T. Hendow, W. W. Chow, and J. G. Small, Single-mode operation of Doppler-broadened lasers by injection locking, Optics Letters, vol.8, issue.6, pp.319-321, 1983.

F. Duport, A. Smerieri, A. Akrout, M. Haelterman, and S. Massar, Relaxation oscillations including a standard chase on French ducks, Asymptotic Analysis II, vol.6, pp.449-497, 2016.

M. C. Eguia and G. B. Mindlin, Distribution of interspike times in noise-driven excitable systems, Physical Review E, vol.61, issue.6, pp.6490-6499, 2000.

P. Enyedi, G. Czirják, ;. Ermentrout, N. Kopell, ;. Ermentrout et al., Parabolic Bursting in an Excitable System Coupled with a Slow Oscillation, Molecular background of leak K+ currents: two-pore domain potassium channels, vol.90, pp.571-585, 1984.

B. Ermentrout-;-t.-erneux, E. A. Viktorov, and P. Mandel, Time scales and relaxation dynamics in quantum-dot lasers, Type I membranes, phase resetting curves, and synchrony. Neural Computation, vol.8, p.23819, 1996.

T. Erneux, E. A. Viktorov, B. Kelleher, D. Goulding, S. P. Hegarty et al., Optically injected quantum-dot lasers, Optics Letters, vol.35, issue.7, p.937, 2010.

I. Farkas, D. Helbing, and T. Vicsek, Mexican waves in an excitable medium, Nature, vol.419, issue.6903, pp.131-132, 2002.

G. Faye, Traveling fronts for lattice neural field equations, Physica D: Nonlinear Phenomena, vol.378, pp.20-32, 2018.
URL : https://hal.archives-ouvertes.fr/hal-01682252

N. Fenichel, Geometric singular perturbation theory for ordinary differential equations, Journal of Differential Equations, vol.31, issue.1, pp.53-98, 1979.

I. Fischer, G. H. Van-tartwijk, A. M. Levine, W. Elsässer, E. Göbel et al., Fast Pulsing and Chaotic Itinerancy with a Drift in the Coherence Collapse of Semiconductor Lasers, Physical Review Letters, vol.76, issue.2, pp.220-223, 1996.

R. Fitzhugh, Mathematical models of threshold phenomena in the nerve membrane, The bulletin of mathematical biophysics, vol.17, pp.257-278, 1955.

N. Fournier and E. Locherbach, On a toy model of interacting neurons, Ann. Inst. H. Poincare Probab. Statist, vol.52, issue.4, pp.1844-1876, 2016.

B. Garbin, D. Goulding, S. P. Hegarty, G. Huyet, B. Kelleher et al., Incoherent optical triggering of excitable pulses in an injection-locked semiconductor laser, Optics Letters, vol.39, issue.5, pp.1254-1257, 2014.

, Excitabilité et solitons temporels de phase dans un système laser neuromorphique, 2015.

B. Garbin, J. Javaloyes, G. Tissoni, and S. Barland, Topological solitons as addressable phase bits in a driven laser, Nature Communications, vol.6, p.5915, 2015.

B. Garbin, A. Dolcemascolo, F. Prati, J. Javaloyes, G. Tissoni et al., Refractory period of an excitable semiconductor laser with optical injection, Physical Review E, vol.95, issue.1, p.12214, 2017.

B. Garbin, J. Javaloyes, S. Barland, and G. Tissoni, Interactions and collisions of topological solitons in a semiconductor laser with optical injection and feedback, Chaos: An Interdisciplinary Journal of Nonlinear Science, vol.27, issue.11, p.114308, 2017.

A. Gavrielides, V. Kovanis, and T. Erneux, Analytical stability boundaries for a semiconductor laser subject to optical injection, Optics Communications, vol.136, issue.3, pp.253-256, 1997.

J. Ginoux, C. Letellier-;-m.-giudici, C. Green, G. Giacomelli, U. Nespolo et al., Van der Pol and the history of relaxation oscillations: Toward the emergence of a concept, Chaos: An Interdisciplinary Journal of Nonlinear Science, vol.22, issue.2, pp.676-682, 1987.
URL : https://hal.archives-ouvertes.fr/hal-01056923

M. Golubitsky, I. Stewart, and D. Schaeffer, Singularities and Groups in Bifurcation Theory: Volume I. Applied Mathematical Sciences, Singularities and Groups in Bifurcation Theory, 1988.

