Average Synchronization and Temporal Order in a Noisy Neuronal Network with Coupling Delay
WANG Qing-Yun1,2, DUAN Zhi-Sheng1, LU Qi-Shao3
1State Key Laboratory for Turbulence and Complex Systems, Department of Mechanics and Aerospace Engineering, College of Engineering, Peking University, Beijing 1008712Department of Statistics and Mathematics, Inner Mongolia Finance and Economics College, Huhhot 0100513School of Science, Beijing University of Aeronautics and Astronautics, Beijing 100083
Average Synchronization and Temporal Order in a Noisy Neuronal Network with Coupling Delay
WANG Qing-Yun1,2;DUAN Zhi-Sheng1;LU Qi-Shao3
1State Key Laboratory for Turbulence and Complex Systems, Department of Mechanics and Aerospace Engineering, College of Engineering, Peking University, Beijing 1008712Department of Statistics and Mathematics, Inner Mongolia Finance and Economics College, Huhhot 0100513School of Science, Beijing University of Aeronautics and Astronautics, Beijing 100083
摘要Average synchronization and temporal order characterized by the rate of firing are studied in a spatially extended network system with the coupling time delay, which is locally modelled by a two-dimensional Rulkov map neuron. It is shown that there exists an optimal noise level, where average synchronization and temporal order are maximum irrespective of the coupling time delay. Furthermore, it is found that temporal order is weakened when the coupling time delay appears. However, the coupling time delay has a twofold effect on average synchronization, one associated with its increase, the other with its decrease. This clearly manifests that random perturbations and time delay play a complementary role in synchronization and temporal order.
Abstract：Average synchronization and temporal order characterized by the rate of firing are studied in a spatially extended network system with the coupling time delay, which is locally modelled by a two-dimensional Rulkov map neuron. It is shown that there exists an optimal noise level, where average synchronization and temporal order are maximum irrespective of the coupling time delay. Furthermore, it is found that temporal order is weakened when the coupling time delay appears. However, the coupling time delay has a twofold effect on average synchronization, one associated with its increase, the other with its decrease. This clearly manifests that random perturbations and time delay play a complementary role in synchronization and temporal order.
WANG Qing-Yun;DUAN Zhi-Sheng;LU Qi-Shao. Average Synchronization and Temporal Order in a Noisy Neuronal Network with Coupling Delay[J]. 中国物理快报, 2007, 24(10): 2759-2761.
WANG Qing-Yun, DUAN Zhi-Sheng, LU Qi-Shao. Average Synchronization and Temporal Order in a Noisy Neuronal Network with Coupling Delay. Chin. Phys. Lett., 2007, 24(10): 2759-2761.
[1] Gerstner W and Kistler W M 2002 Spiking Neuron Models(Cambridge: Cambridge University Press) [2] Izhikevich E M 2000 Int. J. Bifurcat. Chaos 10 117 [3] Balenzuela P and Garc\'{l-Ojalvo J 2005 Phys. Rev. E 021901 [4] Wang Q Y, Lu Q S and Chen G R 2007 Physica A 374 869 [5] Wang Q Y, Lu Q S and Chen G R 2006 Eur. J. Phys. B 54 255 [6] Perc M 2005 Phys. Rev. E 72 016207 [7] Perc M 2007 Chaos, Solitons and Fractals 31 280 [8] Dhamala M, Jirsa V K and Ding M Z 2004 Phys. Rev. Lett. 92 028101 [9] Wang Q Y and Lu Q S 2005 Chin. Phys. Lett. 22 1329 [10] Rulkov N F 2001 Phys. Rev. Lett. 86 183 [11]Pikovsky A S and Kurths J 1997 Phys. Rev. Lett. 78775
2007, Vol. 24 
