文献类型：期刊文献

中文题名：分数阶惯性时滞BAM神经网络全局Mittag-Leffler稳定和全局渐近ω-周期

英文题名：Global Mittag-Leffler stability and global asymptotic ω-period for fractional inertial BAM neural network with time-delay

作者：徐丹宁[1];蒋望东[1]

机构：[1]绍兴文理学院元培学院公共基础教育分院,浙江绍兴312000

年份：2025

卷号：40

期号：1

起止页码：43

中文期刊名：高校应用数学学报(A辑)

外文期刊名：Applied Mathematics A Journal of Chinese Universities(Ser.A)

收录：北大核心2023、、北大核心

基金：绍兴文理学院科研项目(2022LG017);绍兴文理学院元培学院重点科研项目(KY2023C01)。

语种：中文

中文关键词：分数阶;惯性;BAM神经网络;全局Mittag-Leffler稳定;全局渐近ω-周期

外文关键词：fractional;inertial;BAM neural networks;global Mittag-Leffler stability;global asymptotic ω-period

中文摘要：该文研究分数阶惯性时滞BAM神经网络的全局Mittag-Leffler稳定和全局渐近ω-周期问题.首先,利用Riemann-Liouville分数阶微积分性质,通过引入适当的变量代换,将含有两个不同分数阶导数的分数阶惯性时滞BAM神经网络模型简化为只含一个分数阶导数神经网络模型.其次,运用积分区间可加性和初始值条件,当时间变量分别在小于等于时间迟滞有限区间和大于等于时间迟滞无限区间内变化时,推导出含有时间迟滞和不含时间迟滞的状态函数分数阶积分之间的关系,给出了判定分数阶惯性时滞BAM神经网络系统解全局Mittag-Leffler稳定和全局渐近ω-周期的充分条件.最后,通过数值模拟验证所得到理论结果的正确性.

外文摘要：The paper investigates the global Mittag-Leffler stability and global asymptotic ω-periodicity of fractional-order inertial BAM neural networks with time delays.Firstly,by utilizing the properties of Riemann-Liouville fractional calculus and introducing appropriate variable substitutions,the fractional-order inertial BAM neural network model,which involves two different fractional-order derivatives,is simplified to a model containing only one fractional-order derivative.Next,by applying the additivity of integral intervals and initial value conditions,the relationship between the fractional-order integrals of the state functions with and without time delays is derived when the time variable varies within finite intervals less than or equal to the time delay and within infinite intervals greater than or equal to the time delay.Sufficient conditions for determining the global Mittag-Leffler stability and global asymptotic ω-periodicity of the solutions for the fractional-order inertial BAM neural network system are provided.Finally,numerical simulations are conducted to verify the effectiveness and correctness of the theoretical results obtained.