一个分数顺序环-枢纽结构神经网络的稳定性和Hopf分叉分析,在延迟反控制参数下有延迟
1Department of System Science and Applied Mathematics, Kunming University of Science and Technology, Kunming 650500, China.
Mathematical biosciences and engineering : MBE
|December 5, 2023
概括
这项研究研究了具有两个延迟的分数级神经网络. 一个新的依赖参数的反控制器成功地管理了Hopf分叉,提高了系统的稳定性.
科学领域:
- * 计算神经科学 计算神经科学
- * 非线性动力学
- * 控制理论 * 控制理论
背景情况:
- * 分数顺序系统比整数顺序系统提供了增强的建模功能.
- * 时间延迟在神经网络中至关重要,影响稳定性和动态性.
- * 霍夫分叉是动态系统中常见的现象,导致振荡.
研究的目的:
- * 分析一个分数级的双延迟神经网络的稳定性和霍普夫分叉.
- * 设计一个依赖参数的反控制器来管理Hopf分叉.
- * 调查两个同时发生的时间延迟对系统稳定性的影响.
主要方法:
- * 用两个时间延迟和参数依赖性分析特征方程.
- * 确定 $(\tau_{1}, \tau_{2}) $ 平面中的稳定性切换曲线.
- * 应用参数延迟反控制器用于分叉控制.
主要成果:
- * 稳定性和Hopf分叉条件是使用延迟的和作为分叉参数来推导的.
- *同时使用两个延迟作为分叉参数,产生了稳定性切换曲线和交叉方向.
- * 拟议的控制器有效地抑制和控制神经网络中的Hopf分叉.
结论:
- * 分数级双延迟神经网络表现出由时间延迟影响的复杂动态.
- *开发的参数延迟反控制器提供了一种可靠的方法来控制Hopf分叉.
- * 这项研究有助于理解和控制神经科学及其他领域的延迟动态系统.
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