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Dynamics of large cooperative pulsed-coupled networks
1. | Instituto de Matemática y Estadística Rafael Laguardia, Universidad de la República, Av. Herrera y Reissig 565, C.P.11300, Montevideo |
References:
[1] |
E. Accinelli, S. London and E. Sánchez Carrera, A Model of Imitative Behavior in the Population of Firms and Workers, Quaderni del Dipartimento di Economia Politica, 554, University of Siena, Siena, 2009. |
[2] |
S. Bottani, Synchronization of integrate and fire oscillators with global coupling, Physical Review E, 54 (1996), 2334-2350.
doi: 10.1103/PhysRevE.54.2334. |
[3] |
R. Boulet, B. Jouve, F. Rossi and N. Villa, Batch kernel SOM and related Laplacian methods for social network analysis, Neurocomputing, 71 (2008), 1257-1273.
doi: 10.1016/j.neucom.2007.12.026. |
[4] |
E. Catsigeras and P. Guiraud, Integrate and fire neural networks, piecewise contractive maps and limit cycles, Journ. Math. Biol., 67 (2013), 609-655.
doi: 10.1007/s00285-012-0560-7. |
[5] |
B. Cessac, A discrete time neural network model with spiking neurons. Rigorous results on the spontaneous dynamics, Journ. Math. Biol., 56 (2008), 311-345.
doi: 10.1007/s00285-007-0117-3. |
[6] |
B. Cessac and T. Viéville, On Dynamics of Integrate-and-fire Neural Networks with Conductance Based Synapses, Frontiers In Computational Neuroscience, 2008.
doi: 10.3389/neuro.10.002.2008. |
[7] |
J. R. Chazottes and B. Fernandez (Eds), Dynamics of Coupled Map Lattices and of Related Spatially Extended Systems, Lecture Notes in Physics, 671 Springer Berlin, 2005. |
[8] |
M. Cottrell, M. Olteanu, F. Rossi, J. Rynkiewicz and N. Villa-Vialaneix, Neural networks for complex data, Künstliche Intelligenz, 26 (2012), 373-380.
doi: 10.1007/s13218-012-0207-2. |
[9] |
R. Coutinho, B. Fernandez, R. Lima and A. Meyroneinc, Discrete time piecewise affine models of genetic regulatory networks, Journ. Math. Biol., 52 (2006), 524-570.
doi: 10.1007/s00285-005-0359-x. |
[10] |
AL. Dutot, J. Rynkiewicz, F. Steiner and J. Rude, A 24-h forecast of ozone peaks and exceedance levels using neural classifiers and weather predictions, Environ Model Softw, 22 (2007), 1261-1269.
doi: 10.1016/j.envsoft.2006.08.002. |
[11] |
G. B. Ermentrout and N. Kopell, Oscillator death in systems of coupled neural oscillators, SIAM Journal on Applied Mathematics, 50 (1990), 125-146.
doi: 10.1137/0150009. |
[12] |
G. B. Ermentrout and D. H. Terman, Mathematical Foundations of Neuroscience, Interdisc. Appl. Math., 35, Springer, Dordrecht-Heidelberg-London, 2010.
doi: 10.1007/978-0-387-87708-2. |
[13] |
J. Feng, L. Zhu and H. Wang, Stability of Ecosystem induced by mutual interference between predators, Procedia Environmental Sciences, 2 (2010), 42-48.
doi: 10.1016/j.proenv.2010.10.007. |
[14] |
R. Golamen, Why learning doesn't add up: Equilibrium selection with a composition of learning rules, Int. Jroun. Game Theory, 40 (2011), 719-733.