M. Golubitsky and I. Stewart, The Symmetry Perspective: From Equilibrium to Chaos in Phase Space and Physical Space, pp.978-981, 2002.

J. M. Gonzalez-miranda, Phase synchronization and chaos suppression in a set of two coupled nonlinear oscillators, International Journal of Bifurcation and Chaos, vol.12, issue.10, pp.2105-2122, 2002.

D. Goulding, S. P. Hegarty, O. Rasskazov, S. Melnik, M. Hartnett et al., Excitability in a Quantum Dot Semiconductor Laser with Optical Injection, Physical Review Letters, vol.98, issue.15, p.153903, 2007.

G. Groos and S. Daan, The Use of the Biological Clocks in Time Perception, Time, Mind, and Behavior, pp.65-74, 1985.

X. Hachair, F. Pedaci, E. Caboche, S. Barland, M. Giudici et al., Cavity solitons in a driven VCSEL above threshold, IEEE Journal of Selected Topics in Quantum Electronics, vol.12, issue.3, pp.339-351, 2006.

A. M. Hagerstrom, T. E. Murphy, R. Roy, P. Hövel, I. Omelchenko et al., Experimental observation of chimeras in coupled-map lattices, Nature Physics, vol.8, issue.9, pp.658-661, 2012.

V. Hakim and W. Rappel, Dynamics of the globally coupled complex Ginzburg-Landau equation, Physical Review A, vol.46, issue.12, pp.7347-7350, 1992.

R. Hegger, H. Kantz, and T. Schreiber, Practical implementation of nonlinear time series methods: The TISEAN package, An Interdisciplinary Journal of Nonlinear Science, vol.9, issue.2, pp.413-435, 1999.

C. L. Henry-;-a and . Hodgkin, The local electric changes associated with repetitive action in a non-medullated axon, IEEE Journal of Quantum Electronics, vol.18, issue.2, pp.165-181, 1948.

A. L. Hodgkin, A. F. Huxley-;-a, A. F. Hodgkin, B. Huxley, . Katz-;-r et al., A quantitative description of membrane current and its application to conduction and excitation in nerve, Hoppensteadt and E. M. Izhikevich, Weakly Connected Neural Networks. Applied Mathematical Sciences, vol.117, pp.1280-1287, 1952.

R. Horn and S. J. Korn, Prevention of rundown in electrophysiological recording, Methods in Enzymology, vol.207, pp.149-155, 1992.

E. M. Izhikevich, Class 1 neural excitability, conventional synapses, weakly connected networks, and mathematical foundations of pulse-coupled models, IEEE Transactions on Neural Networks, vol.10, issue.3, pp.499-507, 1999.

E. Izhikevich, Phase Equations for Relaxation Oscillators, SIAM Journal on Applied Mathematics, vol.60, issue.5, pp.1789-1804, 2000.

E. M. Izhikevich, Neural excitability, spiking and bursting, International Journal of Bifurcation and Chaos, vol.10, issue.06, pp.1171-1266, 2000.

E. M. Izhikevich, Dynamical systems in neuroscience: the geometry of excitability and bursting. Computational neuroscience, 2007.

]. P. Jagher, W. A. Graaf, and D. Lenstra, Relaxationoscillation phenomena in an injection-locked semiconductor laser. Quantum and Semiclassical Optics, Journal of the European Optical Society Part B, vol.8, issue.4, p.805, 1996.

B. Kelleher, D. Goulding, S. P. Hegarty, G. Huyet, D. Cong et al., Excitable phase slips in an injection-locked single-mode quantum-dot laser, Optics Letters, vol.34, issue.4, pp.440-442, 2009.

B. Kelleher, D. Goulding, B. B. Pascual, S. P. Hegarty, G. Huyet et al., Excitability in optically injected semiconductor lasers: Contrasting quantum-well-and quantum-dot-based devices, The European Physical Journal D, vol.58, issue.2, p.26207, 2010.

