Sincronización de la actividad eléctrica neuronal, utilizando el modelo de Hodgkin-Huxley y el circuito RCLSJ

Main Article Content

Jose A Diaz M http://orcid.org/0000-0002-9661-1863
Oscar Téquita http://orcid.org/0000-0002-2989-7902
Fernando Naranjo http://orcid.org/0000-0002-4146-3277

Keywords

método modelo de Hodgkin-Huxley, uniones Josephson, funciones de Lyapunov

Resumen

Simulamos la actividad eléctrica neuronal mediante el modelo de Hodgkin-Huxley (HH) y un circuito superconductor, que contiene uniones Josephson. El modelo HH simulan las características principales de la dinámica neuronal tales como potenciales de acción, umbrales de disparo y el períodos refractarios. El propósito del manuscrito es mostrar un método para sincronizar un circuito con union Josephson RCLSJ a una dinámica neuronal representado por el modelo HH. Así, el circuito RCLSJ es capaz de imitar el comportamiento de la neurona HH. Controlamos el circuito RCLSJ, utilizando un esquema de control adaptativo, que con funciones de Lyapunov y dos coeficientes de ganancia controlables nos permiten la sincronización de los dos modelos neuronales. Los resultados proporcionan una ruta a seguir adelante en el entendimiento de la sincronización de redes neuronales, generadas por el comportamiento intrinseco del cerebro.

Descargas

Los datos de descargas todavía no están disponibles.
Abstract 1089 | PDF (English) Downloads 687 HTML (English) Downloads 721

Referencias

[1] I. Timofeev, M. Bazhenov, J. Seigneur, and T. Sejnowsk, “Neuronal Synchronization and Thalamocortical Rhythms in Sleep, Wake and Epilepsy, Jasper’s Basic Mechanism of the Epilepsies,” 1974. [Online].Available: http://www.ncbi.nlm.nih.gov/books/NBK50785/ 94

[2] C. Hammond, “Cellular and molecular neurobiology,” Ph.D. dissertation,Academic Press, Great Britain, 1996. 94

[3] A. L. Hodgkin and A. F. Huxley, “A quantitative description of membrane current and its application to conduction and excitation in nerve,” The Journal of Physiology, vol. 117, no. 4, pp. 500–544, 1952. [Online].
Available:http://dx.doi.org/10.1113/jphysiol.1952.sp004764 95, 97

[4] P. Crotty, D. Schult, and K. Segall, “Josephson junction
simulation of neurons,” Phys. Rev. E, vol. 82, p. 011914, Jul 2010. [Online]. Available:http://link.aps.org/doi/10.1103/PhysRevE.82.011914 95, 99, 101

[5] A. L. Hodgkin and A. F. Huxley, “Currents carried by sodium and potassium ions through the membrane of the giant axon of loligo,” TheJournal of Physiology, vol. 116, no. 4, pp. 449–472, 1952. [Online].
Available:http://dx.doi.org/10.1113/jphysiol.1952.sp004717 95, 97

[6] M. Carolina Barriga, C. Humberto Carrillo, and L. Fernando Ongay,“El modelo de Fitzhugh-Nagumo para el potencial eléctrico de una neurona,” 2003. [Online]. Available: http://mmc.geofisica.unam.mx/acl/integra/ManualTutoriales/FHN.pdf 95

[7] D. Aaby, M. Usma, and A. Singh, “A Comparative Study of Numerical Methods for the Hodgkin-Huxley Model of Nerve Cell Action Potentials.” 95, 97

[8] F. Li, Q. Liu, H. Guo, Y. Zhao, J. Tang, and J. Ma, “Simulating the electric activity of fitzhugh-nagumo neuron by using josephson junction model,”Nonlinear Dynamics, vol. 69, no. 4, pp. 2169–2179, 2012. [Online]. Available:http://dx.doi.org/10.1007/s11071-012-0417-z 95, 96, 99, 101

[9] L. H. Nguyen and K.-S. Hong, “Synchronization of coupled chaotic fitzhughnagumo neurons via lyapunov functions,” Mathematics and Computers in Simulation, vol. 82, no. 4, pp. 590– 603, 2011. [Online].
Available:http://www.sciencedirect.com/science/article/pii/S0378475411002540 95,96, 99

[10] D. McCumber, “Effect of ac inpedance on dc voltage-current characteristics of a superconductor weak-link junction,” J. Appl. Phys, vol. 39, no. 3113, pp.6157–6181, 1968. [Online]. Available: http://dx.doi.org/10.1063/1.1656743 95, 96, 98

[11] C. Whan, C. Lobb, and M. Forrester, “Effect of inductance on externally shunted Josephson tunnel junctions,” J. Appl. Phys., vol. 77, no. 382,1995.[Online]. Available:http://dx.doi.org/10.1063/1.359334 95, 101

[12] C. Whan and C. Lobb, “Complex dynamical behavior in rcl-shunted josephson junctions,” Applied Superconductivity, IEEE Transactions on, vol. 5,no. 2, pp. 3094–3097, June 1995. 95, 98

[13] J. Mazo, F. Naranjo, and K. Segall, “Thermal depinning of fluxons in discrete Josephson rings,” Physical Review B, vol. 78, no. 17, 2008. 95

[14] M. Jun, H. Long, X. Zhen-Bo, and C. Wang, “Simulated test of electric activity of neurons by using josephson junction based on synchronization scheme,” Communications in Nonlinear Science and Numerical Simulation,vol. 17, no. 6, pp. 2659 – 2669, 2012. [Online]. Available:http://www.sciencedirect.com/science/article/pii/S1007570411005995 96, 99

[15] S. Dana, D. Sengupta, and C.-K. Hu, “Spiking and bursting in josephson junction,” Circuits and Systems II: Express Briefs, IEEE Transactions on,vol. 53, no. 10, pp. 1031–1034, Oct 2006. 96, 98

[16] D. Sterratt, B. Graham, A. Gillies, and D. Willshaw, Principles of computational modelling in neuroscience. CambridgeUniversity Press, 2011.97

[17] Y. t Hu, T. g Zhou, J. Gu, S. l Yan, L. Fang, and X. j Zhao, “Study on chaotic behaviors of rclsj model josephson junctions,” Journal of Physics:Conference Series, vol. 96, no. 1, p. 012035, 2008. [Online]. Available:http://stacks.iop.org/17426596/96/i=1/a=012035 97, 98

[18] M. Aqil, K.-S. Hong, and M.-Y. Jeong, “Synchronization of coupled chaotic fitzhugh-nagumo systems,” Communications in Nonlinear Science and Numerical Simulation, vol. 17, no. 4, pp. 1615 – 1627, 2012. [Online].
Available:http://www.sciencedirect.com/science/article/pii/S1007570411005363 99

[19] S. H. Strogatz, Nonlinear dynamics and chaos: with applications to physics,biology, chemistry, and engineering. Westview press, 2014. 99