通过洛伦茨地图分析基于地图的神经元模型的动态
Piotr Bartłomiejczyk1, Frank Llovera Trujillo2, Justyna Signerska-Rynkowska1,3
1Faculty of Applied Physics and Mathematics & BioTechMed Centre, Gdańsk University of Technology, Gabriela Narutowicza 11/12, 80-233 Gdańsk, Poland.
Chaos (Woodbury, N.Y.)
|April 1, 2024
概括
这项研究使用立方多项式来模拟神经细胞,揭示了扩展的洛伦茨地图,解释了复杂的尖端模式和神经元行为. 这些发现增强了我们对神经元动力学和混沌理论应用的理解.
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
- 数学生物学 数学生物学
背景情况:
- 对神经元电压动态的准确建模对于理解神经元功能至关重要.
- 之前的模型,如库尔贝奇等人. 这是一个离散的神经元模型,利用了零碎的线性函数.
- 改进这些模型可以揭示更复杂的行为,并提高预测能力.
研究的目的:
- 用立方多项式电压动态分析修改的离散神经元模型的行为.
- 为了研究由这种修改产生的混乱和周期性行为.
- 用动态系统理论来描述神经元尖端模式的复杂性.
主要方法:
- 在离散神经元模型中,用立方多项式取代零碎线性函数.
- 在一个多维参数空间中分析系统的返回地图.
- 应用和扩展洛伦兹类理论和扩展洛伦兹映射.
主要成果:
- 证明神经元模型的返回地图是一个在一个显著参数空间子集上扩展的洛伦兹地图.
- 在修改模型中描述混乱和周期性行为.
- 将系统的动态与观察到的尖端模式的复杂性联系起来.
结论:
- 立方多项式修改为神经元建模提供了更丰富的框架.
- 已识别的扩展的洛伦兹地图动态为神经元信号复杂性提供了洞察力.
- 这项工作将计算神经科学和动态系统联系起来,以更深入地了解神经元功能.
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