B. Kelleher, D. Goulding, B. Pascual, S. P. Hegarty, and G. Huyet, Bounded phase phenomena in the optically injected laser, Physical Review E, vol.85, issue.4, p.46212, 2012.

B. Kelleher, S. P. Hegarty, G. B. Huyet-;-m, R. Kennel, H. D. Brown et al., Ermentrout. Population dynamics of the modified theta model: macroscopic phase reduction and bifurcation analysis link microscopic neuronal interactions to macroscopic gamma oscillation, Modified relaxation oscillation parameters in optically injected semiconductor lasers. JOSA B, vol.29, pp.367-379, 1992.

M. Krupa, N. Popovi´cpopovi´c, N. Kopell, and ;. Kuehn, Mixed-Mode Oscillations in Three Time-Scale Systems: A Prototypical Example, Multiple Time Scale Dynamics. Applied Mathematical Sciences, vol.7, issue.2, pp.978-981, 2008.

L. Kuhnert, K. I. Agladze, and V. I. Krinsky, Image processing using light-sensitive chemical waves, Nature, vol.337, p.244, 1989.

A. Kumar, S. Rotter, A. Aertsen, and ;. Kuramoto, Spiking activity propagation in neuronal networks: reconciling different perspectives on neural coding, International Symposium on Mathematical Problems in Theoretical Physics, vol.11, pp.420-422, 1975.

Y. Kuramoto, Chemical Oscillations, Waves, and Turbulence, Springer Series in Synergetics, pp.978-981, 1984.

Y. Kuramoto, D. Battogtokh, ;. M. Kurt, M. Eriten, D. M. Mcfarland et al., Strongly nonlinear beats in the dynamics of an elastic system with a strong local stiffness nonlinearity: Analysis and identification, Coexistence of Coherence and Incoherence in Nonlocally Coupled Phase Oscillators, vol.5, pp.2054-2072, 2002.

C. Laing, Exact Neural Fields Incorporating Gap Junctions, SIAM Journal on Applied Dynamical Systems, vol.14, issue.4, pp.1899-1929, 2015.

R. Lang and K. Kobayashi, External optical feedback effects on semiconductor injection laser properties, IEEE Journal of Quantum Electronics, vol.16, issue.3, pp.347-355, 1980.

R. Lang, Injection locking properties of a semiconductor laser, IEEE Journal of Quantum Electronics, vol.18, issue.6, pp.976-983, 1982.

L. Larger, B. Penkovsky, Y. A. Maistrenko-;-m, A. Larotonda, J. M. Hnilo et al., Yacomotti. Experimental investigation on excitability in a laser with a saturable absorber, Nature Communications, vol.6, issue.3, p.33812, 2002.

P. Latimer-;-y.-lecun, Y. Bengio, and G. Hinton, Use of the Talbot effect to couple the phases of lasers, Applied Physics Letters, vol.62, issue.3, pp.436-444, 1993.

T. H. Lee, The Design of CMOS Radio-Frequency Integrated Circuits

L. S. Leung and C. C. Yim, Intrinsic membrane potential oscillations in hippocampal neurons in vitro, Brain Research, vol.553, issue.2, pp.261-274, 1991.

T. J. Lewis, J. V. Rinzel-;-v, A. P. Likhanski?, . L. Napartovich-;-g, S. Lippi et al., Invariant Integral and the Transition to Steady States in Separable Dynamical Systems, Journal of Computational Neuroscience, vol.14, issue.3, pp.62-65, 1990.

W. E. Lorensen and H. E. Cline, Marching Cubes: A High Resolution 3d Surface Construction Algorithm, Proceedings of the 14th Annual Conference on Computer Graphics and Interactive Techniques, SIGGRAPH '87, pp.163-169, 1987.

L. A. Lugiato, P. Mandel, and L. M. Narducci, Adiabatic elimination in nonlinear dynamical systems, Physical Review A, vol.29, issue.3, pp.1438-1452, 1984.

L. A. Lugiato and C. Oldano, Stationary spatial patterns in passive optical systems: Two-level atoms, Physical Review A, vol.37, issue.10, pp.3896-3908, 1988.

