Table of Contents Author Guidelines Submit a Manuscript
Discrete Dynamics in Nature and Society
Volume 2014, Article ID 173894, 8 pages
http://dx.doi.org/10.1155/2014/173894
Research Article

Noise and Synchronization Analysis of the Cold-Receptor Neuronal Network Model

1Institute for Cognitive Neurodynamics, School of Science, East China University of Science and Technology, Shanghai 200237, China
2School of Information Science and Technology, Civil Aviation University of China, Tianjin 300300, China

Received 27 January 2014; Accepted 25 May 2014; Published 15 June 2014

Academic Editor: Wenwu Yu

Copyright © 2014 Ying Du et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. W. Horsthemke and R. Lefever, Noise-Induced Transitions: Theory and Applications in Physics, Chemistry and Biology, vol. 15 of Springer Series in Synergetics, Springer, Berlin, Germany, 1984. View at MathSciNet
  2. 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. View at Google Scholar · View at Scopus
  3. P. Channell, G. Cymbalyuk, and A. Shilnikov, “Origin of bursting through homoclinic spike adding in a neuron model,” Physical Review Letters, vol. 98, no. 13, Article ID 134101, 2007. View at Publisher · View at Google Scholar · View at Scopus
  4. D. Linaro, A. Champneys, M. Desroches, and M. Storace, “Codimension-two homoclinic bifurcations underlying spike adding in the Hindmarsh-Rose Burster,” SIAM Journal on Applied Dynamical Systems, vol. 11, no. 3, pp. 939–962, 2012. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  5. R. Benzi, A. Sutera, and A. Vulpiani, “The mechanism of stochastic resonance,” Journal of Physics A, vol. 14, no. 11, pp. L453–L457, 1981. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  6. W. J. Freeman, “Deep analysis of perception through dynamic structures that emerge in cortical activity from self-regulated noise,” Cognitive Neurodynamics, vol. 3, no. 1, pp. 105–116, 2009. View at Publisher · View at Google Scholar · View at Scopus
  7. B. Lindner, J. García-Ojalvo, A. Neiman, and L. Schimansky-Geier, “Effects of noise in excitable systems,” Physics Reports, vol. 392, no. 6, pp. 321–424, 2004. View at Publisher · View at Google Scholar · View at Scopus
  8. M. Yang, Z. Liu, L. Li et al., “Identifying distinct stochastic dynamics from chao: a study on multimodal neural firing patterns,” International Journal of Bifurcation and Chaos, vol. 19, no. 2, pp. 453–485, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  9. J. Mo, Y.-Y. Li, C.-L. Wei et al., “Interpreting a period-adding bifurcation scenario in neural bursting patterns using border-collision bifurcation in a discontinuous map of a slow control variable,” Chinese Physics B, vol. 19, no. 8, Article ID 080513, 2010. View at Publisher · View at Google Scholar · View at Scopus
  10. H. Gu, M. Yang, L. Li, Z. Liu, and W. Ren, “Dynamics of autonomous stochastic resonance in neural period adding bifurcation scenarios,” Physics Letters A, vol. 319, no. 1-2, pp. 89–96, 2003. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  11. Q. Lu, Z. Yang, L. Duan, H. Gu, and W. Ren, “Dynamics and transitions of firing patterns in deterministic and stochastic neuronal systems,” Chaos, Solitons & Fractals, vol. 40, no. 2, pp. 577–597, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  12. Q. Lu, H. Gu, Z. Yang, X. Shi, L. Duan, and Y. Zheng, “Dynamics of firing patterns, synchronization and resonances in neuronal electrical activities: experiments and analysis,” Acta Mechanica Sinica, vol. 24, no. 6, pp. 593–628, 2008. View at Publisher · View at Google Scholar · View at Scopus
  13. H. A. Braun, M. T. Huber, M. Dewald, K. Schäfer, and K. Voigt, “Computer simulations of neuronal signal transduction: the role of nonlinear dynamics and noise,” International Journal of Bifurcation and Chaos, vol. 8, no. 5, pp. 881–889, 1998. View at Google Scholar · View at Scopus
  14. H. A. Braun, K. Schafer, K. Voigt et al., “Low-dimensional dynamics in sensory biology 1: thermally sensitive electroreceptors of the catfish,” Journal of Computational Neuroscience, vol. 4, no. 4, pp. 335–347, 1997. View at Publisher · View at Google Scholar · View at Scopus
  15. H. A. Braun, M. T. Huber, N. Anthes et al., “Noise-induced impulse pattern modifications at different dynamical period-one situations in a computer model of temperature encoding,” BioSystems, vol. 62, no. 1–3, pp. 99–112, 2001. View at Publisher · View at Google Scholar · View at Scopus
  16. H. A. Braun, K. Voigt, and M. T. Huber, “Oscillations, resonances and noise: basis of flexible neuronal pattern generation,” BioSystems, vol. 71, no. 1-2, pp. 39–50, 2003. View at Publisher · View at Google Scholar · View at Scopus
  17. H.-G. Gu, B. Jia, and G.-R. Chen, “Experimental evidence of a chaotic region in a neural pacemaker,” Physics Letters A, vol. 377, no. 9, pp. 718–720, 2013. View at Publisher · View at Google Scholar · View at Scopus
