时间延迟分数顺序大规模双循环神经网络模型与交叉合结构的稳定性和动态分析
概括
本研究介绍了一个大规模的分数顺序双循环神经网络模型. 时间延迟显著影响Hopf分叉,影响复杂神经网络动态的稳定性.
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
- 分数微积分的计算.
背景情况:
- 关于环状神经网络的现有研究往往简化了网络结构.
- 复杂的合模式和大规模网络的探索有限.
- 分数顺序导数提供了一个更准确的神经动力学的描述.
研究的目的:
- 建立一个大规模的时间延迟分数顺序双循环神经网络模型.
- 分析这个复杂网络的稳定性和Hopf分支.
- 调查各种参数对网络动态的影响.
主要方法:
- 开发了一种使用卡普托分数导数的分数顺序双循环神经网络模型.
- 采用Coates流图方法来得出特征方程.
- 使用整体元素方法和大小角公式进行分析.
主要成果:
- 为拟议的网络推导稳定性和Hopf分叉标准.
- 确定了影响稳定性的关键参数:分数顺序,神经元数,分布和自我反系数.
- 证明时间延迟显著影响霍夫分叉的幅度和周期.
结论:
- 分数级双循环神经网络的稳定性对多个参数敏感.
- 时间延迟在调节振荡行为 (霍夫分叉) 中起着至关重要的作用.
- 开发的模型为分析复杂神经网络动态提供了更全面的框架.
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