在一些缓慢快速的混乱系统中,振荡的可靠性和稳定性
Jonathan Jaquette1,2,3, Sonal Kedia3,4, Evelyn Sander5
1Department of Mathematics and Statistics, Boston University, Boston, Massachusetts 02215, USA.
Chaos (Woodbury, N.Y.)
|October 24, 2023
概括
生物系统表现出平衡,但非线性模型显示混乱的行为. 这项研究协调了多时间尺度系统中的混乱和稳态,发现了与生理功能相一致的规律宏观动态.
科学领域:
- 神经科学是一个神经科学.
- 复杂系统生物学 复杂系统生物学
- 动态系统理论 动态系统理论
背景情况:
- 生物系统经常表现出显著的稳定性 (恒常性),尽管非线性动力学会导致混乱的行为.
- 在理解生理调节方面,调和生物系统中混乱和稳态之间的明显矛盾至关重要.
- 类中央模式生成器 (CPG) 提供了一个模型系统,具有与此问题相关的多时间尺度动态.
研究的目的:
- 提出一种精细的混沌定义,弥合混沌动态和生物平衡之间的差距.
- 研究多个时间尺度的系统如何在宏观层面上表现出规律,尽管存在潜在的混乱吸引力.
- 在生物模型中确定正规和不稳定动态之间的过渡机制.
主要方法:
- 分析具有多个时间尺度的非线性模型,重点关注表现出放松周期和混乱吸引力的系统.
- 在鲁尔科夫地图中详细检查混乱的吸引力危机和全球分叉,一个神经元模型.
- 跨多种模型的数值验证,包括甲动物CPG网络,离散立方图和连续流系统.
主要成果:
- 具有穿越混乱吸引子的放松周期的系统表现出宏观的规律性,与生理功能保持一致.
- 全球分叉,特别是混乱吸引力的危机,可以导致这种规律性的破坏,导致不规则的缓慢时间尺度活动.
- 缓慢的放松周期通过混乱的吸引力危机被确定为动态过渡的一般机制.
结论:
- 对混沌的精细理解,包括多个时间尺度的动态,可以解释混沌和稳态在生物系统中的共存.
- 混乱的吸引力危机提供了一个强大的机制,用于在规律的,如同静态的行为和不稳定的动态之间切换.
- 这些发现对理解神经网络功能和其他复杂的生物过程有影响.
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