在基于行为性的自适指数的整合和火模型中,断续性诱导的动态
Mathieu Desroches1,2, Piotr Kowalczyk3, Serafim Rodrigues2,4
1MathNeuro Project-Team, Inria Branch of the University of Montpellier, Montpellier, France.
Bulletin of mathematical biology
|November 14, 2024
概括
本研究探讨了基于行为性的自适应指数 (CAdEx) 模型,揭示了其多个时间尺度如何通过不连续性诱导的分叉和卡纳德解决方案驱动独特的尖端和爆裂行为.
科学领域:
- 计算神经科学是一种计算神经科学.
- 神经动力学的数学建模 神经动力学的数学建模
背景情况:
- 以行为为基础的自适应指数 (CAdEx) 整合和发射模型对于理解神经元刺激性至关重要.
- 它的动态受到多个时间尺度的影响,但塑造其政权的精确机制仍然不完全理解.
研究的目的:
- 通过计算来研究CAdEx模型的多个时间尺度的性质.
- 为了阐明这种特征如何塑造模型的尖和延迟爆裂模式.
主要方法:
- 使用COCO软件包进行数值分叉分析.
- 详细检查不连续性诱导的分叉和卡纳德解决方案.
主要成果:
- 尖端和延迟爆发的模式是由与多个时间尺度相关的不连续性诱导的分叉引发的.
- 尖端增量过渡发生,伴随着折叠和周期翻倍的分叉,沿周期溶液的孤立组织.
- 一个同临床的分叉结束一个canard爆炸,与重置一起,组织了延迟爆破制度.
结论:
- CAdEx模型的多个时间尺度方面对其复杂的动态行为至关重要.
- 不连续性诱导的分叉和卡纳德解决方案在产生独特的发射模式方面发挥着关键作用.
- 这一分析提供了对CadEx模型的制度的精确机制理解.
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