Research Article | Open Access
Transition of Firing Patterns in a Complex Neural Network
We study the effects of random long-range connections (shortcuts) on the firing patterns in a network composed of Hindmarsh-Rose neurons. It is found that the system can achieve the transition of neural firing patterns from the lower period state to the higher one, when the number of shortcuts in the neural network is greater than a threshold, indicating that the nervous system may make the optimal response to the change of stimulation by a corresponding adjustment of the shortcuts. Then we discuss the transition degree of firing patterns of neural network and its critical characteristics for different external stimulation current. Furthermore, the influences of coupling strength on such transition behavior of neural firing patterns are also considered. Our results may be useful in comprehending the real mechanism in neural coding and information transmission in neurobiological systems.
- S. H. Strogatz, “Exploring complex networks,” Nature, vol. 410, no. 6825, pp. 268–276, 2001.
- R. Albert and A.-L. Barabási, “Statistical mechanics of complex networks,” Reviews of Modern Physics, vol. 74, no. 1, pp. 47–97, 2002.
- S. N. Dorogovtsev and J. F. F. Mendes, “Evolution of networks,” Advances in Physics, vol. 51, no. 4, pp. 1079–1187, 2002.
- S. Boccaletti, V. Latora, Y. Moreno, M. Chavez, and D.-U. Hwang, “Complex networks: structure and dynamics,” Physics Reports, vol. 424, no. 4-5, pp. 175–308, 2006.
- D. J. Watts, Small Worlds, Princeton University Press, Princeton, NJ, USA, 1999.
- D. J. Watts and S. H. Strogatz, “Collective dynamics of ‘small-world’ networks,” Nature, vol. 393, no. 6684, pp. 440–442, 1998.
- H. Hasegawa, “Synchronizations in small-world networks of spiking neurons: diffusive versus sigmoid couplings,” Physical Review E, vol. 72, no. 5, Article ID 056139, 8 pages, 2005.
- X. Wang, Y. Lu, M. Jiang, and Q. Ouyang, “Attraction of spiral waves by localized inhomogeneities with small-world connections in excitable media,” Physical Review E, vol. 69, no. 5, Article ID 056223, 5 pages, 2004.
- L. G. Morelli, G. Abramson, and M. N. Kuperman, “Associative memory on a small-world neural network,” European Physical Journal B, vol. 38, no. 3, pp. 495–500, 2004.
- D. He, G. Hu, M. Zhan, W. Ren, and Z. Gao, “Pattern formation of spiral waves in an inhomogeneous medium with small-world connections,” Physical Review E, vol. 65, no. 5, Article ID 055204, 4 pages, 2002.
- D. S. Bassett and E. Bullmore, “Small-world brain networks,” Neuroscientist, vol. 12, no. 6, pp. 512–523, 2006.
- A. Longtin, A. Bulsara, and F. Moss, “Time-interval sequences in bistable systems and the noise-induced transmission of information by sensory neurons,” Physical Review Letters, vol. 67, no. 5, pp. 656–659, 1991.
- W. Gerstner and W. M. Kistler, Spiking Neuron Models, Cambridge University Press, Cambridge, UK, 2002.
- S. F. Huang, J. Q. Zhang, and S. J. Ding, “State-to-state transitions in a Hindmarsh-Rose neuron system,” Chinese Physics Letters, vol. 26, no. 5, Article ID 050502, p. 4, 2009.
- M.-S. Li, Q.-S. Lu, L.-X. Duan, and Q.-Y. Wang, “Firing patterns and transitions in coupled neurons controlled by a pacemaker,” Chinese Physics Letters, vol. 25, no. 8, pp. 2806–2808, 2008.
- Z. Yang and Q. Lu, “Transitions from bursting to spiking due to depolarizing current in the Chay neuronal model,” Communications in Nonlinear Science and Numerical Simulation, vol. 12, no. 3, pp. 357–365, 2007.
- H. Gu, M. H. Yang, L. Li, Z. Liu, and W. Ren, “Noise induced multi-mode neural firings in a period adding bifurcation scenario,” International Journal of Modern Physics B, vol. 17, no. 22–24, pp. 4195–4200, 2003.
- 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.
- O. Kwon and H.-T. Moon, “Coherence resonance in small-world networks of excitable cells,” Physics Letters A, vol. 298, no. 5-6, pp. 319–324, 2002.
- M. Lin and T. Chen, “Self-organized criticality in a simple model of neurons based on small-world networks,” Physical Review E, vol. 71, no. 1, Article ID 016133, 5 pages, 2005.
- P. Checco, M. Righero, M. Biey, and L. Kocarev, “Synchronization in Networks of Hindmarsh-Rose Neurons,” IEEE Transactions on Circuits and Systems II, vol. 55, no. 12, pp. 1274–1278, 2008.
- J.-Q. Zhang, Z.-H. Hou, and H.-W. Xin, “Neural signal tuned by random long-range connections in coupled FitzHugh-Nagumo neurons systems,” Chinese Physics Letters, vol. 23, no. 9, pp. 2364–2367, 2006.
- Q. Li and Y. Gao, “Control of spiking regularity in a noisy complex neural network,” Physical Review E, vol. 77, no. 3, Article ID 036117, 8 pages, 2008.
- J. L. Hindmarsh and R. M. Rose, “A model of neuronal bursting using three coupled first order differential equations,” Proceedings of the Royal Society of London. Series B, vol. 221, no. 1222, pp. 87–102, 1984.
- W. Wang, Y. Wang, and Z. D. Wang, “Firing and signal transduction associated with an intrinsic oscillation in neuronal systems,” Physical Review E, vol. 57, no. 3, supplement A, pp. R2527–R2530, 1998.
- W. Wang, G. Perez, and H. A. Cerdeira, “Dynamical behavior of the firings in a coupled neuronal system,” Physical Review E, vol. 47, no. 4, pp. 2893–2898, 1993.
- M. Bucolo, L. Fortuna, and M. La Rosa, “Network self-organization through “small-worlds” topologies,” Chaos, Solitons and Fractals, vol. 14, no. 7, pp. 1059–1064, 2002.
- M. Wang, Z. Hou, and H. Xin, “Ordering spatiotemporal chaos in small-world neuron networks,” ChemPhysChem, vol. 7, no. 3, pp. 579–582, 2006.
- Y. H. Zheng and Q. S. Lu, “Spatiotemporal patterns and chaotic burst synchronization in a small-world neuronal network,” Physica A, vol. 387, no. 14, pp. 3719–3728, 2008.
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