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Synchronization transition of a coupled system composed of neurons with coexisting behaviors near a Hopf bifurcation |
| Jia Bing (贾冰) |
| Center for Computational System Biology, School of Mathematical Science, Fudan University, Shanghai 200433, China |
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Abstract The coexistence of a resting condition and period-1 firing near a subcritical Hopf bifurcation point, lying between the monostable resting condition and period-1 firing, is often observed in neurons of the central nervous systems. Near such a bifurcation point in the Morris-Lecar (ML) model, the attraction domain of the resting condition decreases while that of the coexisting period-1 firing increases as the bifurcation parameter value increases. With the increase of the coupling strength, and parameter and initial value dependent synchronization transition processes from non-synchronization to compete synchronization are simulated in two coupled ML neurons with coexisting behaviors: one neuron chosen as the resting condition and the other the coexisting period-1 firing. The complete synchronization is either a resting condition or period-1 firing dependent on the initial values of period-1 firing when the bifurcation parameter value is small or middle and is period-1 firing when the parameter value is large. As the bifurcation parameter value increases, the probability of the initial values of a period-1 firing neuron that lead to complete synchronization of period-1 firing increases, while that leading to complete synchronization of the resting condition decreases. It shows that the attraction domain of a coexisting behavior is larger, the probability of initial values leading to complete synchronization of this behavior is higher. The bifurcations of the coupled system are investigated and discussed. The results reveal the complex dynamics of synchronization behaviors of the coupled system composed of neurons with the coexisting resting condition and period-1 firing, and are helpful to further identify the dynamics of the spatiotemporal behaviors of the central nervous system.
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Received: 06 September 2013
Revised: 29 October 2013
Accepted manuscript online:
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PACS:
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05.45.Xt
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(Synchronization; coupled oscillators)
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87.18.Tt
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(Noise in biological systems)
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87.18.Hf
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(Spatiotemporal pattern formation in cellular populations)
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| Fund: Project supported by the National Natural Science Foundation of China (Grant No. 11072135). |
Corresponding Authors:
Jia Bing
E-mail: jiabing427@163.com,jiabing427@gmail.com
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| About author: 05.45.Xt; 87.18.Tt; 87.18.Hf |
Cite this article:
Jia Bing (贾冰) Synchronization transition of a coupled system composed of neurons with coexisting behaviors near a Hopf bifurcation 2014 Chin. Phys. B 23 050510
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