Slow-fast effect and generation mechanism of brusselator based on coordinate transformation
Slow-fast effect and generation mechanism of brusselator based on coordinate transformation
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DOI：
10.1515/phys-2016-0032
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发表时间：
2016
期刊：
影响因子：
1.9
通讯作者：
Xianghong Li;Jingyu Hou;Yongjun Shen
中科院分区：
文献类型：
--
作者：
Xianghong Li;Jingyu Hou;Yongjun Shen
摘要 研究了具有不同时间尺度的经典慢-快效应的Brusselator，其特征在于静态和尖峰状态的耦合。为了利用慢-快分析方法揭示其生成机制，在经典Brusselator中引入坐标变换，使得变换后的系统可以分为快子系统和慢子系统。进一步分析了快速子系统的稳定性条件和分岔现象，并分别通过理论分析和数值模拟给出了不同平衡点的吸引域。基于变换后的系统，可以发现静止态和尖峰态之间的生成机制是折叠分岔和快速子系统吸引域的变化。结果对于具有多个时间尺度的类似系统也可能有帮助。
Abstract The Brusselator with different time scales, which behaves in the classical slow-fast effect, is investigated, and is characterized by the coupling of the quiescent and spiking states. In order to reveal the generation mechanism by using the slow-fast analysis method, the coordinate transformation is introduced into the classical Brusselator, so that the transformed system can be divided into the fast and slow subsystems. Furthermore, the stability condition and bifurcation phenomenon of the fast subsystem are analyzed, and the attraction domains of different equilibria are presented by theoretical analysis and numerical simulation respectively. Based on the transformed system, it could be found that the generation mechanism between the quiescent and spiking states is Fold bifurcation and change of the attraction domain of the fast subsystem. The results may also be helpful to the similar system with multiple time scales.