Development and transition of spiral wave in the coupled Hindmarsh--Rose neurons in two-dimensional space
Ma Jun(马军)a)b)†, Ying He-Ping(应和平)c), Liu Yong(刘勇)d), and Li Shi-Rong(李世荣)a)
a School of Science, Lanzhou University of Technology, Lanzhou 730050, China; b Department of Physics, Central China Normal University, Wuhan 430079, China; c Zhejiang Institute of Modern Physics in the Zhejiang University, Hangzhou 310027, China; d Department of Mathematics, Yancheng Teachers University, Yancheng 224009, China
Abstract The dynamics and the transition of spiral waves in the coupled Hindmarsh--Rose (H--R) neurons in two-dimensional space are investigated in the paper. It is found that the spiral wave can be induced and developed in the coupled HR neurons in two-dimensional space, with appropriate initial values and a parameter region given. However, the spiral wave could encounter instability when the intensity of the external current reaches a threshold value of 1.945. The transition of spiral wave is found to be affected by coupling intensity D and bifurcation parameter r. The spiral wave becomes sparse as the coupling intensity increases, while the spiral wave is eliminated and the whole neuronal system becomes homogeneous as the bifurcation parameter increases to a certain threshold value. Then the coupling action of the four sub-adjacent neurons, which is described by coupling coefficient D’, is also considered, and it is found that the spiral wave begins to breakup due to the introduced coupling action from the sub-adjacent neurons (or sites) and together with the coupling action of the nearest-neighbour neurons, which is described by the coupling intensity D.
Received: 12 June 2008
Revised: 30 August 2008
Accepted manuscript online:
Fund: Project supported by
the National Natural Science Foundation of China (Grant Nos
10747005, 10572056 and 10774130), and the Natural Science Foundation
of Lanzhou University, China (Grant No Q200706).
Cite this article:
Ma Jun(马军), Ying He-Ping(应和平), Liu Yong(刘勇), and Li Shi-Rong(李世荣) Development and transition of spiral wave in the coupled Hindmarsh--Rose neurons in two-dimensional space 2009 Chin. Phys. B 18 98
Altmetric calculates a score based on the online attention an article receives. Each coloured thread in the circle represents a different type of online attention. The number in the centre is the Altmetric score. Social media and mainstream news media are the main sources that calculate the score. Reference managers such as Mendeley are also tracked but do not contribute to the score. Older articles often score higher because they have had more time to get noticed. To account for this, Altmetric has included the context data for other articles of a similar age.
