关于复杂估值神经网络的统一稳定性和数值模拟,涉及一般化的卡普托分数顺序
Sumati Kumari Panda1, Thabet Abdeljawad2,3,4, A M Nagy5,6
1Department of Mathematics, GMR Institute of Technology, Rajam, Andhra Pradesh, 532127, India.
Scientific reports
|February 19, 2024
概括
这项研究探讨了复杂值神经网络的统一稳定性和平衡性,使用通用卡普托分数导数. 它介绍了关于间歇性行为的新发现,并从数值上验证了它们.
科学领域:
- 分数微积分的计算.
- 神经网络理论 神经网络理论
- 复杂系统动力学 复杂系统动力学
背景情况:
- 一般化卡普托分数导数已经确立,但在复杂值神经网络中未得到充分探索.
- 实值分数级神经网络的统一稳定性和平衡性是已知的,但对于复杂值的对应网络来说,这种稳定性和平衡性较少.
- 现有的研究还没有广泛地涵盖复杂值神经网络的统一稳定性和平衡,这些神经网络具有通用的卡普托衍生品.
研究的目的:
- 为了研究复杂值神经网络 (CVNNs) 的统一稳定性和平衡性,使用一般化的卡普托分数导数.
- 分析这些CVNN的间歇性行为在一般化的卡普托分数顺序框架内.
- 将分数级神经网络动态的理解扩展到复杂值系统.
主要方法:
- 使用复杂值系统的一般化卡普托分数导数定义.
- 将稳定理论和平衡分析技术应用于分数级复杂值神经网络.
- 使用数值模拟来验证理论发现,并证明拟议方法的准确性.
主要成果:
- 根据一般化的卡普托分数导数,建立了复杂值神经网络的统一稳定性和平衡结果.
- 研究并描述了这些网络的间歇动态.
- 证明了所介绍的分析和数值方法的有效性和精度.
结论:
- 该研究成功地将稳定性和平衡分析扩展到复杂值分数顺序神经网络.
- 这些发现为了解这些系统的复杂动态提供了基础.
- 数字验证证实了理论结果,为未来对开放问题的研究铺平了道路.
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