L. A. Lugiato, C. Oldano, and L. M. Narducci, Cooperative frequency locking and stationary spatial structures in lasers, JOSA B, vol.5, issue.5, pp.879-888, 1988.

L. Lugiato, F. Prati, and M. Brambilla, Nonlinear Optical Systems, 2015.

T. B. Luke, E. Barreto, P. So, ;. Maass, T. Natschläger et al., Complete Classification of the Macroscopic Behavior of a Heterogeneous Network of Theta Neurons, Real-time computing without stable states: a new framework for neural computation based on perturbations. Neural Computation, vol.25, pp.3431-3434, 2001.

L. I. Manevitch, A. I. Musienko, ;. Marino, G. Catalán, P. Sánchez et al., Limiting phase trajectories and energy exchange between anharmonic oscillator and external force, Canard Orbits" and Excitable Limit Cycles. Physical Review Letters, vol.58, issue.4, p.94101, 2004.
DOI : 10.1007/s11071-009-9506-z

F. Marino, F. Marin, S. Balle, and O. Piro, Chaotically Spiking Canards in an Excitable System with 2d Inertial Fast Manifolds, Physical Review Letters, vol.98, issue.7, p.74104, 2007.
DOI : 10.1103/physrevlett.98.074104

URL : https://digital.csic.es/bitstream/10261/47168/1/PhysRevLett.98.074104.pdf

F. Marino, M. Ciszak, S. F. Abdalah, K. Al-naimee, R. Meucci et al., Mixed-mode oscillations via canard explosions in light-emitting diodes with optoelectronic feedback, Physical Review E, vol.84, issue.4, p.47201, 2011.

J. Martin-regalado, F. Prati, M. S. Miguel, and N. B. Abraham, Masoller and A. C. Martí. Random Delays and the Synchronization of Chaotic Maps, IEEE Journal of Quantum Electronics, vol.33, issue.5, pp.765-783, 1997.

C. Mayol, M. A. Natiello, and M. G. Zimmermann, RESO-NANCE STRUCTURE IN A WEAKLY DETUNED LASER WITH INJECTED SIGNAL, International Journal of Bifurcation and Chaos, vol.11, issue.10, pp.2587-2605, 2001.

C. Mayol, R. Toral, C. R. Mirasso, and M. A. Natiello, Class-A lasers with injected signal: Bifurcation set and Lyapunov-potential function, Physical Review A, vol.66, issue.1, p.13808, 2002.
DOI : 10.1103/physreva.66.013808

URL : https://digital.csic.es/bitstream/10261/15306/2/PRA13808.pdf

A. Miazek, Synchronisation d'un ensemble de lasers chaotiques, couplés en réseauentì erement connecté, 2018.

]. D. Michaels, E. P. Matyas, and J. Jalife, Mechanisms of sinoatrial pacemaker synchronization: a new hypothesis, 1987.

R. E. Mirollo and S. H. Strogatz, Synchronization of PulseCoupled Biological Oscillators, SIAM Journal on Applied Mathematics, vol.50, issue.6, pp.1645-1662, 1990.

D. S. Modha, R. Ananthanarayanan, S. K. Esser, A. Ndirango, A. J. Sherbondy et al., Cognitive Computing, Commun. ACM, vol.54, issue.8, pp.62-71, 2011.

F. Mogensen, H. Olesen, and G. Jacobsen, Locking conditions and stability properties for a semiconductor laser with external light injection. Quantum Electronics, IEEE Journal, vol.21, p.784, 1985.

E. Montbrió, D. Pazó, and A. Roxin, Macroscopic Description for Networks of Spiking Neurons, Physical Review X, vol.5, issue.2, p.21028, 2015.

C. Morris and H. Lecar, Voltage oscillations in the barnacle giant muscle fiber, Biophysical Journal, vol.35, issue.1, pp.193-213, 1981.

I. N. Motoike, K. A. Yoshikawa-;-m, A. N. Nahmias, ;. Tait, Y. Nakagawa et al., Phase reduction and synchronization of a network of coupled dynamical elements exhibiting collective oscillations, The European Physical Journal B -Condensed Matter and Complex Systems, vol.19, issue.5, pp.533-543, 1994.