doi: 10.1007/s00182-010-0265-3. |
[15] |
H. Höglund, Detecting Earnings Management Using Neural Networks, Doctoral Thesis Hanken School of Economics, Economics and Society Series 121, Edita Prima Ltd., Helsinki, 2010. Available from: https://helda.helsinki.fi/handle/10227/742 (Last retrieved 7 Feb. 2013). |
[16] |
E. M. Izhikevich, Dynamical Systems in Neuroscience: The Geometry of Excitability and Bursting, MIT Press, 2007. |
[17] |
B. Maillet, M. Olteanu and J. Rynkiewicz, Nonlinear analysis of shocks when financial markets are subject to changes in regime, in Proc of XIIth European Symposium on Artificial Neural Networks, (2004), 87-92. |
[18] |
W. Mass and C. M. Bishop (Eds), Pulsed Neural Networks, MIT Press, Cambridge, 2001. |
[19] |
I. Milchtaich, Representation of finite games as network of congestion, Int. Journ. Game Theory, 42 (2013), 1085-1096.
doi: 10.1007/s00182-012-0363-5. |
[20] |
R. E. Mirollo and S. H. Strogatz, Synchronization of pulse-coupled biological oscillators, SIAM J. Appl. Math., 50 (1990), 1645-1662.
doi: 10.1137/0150098. |
[21] |
M. A. Jalil and M. Misas, Evaluación de pronósticos de tipo de cambio utilizando redes neuronales y funciones de pérdida asimétricas (Spanish), Revista Colombiana de Estadística, 30 (2007), 143-161. |
[22] |
M. E. J. Newman, D. J. Watts, and S. H. Strogatz, Random graph models of social networks, Proc. Nal. Acad. Sci. USA, 99 (2002), 2566-2572.
doi: 10.1073/pnas.012582999. |
[23] |
A. Pikovsky and Y. Maistrenko (Editors), Synchronization: Theory and Application, Kluwer Academic Publ, Dordrecht, 2003.
doi: 10.1007/978-94-010-0217-2. |
[24] |
A. Politi and A. Torcini, Stable chaos, in Nonlinear Dynamics and Chaos: Advances and Perspectives, (eds. M. Thiel, J. Kurths, M. C. Romano, G. Károlyi and A. Moura), Understanding Complex Systems, Springer, 2010.
doi: 10.1007/978-3-642-04629-2. |
[25] |
G. M. Ramírez Ávila, J. L. Guisset and J. L. Deneubourg, Synchronization in light-controlled oscillators, Physica D, 182 (2003), 254-273.
doi: 10.1016/S0167-2789(03)00135-0. |
[26] |
V. S. H. Raoa and M. N. Kumarb, Estimation of the parameters of an infectious disease model using neural networks, Nonlinear Analysis: Real World Applications, 11 (2010), 1810-1818.
doi: 10.1016/j.nonrwa.2009.04.006. |
[27] |
N. Rubido, C. Cabeza, S. Kahan, G. M. Ramírez Ávila and A. C. Marti, Synchronization regions of two pulse-coupled electronic piecewise linear oscillators, Europ. Phys. Journ. D, 62 (2011), 51-56.
doi: 10.1140/epjd/e2010-00215-4. |
[28] |
G. T. Stamov and I. Stamova, Almost periodic solutions for impulsive neural networks with delay, Applied Mathematical Modelling, 31 (2007), 1263-1270.
doi: 10.1016/j.apm.2006.04.008. |
[29] |
C. van Vreeswijk, L. F. Abbott and B. Ermentrout, When inhibition not excitation synchronizes neural firing, Journ. Comput. Neuroscience, 1 (1994), 313-321.
doi: 10.1007/BF00961879. |
[30] |
D. A. Vasseur and J. Fox, Phase-locking and environmental fluctuations generate synchrony in a predator-prey community, Nature, 460 (2009), 1007-1010.
doi: 10.1038/nature08208. |
[31] |
D. J. Watts and S. H. Strogatz, Collective Dynamics of Small-World, Nature (London), 393 (1998), 440-440. |
[32] |
T. Yang and L. O. Chua, Impulsive stabilization for control and synchronization of chaotic systems: theory and application to secure communication, IEEE Trans. Circuits Syst., 44 (1997), 976-988.
doi: 10.1109/81.633887. |
[33] |
Young L.-S, Chaotic phenomena in three setting: Large, noisy and out of equilibrium, Nonlinearity, 21 (2008), T245-T252.
