Abstract
In the paper, based on the neurodynamics theory and the existing neuron synchronization’s research findings, the dynamic phase function which can describe the neuron’s discharge characteristics is defined and revised, and the neuron synchronization decision algorithm and procedure based on the dynamic phase function is put forward. The synchronization characteristics and rule of the two uncoupled HR neurons are discussed by the synchronization decision algorithm. Compared with other decision indexes and algorithms, the neuron synchronization decision algorithm based on the dynamic phase function can not only judge the three common synchronization types: asynchronization, the generalized synchronization, and the phase synchronization, but also quantitatively solve the critical value of the neurons’ realizing synchronization such as the stimulation current amplitude.
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
Izhikevich, E.M.: Dynamical Systems in Neuroscience: The Geometry of Excitability and Bursting. The MIT Press (2005)
Neiman, A.B., Russell, D.F.: Synchronization of noise-induced bursts in noncoupled sensory neurons. Phys. Rev. Lett. 88(13), 138103-1–138103-4 (2002)
He, D., Shi, P., Stone, L.: Noise-induced synchronization in realistic models. Physical Review: E 67(2), 0272011–0272013 (2003)
Schafer, C., Rosenblum, M.G., Abel, H.H., et al.: Synchronization in the human cardiorespiratory system. Phys. Rev. E 60(1), 857–870 (1999)
Park, J.H.: Chaos synchronization between two different chaotic dynamical systems. Chaos, Solitons & Fractals 27(2), 549–554 (2006)
Rosemblum, M.G., Pikovsky, A.S., Kurths, J.: Phase Synchronization of Chaotic Oscillators. Chaos Phys. Rev. Lett. 76, 1804–1808 (1996)
Roscnblm, M.G., Pikovsky, A.S., Kurths, J.: From Phase to Lag Synchronization in Coupled Chaotic Oscillators. Phys. Rev. Lett. 78, 4193–4197 (1997)
Kocarev, L., Parlitz, U.: General Approach for Chaotic Synchronization with Applications to Communication. Phys. Rev. Lett. 74, 5028–5032 (1995)
Rulkov, N.F., Sushchik, M.M., Tsimring, L.S., et al.: Generalized synchronization of chaos in directionally coupled chaotic systems. Phys. Rev. E 51, 980–984 (1995)
Lee, D.-S., Kye, W.-H., Rim, S., Kwon, T.-Y., Kim, C.-M.: Generalized Phase Synchronization In Unidirectionally Coupled Chaotic Oscillators. Phys. Rev. E 67, 045201 (2003)
Zaks, M.A., Park, E.H., Rosenblum, M.G., et al.: Alternating Locking Ratios in Imperfect Phase Synchronization. Phys. Rev. Lett. 82, 4228–4232 (1999)
Shuai, J.-W., Durand, D.M.: Phase synchronization in two coupled chaotic neurons. Physics Letters: A 264(12), 289–296 (1999)
Wu, Y., Xu, J., He, D., Jin, W.: Study on nonlinear characteristic of two synchronizing uncoupled Hindmarsh-Rose neurons. Acta Physica Sinica 54(7), 3457–3464 (2005)
Hindmarsh, J.L., Rose, R.M.: A mode of the nerve impulse using two first-order differential equation. Nature 296, 162–164 (1982)
Hindmarsh, J.L., Rose, R.M.: A mode of neuronal bursting using three coupled first order differential equations. Proceedings of the Royal Society of London, Series B, Biological Sciences 221(1222), 87–102 (1984)
Rosenblum, M.G., Pikovsky, A.S., Kurths, J.: Phys. Rev. Lett. 76, 1804 (1996)
Osipov, G.V., Pikovsky, A.S., Rosenblum, M.G., Kurths, J.: Phys. Rev. E 55, 2353 (1997)
Rosenblum, M.G., Pikovsky, A.S., Kurths, J.: Phys. Rev. Lett. 78, 4193 (1997)
Pikovsky, A.S., Rosenblum, M.G., Osipov, G.V., Kurths, J.: Physica D 104, 219 (1997)
Lee, K.J., Kwak, Y., Lim, T.K.: Phys. Rev. Lett. 81, 321 (1998)
Peng, Y., Jian, Z., Wang, J.: Study on Discharge Patterns of Hindmarsh-Rose Neurons Under Slow Wave Current Stimulation. In: Jiao, L., Wang, L., Gao, X.-b., Liu, J., Wu, F. (eds.) ICNC 2006. LNCS, vol. 4221, pp. 127–134. Springer, Heidelberg (2006)
Peng, Y., et al.: Synchrony of two uncoupled neurons under half wave sine current stimulation. Communications in Nonlinear Science and Numerical Simulation 14(4), 1570–1575 (2009)
Peng, Y.: Study on the Synchrony Intensity Threshold of Two Uncoupled Neurons under Different Currents’ Stimulation. In: Liu, D., Zhang, H., Polycarpou, M., Alippi, C., He, H. (eds.) ISNN 2011, Part I. LNCS, vol. 6675, pp. 42–51. Springer, Heidelberg (2011)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2012 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
He, X., Peng, Y. (2012). Study on Decision Algorithm of Neurons’ Synchronization Based on Neurodynamics. In: Wang, J., Yen, G.G., Polycarpou, M.M. (eds) Advances in Neural Networks – ISNN 2012. ISNN 2012. Lecture Notes in Computer Science, vol 7367. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-31346-2_26
Download citation
DOI: https://doi.org/10.1007/978-3-642-31346-2_26
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-31345-5
Online ISBN: 978-3-642-31346-2
eBook Packages: Computer ScienceComputer Science (R0)