Complex transitions between spike, burst or chaos synchronization states in coupled neurons with coexisting bursting patterns

doi:10.1088/1674-1056/24/5/050505

中国物理B ›› 2015, Vol. 24 ›› Issue (5): 50505-050505.doi: 10.1088/1674-1056/24/5/050505

Complex transitions between spike, burst or chaos synchronization states in coupled neurons with coexisting bursting patterns

古华光^a, 陈胜根^a, 李玉叶^b

a School of Aerospace Engineering and Applied Mechanic, Tongji University, Shanghai 200092, China;
b Mathematics & Statistics Institute, Chifeng University, Chifeng 024000, China

收稿日期:2014-09-02 修回日期:2014-10-15 出版日期:2015-05-05 发布日期:2015-05-05
基金资助:
Project supported by the National Natural Science Foundation of China (Grant Nos. 11372224 and 11402039) and the Fundamental Research Funds for Central Universities designated to Tongji University (Grant No. 1330219127).

Complex transitions between spike, burst or chaos synchronization states in coupled neurons with coexisting bursting patterns

Gu Hua-Guang (古华光)^a, Chen Sheng-Gen (陈胜根)^a, Li Yu-Ye (李玉叶)^b

a School of Aerospace Engineering and Applied Mechanic, Tongji University, Shanghai 200092, China;
b Mathematics & Statistics Institute, Chifeng University, Chifeng 024000, China

Received:2014-09-02 Revised:2014-10-15 Online:2015-05-05 Published:2015-05-05
Contact: Gu Hua-Guang E-mail:guhuaguang@tongji.edu.cn
About author:05.45.Xt; 87.18.Tt; 87.18.Hf
Supported by:
Project supported by the National Natural Science Foundation of China (Grant Nos. 11372224 and 11402039) and the Fundamental Research Funds for Central Universities designated to Tongji University (Grant No. 1330219127).

摘要/Abstract

摘要： We investigated the synchronization dynamics of a coupled neuronal system composed of two identical Chay model neurons. The Chay model showed coexisting period-1 and period-2 bursting patterns as a parameter and initial values are varied. We simulated multiple periodic and chaotic bursting patterns with non-(NS), burst phase (BS), spike phase (SS), complete (CS), and lag synchronization states. When the coexisting behavior is near period-2 bursting, the transitions of synchronization states of the coupled system follows very complex transitions that begins with transitions between BS and SS, moves to transitions between CS and SS, and to CS. Most initial values lead to the CS state of period-2 bursting while only a few lead to the CS state of period-1 bursting. When the coexisting behavior is near period-1 bursting, the transitions begin with NS, move to transitions between SS and BS, to transitions between SS and CS, and then to CS. Most initial values lead to the CS state of period-1 bursting but a few lead to the CS state of period-2 bursting. The BS was identified as chaos synchronization. The patterns for NS and transitions between BS and SS are insensitive to initial values. The patterns for transitions between CS and SS and the CS state are sensitive to them. The number of spikes per burst of non-CS bursting increases with increasing coupling strength. These results not only reveal the initial value- and parameter-dependent synchronization transitions of coupled systems with coexisting behaviors, but also facilitate interpretation of various bursting patterns and synchronization transitions generated in the nervous system with weak coupling strength.

关键词: synchronization transition, phase synchronization, coexisting attractors, coupled neuronal system

Abstract: We investigated the synchronization dynamics of a coupled neuronal system composed of two identical Chay model neurons. The Chay model showed coexisting period-1 and period-2 bursting patterns as a parameter and initial values are varied. We simulated multiple periodic and chaotic bursting patterns with non-(NS), burst phase (BS), spike phase (SS), complete (CS), and lag synchronization states. When the coexisting behavior is near period-2 bursting, the transitions of synchronization states of the coupled system follows very complex transitions that begins with transitions between BS and SS, moves to transitions between CS and SS, and to CS. Most initial values lead to the CS state of period-2 bursting while only a few lead to the CS state of period-1 bursting. When the coexisting behavior is near period-1 bursting, the transitions begin with NS, move to transitions between SS and BS, to transitions between SS and CS, and then to CS. Most initial values lead to the CS state of period-1 bursting but a few lead to the CS state of period-2 bursting. The BS was identified as chaos synchronization. The patterns for NS and transitions between BS and SS are insensitive to initial values. The patterns for transitions between CS and SS and the CS state are sensitive to them. The number of spikes per burst of non-CS bursting increases with increasing coupling strength. These results not only reveal the initial value- and parameter-dependent synchronization transitions of coupled systems with coexisting behaviors, but also facilitate interpretation of various bursting patterns and synchronization transitions generated in the nervous system with weak coupling strength.

Key words: synchronization transition, phase synchronization, coexisting attractors, coupled neuronal system

中图分类号: (Synchronization; coupled oscillators)

05.45.Xt

87.18.Tt (Noise in biological systems) 87.18.Hf (Spatiotemporal pattern formation in cellular populations)

古华光, 陈胜根, 李玉叶. Complex transitions between spike, burst or chaos synchronization states in coupled neurons with coexisting bursting patterns[J]. 中国物理B, 2015, 24(5): 50505-050505.

Gu Hua-Guang (古华光), Chen Sheng-Gen (陈胜根), Li Yu-Ye (李玉叶). Complex transitions between spike, burst or chaos synchronization states in coupled neurons with coexisting bursting patterns[J]. Chin. Phys. B, 2015, 24(5): 50505-050505.

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Complex transitions between spike, burst or chaos synchronization states in coupled neurons with coexisting bursting patterns

Complex transitions between spike, burst or chaos synchronization states in coupled neurons with coexisting bursting patterns

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