doi: 10.1088/0951-7715/21/11/T04. |
show all references
References:
[1] |
E. Accinelli, S. London and E. Sánchez Carrera, A Model of Imitative Behavior in the Population of Firms and Workers, Quaderni del Dipartimento di Economia Politica, 554, University of Siena, Siena, 2009. |
[2] |
S. Bottani, Synchronization of integrate and fire oscillators with global coupling, Physical Review E, 54 (1996), 2334-2350.
doi: 10.1103/PhysRevE.54.2334. |
[3] |
R. Boulet, B. Jouve, F. Rossi and N. Villa, Batch kernel SOM and related Laplacian methods for social network analysis, Neurocomputing, 71 (2008), 1257-1273.
doi: 10.1016/j.neucom.2007.12.026. |
[4] |
E. Catsigeras and P. Guiraud, Integrate and fire neural networks, piecewise contractive maps and limit cycles, Journ. Math. Biol., 67 (2013), 609-655.
doi: 10.1007/s00285-012-0560-7. |
[5] |
B. Cessac, A discrete time neural network model with spiking neurons. Rigorous results on the spontaneous dynamics, Journ. Math. Biol., 56 (2008), 311-345.
doi: 10.1007/s00285-007-0117-3. |
[6] |
B. Cessac and T. Viéville, On Dynamics of Integrate-and-fire Neural Networks with Conductance Based Synapses, Frontiers In Computational Neuroscience, 2008.
doi: 10.3389/neuro.10.002.2008. |
[7] |
J. R. Chazottes and B. Fernandez (Eds), Dynamics of Coupled Map Lattices and of Related Spatially Extended Systems, Lecture Notes in Physics, 671 Springer Berlin, 2005. |
[8] |
M. Cottrell, M. Olteanu, F. Rossi, J. Rynkiewicz and N. Villa-Vialaneix, Neural networks for complex data, Künstliche Intelligenz, 26 (2012), 373-380.
doi: 10.1007/s13218-012-0207-2. |
[9] |
R. Coutinho, B. Fernandez, R. Lima and A. Meyroneinc, Discrete time piecewise affine models of genetic regulatory networks, Journ. Math. Biol., 52 (2006), 524-570.
doi: 10.1007/s00285-005-0359-x. |
[10] |
AL. Dutot, J. Rynkiewicz, F. Steiner and J. Rude, A 24-h forecast of ozone peaks and exceedance levels using neural classifiers and weather predictions, Environ Model Softw, 22 (2007), 1261-1269.
doi: 10.1016/j.envsoft.2006.08.002. |
[11] |
G. B. Ermentrout and N. Kopell, Oscillator death in systems of coupled neural oscillators, SIAM Journal on Applied Mathematics, 50 (1990), 125-146.
doi: 10.1137/0150009. |
[12] |
G. B. Ermentrout and D. H. Terman, Mathematical Foundations of Neuroscience, Interdisc. Appl. Math., 35, Springer, Dordrecht-Heidelberg-London, 2010.
doi: 10.1007/978-0-387-87708-2. |
[13] |
J. Feng, L. Zhu and H. Wang, Stability of Ecosystem induced by mutual interference between predators, Procedia Environmental Sciences, 2 (2010), 42-48.
doi: 10.1016/j.proenv.2010.10.007. |
[14] |
R. Golamen, Why learning doesn't add up: Equilibrium selection with a composition of learning rules, Int. Jroun. Game Theory, 40 (2011), 719-733.
