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在三次尺度合的莫里斯-莱卡系统中混合模式振荡
Ngoc Anh Phan1, Yangyang Wang2
1Department of Mathematics, University of Iowa, Iowa City, Iowa 52242, USA.
Chaos (Woodbury, N.Y.)
|May 8, 2024
概括
在三次尺度系统中,混合模式振荡 (MMO) 具有更强大的canard-delayed-Hopf (CDH) 奇点. 了解这些复杂的动力学揭示了和延迟的安德罗诺夫-霍夫分叉机制如何相互作用.
科学领域:
- 计算神经科学是一种神经科学.
- 动态系统理论 动态系统理论
- 非线性动力学是一种非线性动力学.
背景情况:
- 混合模式振荡 (MMO) 是多时间尺度系统中的复杂行为,其特点是交替的大小振荡.
- 在两个时间尺度系统中,MMOs通常来自canard机制或延迟的Andronov-Hopf分叉 (DHB).
- 三次尺度系统中的MMOs相对于其两次尺度的对应物来说,理解程度仍然较低.
研究的目的:
- 为了研究三种不同的时间尺度的合莫里斯-莱卡神经元中MMO背后的机制.
- 在存在或没有canard-delayed-Hopf (CDH) 奇点的情况下分析MMOs.
- 探索时间尺度变化对MMO特征和机制的影响.
主要方法:
- 用三个不同的时间尺度对联的莫里斯-莱卡神经元模型的数值模拟.
- 在存在canard-delayed-Hopf (CDH) 奇点的情况下对MMOs的分析.
- 对有CDH和没有CDH的MMOs进行比较研究,检查对时间尺度变化的稳定性.
主要成果:
- 由CDH奇点支持的MMOs与没有它的MMOs相比,表现出明显更大的稳定性.
- 仅仅CDH的存在并不能保证MMOs的发生.
- 时间尺度的变化影响了MMOs的特征和潜在机制.
结论:
- 在三次时间尺度系统中,canard和DHB机制之间的相互作用可以产生更强大的MMOs,特别是在时间尺度变化方面.
- 在复杂的神经系统中,CDH奇点在增强MMO的稳定性方面发挥着至关重要的作用.
- 这项研究提供了对有利于在多时间尺度神经元动态中强大的MMOs条件的关键见解.
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