超扩散合神经元系统中的同步过渡:仿真体,孤独状态和相波的相互作用
1P.N. Lebedev Physical Institute of the Russian Academy of Sciences, 53 Leninskiy Prospekt, Moscow 119991, Russian Federation.
Chaos (Woodbury, N.Y.)
|September 23, 2024
概括
这项研究探讨了神经网络同步使用微积分计算,揭示复杂的过渡和多样化的动态状态,如喜梅拉状态和相波. 研究结果将网络拓与内部动态联系起来,有助于神经科学研究.
科学领域:
- 计算神经科学是一种神经科学.
- 复杂系统理论 复杂系统理论
- 分数微积分的计算.
背景情况:
- 神经网络表现出复杂的动态,包括同步现象.
- 了解这些动态对于神经科学和其他复杂系统至关重要.
研究的目的:
- 在一个双组分神经网络模型中研究同步过渡.
- 分析断片拉普拉斯运算子在合配置中的作用.
- 在参数空间内绘制不同的动态状态.
主要方法:
- 采用了两个组件的反应超扩散系统,使用了分数拉普拉斯运算符.
- 在非线性神经元动力学中采用了Hindmarsh-Rose模型.
- 在分数指数空间研究了同步过渡.
主要成果:
- 确定了均和不均同步过渡的区域.
- 描述了嵌合体状态,孤独状态和相波的参数区域.
- 观察到与部分同步模式相关的丝状结构.
结论:
- 分数指数显著影响网络动态和同步模式.
- 网络拓学的变化与内部动态相关,为神经科学提供了洞察力.
- 这些方法适用于各种自然科学学科.
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