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  

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

作　　者：徐丹宁 蒋望东 XU Dan-ning;JIANG Wang-dong(Yuanpei College,Shaoxing University,Shaoxing 312000,China)

机构地区：[1]绍兴文理学院元培学院公共基础教育分院,浙江绍兴312000

出　　处：《高校应用数学学报(A辑)》2025年第1期43-56,共14页Applied Mathematics A Journal of Chinese Universities(Ser.A)

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)。

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.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.

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 

分 类 号：O175.12[理学—数学]