Abstract
In this work, we studied the dynamics of modified FitzHugh-Nagumo (MFHN) neuron model. This model shows how the potential difference between spine head and its surrounding medium vacillates between a relatively constant period called the silent phase and large scale oscillation reffered to as the active phase or bursting. We investigated bifurcation in the dynamics of two MFHN neurons coupled to each other through an electrical coupling. It is found that the variation in coupling strength between the neurons leads to different types of bifurcations and the system exhibits the existence of fixed point, periodic and chaotic attractor.
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References
Ermentrout, G.B., Kopell, N.: Parabolic Bursting in an Excitable System Coupled with a Slow Oscillation. SIAMJournal on Applied Mathematics 46, 233–253 (1986)
Ermentrout, G.B.: Type I Membranes, Phase Resetting Curves and Synchrony. Neural Computing 8, 979–1001 (1996)
Fitzhugh, R.: Impulses and Physiological States in Models of Nerve Membrane. Biophysical Journal 1, 445–466 (1961)
Hodgkin, A.L., Huxley, A.F.: A Quantitative Description of Membrane Current and Application to Conduction and Excitation in Nerve. Journal of Physiology 117, 500–544 (1954)
Morris, C., Lecar, H.: Voltage Oscillations in the Barnacle Giant Muscle Fiber. Journal of Biophysics 35, 193–213 (1981)
Rinzel, J.: Models in neurobiology. In: Nonlinear Phenomena in Physics and Biology, pp. 345–367. Plenum Press, New York (1981)
Hodgkin, A.L.: The Local Changes Associated with Repetitive Action in a Non- Modulated Axon. Journal of Physiology 107, 165–181 (1948)
Izhikevich, E.M.: Class 1 Neural Excitability, Conventional Synapses, Weakly Connected Networks and Mathematical Foundations of Pulse Coupled Models. IEEE Transactions on Neural Networks 10, 499–507 (1999)
Rinzel, J., Ermentrout, G.B.: Analysis of Neural Excitability and Oscillations. Methods in Neuronal Modeling. MIT press, Cambridge (1989)
Ehibilik, A.I., Borisyuk, R.M., Roose, D.: Numerical Bifurcation Analysis of a Model of Coupled Neural Oscillators. International Series of Numerical Mathematics 104, 215–228 (1992)
Hoppensteadt, F.C., Izhikevich, E.M.: Weakly Connected Neural Networks. Springer, Heidelberg (1997)
Rinzel, J.: A Formal Classification of Bursting Mechanisms in Excitable Systems. In: Mathematical Topics in Population Biology, Morphogenesis and Neurosciences. Lecture Notes in Biomathematics, vol. 71, pp. 267–281. Springer, New York (1987)
Izhikevich, E.M.: Neural Excitability, spiking and bursting. International Journal of Bifurcation and Chaos 10, 1171–1266 (2000)
Mishra, D., Yadav, A., Kalra, P.K.: Chaotic Behavior in Neural Network and FitzHugh-Nagumo Neuronal Model. In: Pal, N.R., Kasabov, N., Mudi, R.K., Pal, S., Parui, S.K. (eds.) ICONIP 2004. LNCS, vol. 3316, pp. 868–873. Springer, Heidelberg (2004)
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Mishra, D., Yadav, A., Ray, S., Kalra, P.K. (2005). Nonlinear Dynamical Analysis on Coupled Modified Fitzhugh-Nagumo Neuron Model. In: Wang, J., Liao, X., Yi, Z. (eds) Advances in Neural Networks – ISNN 2005. ISNN 2005. Lecture Notes in Computer Science, vol 3496. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11427391_14
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DOI: https://doi.org/10.1007/11427391_14
Publisher Name: Springer, Berlin, Heidelberg
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