E. Neumann and J. Bernhardt, Physical Chemistry of Excitable Biomembranes. Annual Review of Biochemistry, vol.46, issue.1, pp.117-141, 1977.

M. Nixon, M. Friedman, E. Ronen, A. A. Friesem, N. Davidson et al., Synchronized Cluster Formation in Coupled Laser Networks, Physical Review Letters, vol.106, issue.22, p.223901, 2011.

M. Nixon, M. Fridman, E. Ronen, A. A. Friesem, N. Davidson et al., Controlling Synchronization in Large Laser Networks, Physical Review Letters, vol.108, issue.21, p.214101, 2012.

M. Nixon, E. Ronen, A. A. Friesem, and N. Davidson, Observing Geometric Frustration with Thousands of Coupled Lasers, Physical Review Letters, vol.110, issue.18, p.184102, 2013.

S. Nkomo, M. R. Tinsley, and K. Showalter, Chimera States in populations of nonlocally coupled chemical oscillators, Physical Review Letters, vol.110, issue.24, p.244102, 2013.

X. Noblin, N. O. Rojas, J. Westbrook, C. Llorens, M. Argentina et al., The fern sporangium: a unique catapult, Science, vol.335, issue.6074, p.1322, 2012.
URL : https://hal.archives-ouvertes.fr/hal-00826001

D. O'brien, S. P. Hegarty, G. Huyet, and A. V. Uskov, Sensitivity of quantum-dot semiconductor lasers to optical feedback, Optics Letters, vol.29, issue.10, pp.1072-1074, 2004.

L. Olejniczak, K. Panajotov, H. Thienpont, M. A. Sciamanna-;-r, S. H. Oliva et al., Self-pulsations and excitability in optically injected quantumdot lasers: Impact of the excited states and spontaneous emission noise, DYNAMICS OF A LARGE AR-RAY OF GLOBALLY COUPLED LASERS WITH DISTRIBUTED FREQUENCIES. International Journal of Bifurcation and Chaos, vol.82, issue.2, pp.2359-2374, 2001.
URL : https://hal.archives-ouvertes.fr/hal-00517326

H. M. Oliveira, L. V. Melo, ;. S. Olmi, A. Politi, and A. Torcini, Collective chaos in pulsecoupled neural networks, Europhysics Letters, vol.5, issue.6, p.60007, 2010.

S. Olmi, A. Navas, S. Boccaletti, and A. Torcini, Hysteretic transitions in the Kuramoto model with inertia, Physical Review E, vol.90, issue.4, p.42905, 2014.

S. Olmi, Chimera states in coupled Kuramoto oscillators with inertia, Chaos: An Interdisciplinary Journal of Nonlinear Science, vol.25, issue.12, p.123125, 2015.

G. L. Oppo and A. Politi, Toda potential in laser equations, Zeitschrift für Physik B Condensed Matter, vol.59, issue.1, pp.111-115, 1985.

G. L. Oppo, A. Politi, G. L. Lippi, and F. T. Arecchi, Frequency pushing in lasers with injected signal, Physical Review A, vol.34, issue.5, pp.4000-4007, 1986.

S. Ostojic, Two types of asynchronous activity in networks of excitatory and inhibitory spiking neurons, Nature Neuroscience, vol.17, issue.4, pp.594-600, 2014.

E. Ott and T. M. Antonsen, Low dimensional behavior of large systems of globally coupled oscillators, Chaos: An Interdisciplinary Journal of Nonlinear Science, vol.18, issue.3, p.37113, 2008.

E. Ott and T. M. Antonsen, Long time evolution of phase oscillator systems, Chaos: An Interdisciplinary Journal of Nonlinear Science, vol.19, issue.2, p.23117, 2009.

E. Ott, B. R. Hunt, and T. M. Antonsen, Comment on "Long time evolution of phase oscillator systems, Chaos, vol.19, p.23117, 2009.

, An Interdisciplinary Journal of Nonlinear Science, vol.21, issue.2, p.25112, 2011.

