Neuronal Synchronization of Electrical Activity, Using the Hodgkin-Huxley Model and RCLSJ Circuit
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Keywords
Hodgkin-Huxley model, Josephson Junction, Lyapunov Method
Abstract
We simulated the neuronal electrical activity using the Hodgkin-Huxley model (HH) and a superconductor circuit, containing Josephson junctions. These HH model make possible simulate the main neuronal dynamics characteristics such as action potentials, firing threshold and refractory period. The purpose of the manuscript is show a method to syncronize a RCLshunted Josephson junction to a neuronal dynamics represented by the HH model. Thus the RCLSJ circuit is able to mimics the behavior of the HH neuron. We controlated the RCLSJ circuit, using and improved adaptative track scheme, that with the improved Lyapunov functions and the two controllable gain coefficients allowing synchronization of two neuronal models. Results will provide the path to follow forward the understanding neuronal networks synchronization about, generating the intrinsic brain behavior.
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References
[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