  18. H. Gu, “Experimental observation of transition from chaotic bursting to chaotic spiking in a neural pacemaker,” Chaos, vol. 23, no. 2, Article ID 023126, 2013. View at Publisher · View at Google Scholar · View at Scopus
  19. H. Gu, W. Ren, Q. Lu, S. Wu, M. Yang, and W. Chen, “Integer multiple spiking in neuronal pacemakers without external periodic stimulation,” Physics Letters A, vol. 285, no. 1-2, pp. 63–68, 2001. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  20. H. Gu, B. Jia, and Q. Lu, “Exponential decay characteristics of the stochastic integer multiple neural firing patterns,” Cognitive Neurodynamics, vol. 5, no. 1, pp. 87–101, 2011. View at Publisher · View at Google Scholar · View at Scopus
  21. A. Pikovsky, M. Rosenblum, and J. Kurths, Synchronization: A Universal Concept in Nonlinear Scicencs, Cambridge Nonlinear Science Series, Cambridge Unversity Ress, New York, NY, USA, 2001. View at Publisher · View at Google Scholar · View at MathSciNet
  22. A. P. Davison, J. Feng, and D. Brown, “Spike synchronization in a biophysically-detailed model of the olfactory bulb,” Neurocomputing, vol. 38-40, pp. 515–521, 2001. View at Publisher · View at Google Scholar · View at Scopus
  23. W. Singer, Time as Coding Space in Neocortical Processing, Springer, Berlin, Germany, 1994.
  24. R. Eckhorn, “Neural mechanisms of scene segmentation: recordings from the visual cortex suggest basic circuits for linking field models,” IEEE Transactions on Neural Networks, vol. 10, no. 3, pp. 464–479, 1999. View at Publisher · View at Google Scholar · View at Scopus
  25. S. Postnova, K. Voigt, and H. A. Braun, “Neural synchronization at tonic-to-bursting transitions,” Journal of Biological Physics, vol. 33, no. 2, pp. 129–143, 2007. View at Publisher · View at Google Scholar · View at Scopus
  26. M. Nomura, T. Fukai, and T. Aoyagi, “Synchrony of fast-spiking interneurons interconnected by GABAergic and electrical synapses,” Neural Computation, vol. 15, no. 9, pp. 2179–2198, 2003. View at Publisher · View at Google Scholar · View at Scopus
  27. W. J. Freeman, Neurodynamics: An Exploration in Mesoscopic Brain Dynamics, Springer, London, UK, 2000.
  28. S. Postnova, C. Finke, W. Jin, H. Schneider, and H. A. Braun, “A computational study of the interdependencies between neuronal impulse pattern, noise effects and synchronization,” Journal of Physiology, vol. 104, no. 3-4, pp. 176–189, 2010. View at Publisher · View at Google Scholar · View at Scopus
  29. Y. D. Sato and M. Shiino, “Generalization of coupled spiking models and effects of the width of an action potential on synchronization phenomena,” Physical Review E, vol. 75, no. 1, Article ID 011909, 15 pages, 2007. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  30. Q. Y. Wang, Q. S. Lu, and Z. S. Duan, “Adaptive lag synchronization in coupled chaotic systems with unidirectional delay feedback,” International Journal of Non-Linear Mechanics, vol. 45, no. 6, pp. 640–646, 2010. View at Publisher · View at Google Scholar · View at Scopus
  31. W. Yu, J. Cao, and W. Lu, “Synchronization control of switched linearly coupled neural networks with delay,” Neurocomputing, vol. 73, no. 4-6, pp. 858–866, 2010. View at Publisher · View at Google Scholar · View at Scopus
  32. Y.-Q. Che, J. Wang, K.-M. Tsang, and W.-L. Chan, “Unidirectional synchronization for Hindmarsh-Rose neurons via robust adaptive sliding mode control,” Nonlinear Analysis: Real World Applications, vol. 11, no. 2, pp. 1096–1104, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  33. Y. Hao, Y. Gong, X. Lin, Y. Xie, and X. Ma, “Transition and enhancement of synchronization by time delays in stochastic Hodgkin-Huxley neuron networks,” Neurocomputing, vol. 73, no. 16-18, pp. 2998–3004, 2010. View at Publisher · View at Google Scholar · View at Scopus
  34. J. Ma, F. Li, L. Huang, and W.-Y. Jin, “Complete synchronization, phase synchronization and parameters estimation in a realistic chaotic system,” Communications in Nonlinear Science and Numerical Simulation, vol. 16, no. 9, pp. 3770–3785, 2011. View at Publisher · View at Google Scholar · View at Scopus
  35. T. Kreuz, D. Chicharro, R. G. Andrzejak, J. S. Haas, and H. D. I. Abarbanel, “Measuring multiple spike train synchrony,” Journal of Neuroscience Methods, vol. 183, no. 2, pp. 287–299, 2009. View at Publisher · View at Google Scholar · View at Scopus
  36. T. Kreuz, J. S. Haas, A. Morelli, H. D. I. Abarbanel, and A. Politi, “Measuring spike train synchrony,” Journal of Neuroscience Methods, vol. 165, no. 1, pp. 151–161, 2007. View at Publisher · View at Google Scholar · View at Scopus
  37. R. F. Fox, I. R. Gatland, R. Roy, and G. Vemuri, “Fast, accurate algorithm for numerical simulation of exponentially correlated colored noise,” Physical Review A, vol. 38, no. 11, pp. 5938–5940, 1988. View at Publisher · View at Google Scholar · View at Scopus