M. J. Panaggio, D. M. Abrams, ;. Paugam-moisy, and S. Bohte, Computing with Spiking Neuron Networks, Chimera states: coexistence of coherence and incoherence in networks of coupled oscillators. Nonlinearity, vol.28, pp.335-376, 2012.

D. Pazó and E. Montbrió, From Quasiperiodic Partial Synchronization to Collective Chaos in Populations of Inhibitory Neurons with Delay, Physical Review Letters, vol.116, issue.23, pp.365-371, 2009.

]. L. Pecora and T. L. Carroll, Synchronization in chaotic systems, Physical Review Letters, vol.64, issue.8, pp.821-824, 1990.

I. Petitbon, P. Gallion, G. Debarge, and C. Chabran, Locking bandwidth and relaxation oscillations of an injection-locked semiconductor laser, Electronics Letters, vol.22, pp.889-890, 1986.

B. Pietras and A. Daffertshofer, Ott-Antonsen attractiveness for parameter-dependent oscillatory systems, Chaos: An Interdisciplinary Journal of Nonlinear Science, vol.26, issue.10, p.103101, 2016.

A. Pikovsky, M. Rosenblum, and J. Kurths, Synchronization: A Universal Concept in Nonlinear Sciences, 2003.

V. N. Pilipchuk, Transitions from strongly to weaklynonlinear dynamics in a class of exactly solvable oscillators and nonlinear beat phenomena, Nonlinear Dynamics, vol.52, issue.3, pp.263-276, 2008.

A. Politi, G. L. Oppo, and R. Badii, Coexistence of conservative and dissipative behavior in reversible dynamical systems, Physical Review A, vol.33, issue.6, pp.4055-4060, 1986.

F. Prati, G. Tissoni, C. Mcintyre, and G. L. Oppo, Static and dynamic properties of cavity solitons in VCSELs with optical injection, The European Physical Journal D, vol.59, issue.1, pp.139-147, 2010.

S. A. Prescott, S. Ratté, Y. D. Koninck, and T. J. Sejnowski, Pyramidal neurons switch from integrators in vitro to resonators under in vivo-like conditions, Journal of Neurophysiology, vol.100, issue.6, pp.3030-3042, 2008.

P. R. Prucnal, B. J. Shastri, T. F. Lima, M. A. Nahmias, and A. N. Tait, Recent progress in semiconductor excitable lasers for photonic spike processing, Advances in Optics and Photonics, vol.8, issue.2, pp.228-299, 2016.

R. Pyle and R. Rosenbaum, Spatiotemporal Dynamics and Reliable Computations in Recurrent Spiking Neural Networks, vol.118, p.18103, 2017.

S. Rakshit, B. K. Bera, M. Perc, and D. Ghosh, Basin stability for chimera states, Scientific Reports, vol.7, issue.1, p.2412, 2017.

J. W. Rayleigh, The theory of sound, 1894.

C. Rimoldi, F. Gustave, L. Columbo, M. Brambilla, S. Barland et al., Abnormal chiral events in a semiconductor laser with coherent injection, Optics Express, vol.25, issue.18, pp.22017-22031, 2017.

J. Rinzel and G. Huguet, Nonlinear Dynamics of Neuronal Excitability, Oscillations, and Coincidence Detection, Communications on pure and applied mathematics, vol.66, issue.9, pp.1464-1494, 2013.

B. Romeira, J. Javaloyes, C. N. Ironside, J. M. Figueiredo, S. Balle et al., Excitability and optical pulse generation in semiconductor lasers driven by resonant tunneling diode photo-detectors, Optical Control of Endogenous Proteins with a Photoswitchable Conditional Subunit Reveals a Role for TREK1 in GABAB Signaling. Neuron, vol.21, pp.1005-1014, 1993.

R. Sarpeshkar, Analog versus digital: extrapolating from electronics to neurobiology, Neural Computation, vol.10, issue.7, pp.1601-1638, 1998.

H. Schmidt, D. Avitabile, E. Montbrió, A. Roxin, ;. Schwalger et al., Towards a theory of cortical columns: From spiking neurons to interacting neural populations of finite size, PLOS Computational Biology, vol.14, issue.9, p.1005507, 2017.

