嵌合体状态在一个超扩散合的神经元链中
1P.N. Lebedev Physical Institute of the Russian Academy of Sciences, 53 Leninskiy Prospekt, Moscow 119991, Russian Federation.
Chaos (Woodbury, N.Y.)
|October 13, 2023
概括
使用分数拉普拉斯运算符的超扩散方程可以在神经元模型中实现嵌合体状态. 局部合导致同步行为,而分数指数控制着奇默的进化和不连贯性.
科学领域:
- 计算神经科学是一种神经科学.
- 复杂系统动力学 复杂系统动力学
- 数学生物学 数学生物学
背景情况:
- 动作潜力的传播是神经通信的基础.
- 了解神经网络中像喜梅拉状态这样的新兴行为至关重要.
- 非局部相互作用和超扩散现象在生物系统中越来越多地得到认可.
研究的目的:
- 研究超扩散的神经系统中奇默状态的出现和特征.
- 分析非局部合的作用,特别是分数拉普拉斯运算子,在支持嵌合体状态.
- 检查神经元激活特性和系统维度对嵌合体动态的影响.
主要方法:
- 分析超扩散方程的两组和三组分系统.
- 使用Hindmarsh-Rose非线性函数建模神经元动态.
- 使用分数拉普拉斯运算符来描述超扩散动力学和非局部合.
主要成果:
- 基于分数拉普拉斯运算符的非局部合支持虚幻状态.
- 局部合 (经典拉普拉斯运算符) 会导致同步的神经元行为.
- 奇梅拉状态的结构和进化显著依赖于分数拉普拉斯指数,表明非局部性的重要性.
结论:
- 分数超扩散动力学为非局部合的神经元中嵌合体状态的形成提供了一种机制.
- 由分数指数控制的非局部度决定了从连贯状态到不连贯状态的过渡.
- 引入额外的缓慢变量可能会导致复杂的过渡和中间奇默状态的形成.
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