doi: 10.1007/s00182-010-0265-3. |
[15] |
H. Höglund, Detecting Earnings Management Using Neural Networks, Doctoral Thesis Hanken School of Economics, Economics and Society Series 121, Edita Prima Ltd., Helsinki, 2010. Available from: https://helda.helsinki.fi/handle/10227/742 (Last retrieved 7 Feb. 2013). |
[16] |
E. M. Izhikevich, Dynamical Systems in Neuroscience: The Geometry of Excitability and Bursting, MIT Press, 2007. |
[17] |
B. Maillet, M. Olteanu and J. Rynkiewicz, Nonlinear analysis of shocks when financial markets are subject to changes in regime, in Proc of XIIth European Symposium on Artificial Neural Networks, (2004), 87-92. |
[18] |
W. Mass and C. M. Bishop (Eds), Pulsed Neural Networks, MIT Press, Cambridge, 2001. |
[19] |
I. Milchtaich, Representation of finite games as network of congestion, Int. Journ. Game Theory, 42 (2013), 1085-1096.
doi: 10.1007/s00182-012-0363-5. |
[20] |
R. E. Mirollo and S. H. Strogatz, Synchronization of pulse-coupled biological oscillators, SIAM J. Appl. Math., 50 (1990), 1645-1662.
doi: 10.1137/0150098. |
[21] |
M. A. Jalil and M. Misas, Evaluación de pronósticos de tipo de cambio utilizando redes neuronales y funciones de pérdida asimétricas (Spanish), Revista Colombiana de Estadística, 30 (2007), 143-161. |
[22] |
M. E. J. Newman, D. J. Watts, and S. H. Strogatz, Random graph models of social networks, Proc. Nal. Acad. Sci. USA, 99 (2002), 2566-2572.
doi: 10.1073/pnas.012582999. |
[23] |
A. Pikovsky and Y. Maistrenko (Editors), Synchronization: Theory and Application, Kluwer Academic Publ, Dordrecht, 2003.
doi: 10.1007/978-94-010-0217-2. |
[24] |
A. Politi and A. Torcini, Stable chaos, in Nonlinear Dynamics and Chaos: Advances and Perspectives, (eds. M. Thiel, J. Kurths, M. C. Romano, G. Károlyi and A. Moura), Understanding Complex Systems, Springer, 2010.
doi: 10.1007/978-3-642-04629-2. |
[25] |
G. M. Ramírez Ávila, J. L. Guisset and J. L. Deneubourg, Synchronization in light-controlled oscillators, Physica D, 182 (2003), 254-273.
doi: 10.1016/S0167-2789(03)00135-0. |
[26] |
V. S. H. Raoa and M. N. Kumarb, Estimation of the parameters of an infectious disease model using neural networks, Nonlinear Analysis: Real World Applications, 11 (2010), 1810-1818.
doi: 10.1016/j.nonrwa.2009.04.006. |
[27] |
N. Rubido, C. Cabeza, S. Kahan, G. M. Ramírez Ávila and A. C. Marti, Synchronization regions of two pulse-coupled electronic piecewise linear oscillators, Europ. Phys. Journ. D, 62 (2011), 51-56.
doi: 10.1140/epjd/e2010-00215-4. |
[28] |
G. T. Stamov and I. Stamova, Almost periodic solutions for impulsive neural networks with delay, Applied Mathematical Modelling, 31 (2007), 1263-1270.
doi: 10.1016/j.apm.2006.04.008. |
[29] |
C. van Vreeswijk, L. F. Abbott and B. Ermentrout, When inhibition not excitation synchronizes neural firing, Journ. Comput. Neuroscience, 1 (1994), 313-321.
doi: 10.1007/BF00961879. |
[30] |
D. A. Vasseur and J. Fox, Phase-locking and environmental fluctuations generate synchrony in a predator-prey community, Nature, 460 (2009), 1007-1010.
doi: 10.1038/nature08208. |
[31] |
D. J. Watts and S. H. Strogatz, Collective Dynamics of Small-World, Nature (London), 393 (1998), 440-440. |
[32] |
T. Yang and L. O. Chua, Impulsive stabilization for control and synchronization of chaotic systems: theory and application to secure communication, IEEE Trans. Circuits Syst., 44 (1997), 976-988.
doi: 10.1109/81.633887. |
[33] |
Young L.-S, Chaotic phenomena in three setting: Large, noisy and out of equilibrium, Nonlinearity, 21 (2008), T245-T252.
doi: 10.1088/0951-7715/21/11/T04. |
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