F. Selmi, R. Braive, G. Beaudoin, I. Sagnes, R. Kuszelewicz et al., Relative Refractory Period in an Excitable Semiconductor Laser, Physical Review Letters, vol.112, issue.18, p.183902, 2014.

F. Selmi, R. Braive, G. Beaudoin, I. Sagnes, R. Kuszelewicz et al., SIMPEL: Circuit model for photonic spike processing laser neurons, Prucnal. Spike processing with a graphene excitable laser. Scientific Reports, vol.40, issue.23, p.19126, 2015.

A. Shil'nikov, G. Nicolis, and C. Nicolis, Bifurcation and predictability analysis of a low-order atmospheric circulation model, International Journal of Bifurcation and Chaos, vol.05, issue.06, pp.1701-1711, 1995.

L. P. Shilnikov, A. Shilnikov, and ;. E. Barreto, Generating macroscopic chaos in a network of globally coupled phase oscillators, Shilnikov bifurcation -Scholarpedia, vol.144, p.33127, 2007.

P. So, T. B. Luke, and E. Barreto, Networks of theta neurons with time-varying excitability: Macroscopic chaos, multistability, and finalstate uncertainty, Physica D: Nonlinear Phenomena, vol.267, pp.16-26, 2014.

H. G. Solari and G. Oppo, Laser with injected signal: perturbation of an invariant circle, Optics Communications, vol.111, issue.1, pp.173-190, 1994.

F. Sorrentino and E. Ott, Network synchronization of groups, Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics, vol.76, issue.5, p.56114, 2007.

A. Spiegler, T. R. Knösche, K. Schwab, J. Haueisen, F. M. Atay-;-s et al., From Kuramoto to Crawford: exploring the onset of synchronization in populations of coupled oscillators, Physica D: Nonlinear Phenomena, vol.7, issue.12, pp.1-20, 2000.

O. Svelto, Principles of Lasers, pp.978-979, 2010.

R. Szalai, Knut: A continuation and bifurcation software for delay-differential equations, 2013.

A. N. Tait, M. A. Nahmias, Y. Tian, B. J. Shastri, and P. , Prucnal, Photonic neuromorphic signal processing and computing, 2013.

G. H. Tartwijk, D. Lenstra-;-s.-terrien, B. Krauskopf, N. G. Broderick, R. Braive et al., Semiconductor lasers with optical injection and feedback. Quantum and Semiclassical Optics, Journal of the European Optical Society Part B, vol.7, issue.2, pp.3013-3016, 1995.

S. Thorpe, A. Delorme, R. V. Rullen, ;. Timofeev, M. Bazhenov et al., Neuronal Synchronization and Thalamocortical Rhythms in Sleep, Wake and Epilepsy, National Center for Biotechnology Information (US), vol.14, issue.6-7, pp.662-665, 2001.

G. Tononi, Consciousness as integrated information: a provisional manifesto, The Biological Bulletin, vol.215, issue.3, pp.216-242, 2008.

J. Touboul, F. Wendling, P. Chauvel, and O. Faugeras, Neural mass activity, bifurcations, and epilepsy. Neural Computation, vol.23, pp.3232-3286, 2011.
URL : https://hal.archives-ouvertes.fr/inria-00592529

K. Trebacz, H. Dziubinska, and E. Krol, Electrical Signals in Long-Distance Communication in Plants, Communication in Plants: Neuronal Aspects of Plant Life, pp.277-290, 2006.

J. R. Tredicce, F. T. Arecchi, G. L. Lippi, and G. P. Puccioni, Instabilities in lasers with an injected signal, JOSA B, vol.2, issue.1, pp.173-183, 1985.

N. Trela, H. J. Baker, and D. R. Hall, Locking and wavelength selection of an ultra-collimated single-mode diode laser bar by a volume holographic grating, Optics Express, vol.21, issue.4, pp.4512-4517, 2013.

M. Turconi, B. Garbin, M. Feyereisen, M. Giudici, and S. Barland, Control of excitable pulses in an injection-locked semiconductor laser, Physical Review E, vol.88, issue.2, p.22923, 2013.

