Abstract
We study the stochastic dynamics of three FitzHugh-Nagumo neurons with chemical coupling and electrical coupling (gap junction) respectively. For both of the coupling cases, optimal coherence resonance and weak signal propagation can be achieved with intermediate noise intensity. Through comparisons and analysis, we can make conclusions that chemical synaptic coupling is more efficient than the well known linear electrical coupling for both coherence resonance and weak signal propagation. We also find that neurons with parameters locate near the bifurcation point (canard regime) can exhibit the best response of coherence resonance and weak signal propagation.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Ullner, E.: Noise-induced Phenomena of Signal Transmission in Excitable Neural Models. DISSERTATION (2004)
Perc, M., Marhl, M.: Amplification of information transfer in excitable systems that reside in a steady state near a bifurcation point to complex oscillatory behavior. Physical Review EÂ 71(2), 26229 (2005)
Volkov, E.I., Ullner, E., Zaikin, A.A., Kurths, J.: Oscillatory amplification of stochastic resonance in excitable systems. Physical Review EÂ 68(2), 26214 (2003)
Zhao, G., Hou, Z., Xin, H.: Frequency-selective response of FitzHugh-Nagumo neuron networks via changing random edges. Chaos: An Interdisciplinary Journal of Nonlinear Science 16, 043107 (2006)
Zaks, M.A., Sailer, X., Schimansky-Geier, L., Neiman, A.B.: Noise induced complexity: From subthreshold oscillations to spiking in coupled excitable systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 15, 026117 (2005)
Makarov, V.A., Nekorkin, V.I., Velarde, M.G.: Spiking Behavior in a Noise-Driven System Combining Oscillatory and Excitatory Properties. Physical Review Letters 86(15), 3431–3434 (2001)
Shishkin, A., Postnov, D.: Stochastic dynamics of FitzHugh-Nagumo model near the canard explosion, Physics and Control, 2003. In: Proceedings of 2003 International Conference, vol. 2 (2003)
Wellens, T., Shatokhin, V., Buchleitner, A.: Stochastic resonance. Reports on Progress in Physics 67(1), 45–105 (2004)
Ullner, E., Zaikin, A., GarcÃa-Ojalvo, J., Báscones, R., Kurths, J.: Vibrational resonance and vibrational propagation in excitable systems. Physics Letters A 312(5-6), 348–354 (2003)
Volkov, E.I., Ullner, E., Zaikin, A.A., Kurths, J.: Frequency-dependent stochastic resonance in inhibitory coupled excitable systems. Physical Review EÂ 68(6), 61112 (2003)
Ullner, E., Zaikin, A., GarcÃa-Ojalvo, J., Kurths, J.: Noise-Induced Excitability in Oscillatory Media. Physical Review Letters 91(18), 180601 (2003)
Zhou, C., Kurths, J., Hu, B.: Array-Enhanced Coherence Resonance: Nontrivial Effects of Heterogeneity and Spatial Independence of Noise. Physical Review Letters 87(9), 98101 (2001)
Gong, P.L., Xu, J.X.: Global dynamics and stochastic resonance of the forced FitzHugh-Nagumo neuron model. Physical Review EÂ 63(3), 31906 (2001)
Toral, R., Mirasso, C.R., Gunton, J.D.: System size coherence resonance in coupled FitzHugh-Nagumo models. Europhysics Letters 61(2), 162–167 (2003)
Casado, J.M., Baltanás, J.P.: Phase switching in a system of two noisy Hodgkin-Huxley neurons coupled by a diffusive interaction. Physical Review E 68(6), 61917 (2003)
Balenzuela, P., Garcia-Ojalvo, J.: On the role of chemical synapses in coupled neurons with noise. Arxiv preprint q-bio. NC/0502025 (2005)
Wang, J., Li, X., Hu, W.: Canards and Bifurcations in the Chemical Synaptic Coupled FHN Neurons (2006)
Drover, J., Rubin, J., Su, J., Ermentrout, B.: Analysis of a canard mechanism by which excitatory synaptic coupling can synchronize neurons at low firing frequencies. SIAM J. Appl. Math. 65, 69–92 (2004)
Wechselberger, M.: Existence and bifurcation of canards in R3 in the case of a folded node. SIAM J. Applied Dynamical Systems 4, 101–139 (2005)
Cronin, J.: Mathematical Aspects of Hodgkin-Huxley Neural Theory. Cambridge University Press, Cambridge (1987)
Higham, D.J.: An algorithmic introduction to numerical simulation of stochastic differential equations. SIAM REVIEW 43, 525–546 (2001)
Szmolyan, P., Wechselberger, M.: Canards in R3. Journal of Differential Equations 177(2), 419–453 (2001)
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 2007 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Wang, J., Li, X., Feng, D. (2007). Comparisons of Chemical Synapses and Gap Junctions in the Stochastic Dynamics of Coupled Neurons. In: Li, K., Li, X., Irwin, G.W., He, G. (eds) Life System Modeling and Simulation. LSMS 2007. Lecture Notes in Computer Science(), vol 4689. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-74771-0_29
Download citation
DOI: https://doi.org/10.1007/978-3-540-74771-0_29
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-74770-3
Online ISBN: 978-3-540-74771-0
eBook Packages: Computer ScienceComputer Science (R0)