A. V. Uskov, Y. Boucher, J. L. Bihan, and J. Mcinerney, Theory of a self-assembled quantum-dot semiconductor laser with Auger carrier capture: Quantum efficiency and nonlinear gain, Applied Physics Letters, vol.73, issue.11, pp.1499-1501, 1998.

A. V. Uskov, J. Mcinerney, F. Adler, H. Schweizer, M. H. Pilkuhn et al., van der Pol. VII. Forced oscillations in a circuit with non-linear resistance. (Reception with reactive triode). The London, Edinburgh, and Dublin Philosophical Magazine, Applied Physics Letters, vol.72, issue.1, pp.65-80, 1927.

C. Van-vreeswijk, L. F. Abbott, G. B. Ermentrout, ;. Vandoorne, P. Mechet et al., Experimental demonstration of reservoir computing on a silicon photonics chip, Journal of Computational Neuroscience, vol.1, issue.4, p.3541, 1994.

F. Varela, J. Lachaux, E. Rodriguez, and J. Martinerie, The brainweb: Phase synchronization and large-scale integration, Nature Reviews Neuroscience, vol.2, p.229, 2001.

R. Veltz, O. J. Faugeras-;-t, and . Walker, Stability of the stationary solutions of neural field equations with propagation delays, The Journal of Mathematical Neuroscience, vol.1, issue.1, pp.891-894, 1969.
URL : https://hal.archives-ouvertes.fr/hal-00784425

C. P. Wang, ;. S. Watanabe, S. H. Strogatz, ;. S. Wieczorek, B. Krauskopf et al., A unifying view of bifurcations in a semiconductor laser subject to optical injection, Master and slave oscillator array system for very large multiline lasers. Applied Optics, vol.17, p.63901, 1978.

S. Wieczorek, B. Krauskopf, T. B. Simpson, and D. Lenstra, The dynamical complexity of optically injected semiconductor lasers, Wieczorek 2005b] S. Wieczorek and B. Krauskopf. Bifurcations of nhomoclinic orbits in optically injected lasers. Nonlinearity, vol.416, pp.1095-1120, 2005.

H. R. Wilson and J. D. Cowan, Excitatory and inhibitory interactions in localized populations of model neurons, Biophysical Journal, vol.12, issue.1, pp.1-24, 1972.

H. R. Wilson, J. D. Cowan-;-a, . T. Winfree-;-a, . T. Winfree-;-a, and . Winfree, Biological rhythms and the behavior of populations of coupled oscillators, A mathematical theory of the functional dynamics of cortical and thalamic nervous tissue. Kybernetik, vol.13, p.661, 1967.

A. M. Yacomotti, P. Monnier, F. Raineri, B. B. Bakir, C. Seassal et al., Fast Thermo-Optical Excitability in a Two-Dimensional Photonic Crystal, Physical Review Letters, vol.97, issue.14, p.143904, 2006.

R. York and R. Compton, Quasi-optical power combining using mutually synchronized oscillator arrays, IEEE Transactions on Microwave Theory and Techniques, vol.39, pp.1000-1009, 1991.

D. Yu, W. Lu, and R. G. Harrison, Dynamic bistability and spiral waves in a laser, Journal of Optics B: Quantum and Semiclassical Optics, vol.1, issue.1, p.25, 1999.

H. Zeberg, H. P. Robinson, and P. Arhem, Density of voltagegated potassium channels is a bifurcation parameter in pyramidal neurons, Journal of Neurophysiology, vol.113, issue.2, pp.537-549, 2015.

V. Zehnlé and H. Zeghlache, Theoretical study of a laser with injected signal. II. Periodic perturbation, Physical Review A, vol.46, issue.9, pp.6028-6035, 1992.

C. Zhou and J. Kurths, Spatiotemporal coherence resonance of phase synchronization in weakly coupled chaotic oscillators, Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics, vol.65, issue.4, p.40101, 2002.

Q. G. Zhou-;-m, M. A. Zimmermann, H. G. Natiello, and . Solari, Global bifurcations in a laser with injected signal: Beyond Adler's approximation, Mesh Processing -PyMesh 0.2.0 documentation, vol.11, pp.500-513, 2001.