分数阶变时滞惯性Cohen-Grossberg神经网络全局Mittag-Leffler稳定和全局渐近ω-周期

Global Mittag-Leffler Stability and Global Asymptoticω-Period for a Class of Fractional-Order Cohen-Grossberg Inertial Neural Networks with Time-Varying Delays

主要研究分数阶变时滞惯性Cohen-Grossberg神经网络动力学行为.利用RiemannLiouville分数阶微积分性质和初始值条件,当系统变时滞τ_(ij)(t)>0时,将时间变量t的定义域[0,+∞)分成两个区间:[0,τ_(ij)(t)]和[τ_(ij)(t),+∞),推导出当t分别在[0,τ_(ij)(t)]和τ_(ij)(t),+∞)中变化时,含有变时滞τ_(ij)(t)的状态函数x_(i)(t-τ_(ij)(t)的分数阶积分之间的关系式.引入Mittag-leffler函数,借助于拉格朗日中值定理有限增量公式,Arzela-Ascoli定理当函数序列等度连续且一致时,存在一个一致收敛的子序列等分析知识,给出判定其系统解全局Mittag-Leffler稳定和全局渐近ω-周期充分条件.最后,通过数值模拟例子验证所得到理论结果的有效性.

This paper focuses on the dynamic behavior of fractional-order inertial Cohen-Grossberg neural networks with time-varying delays.Using Riemann-Liouville fractional calculus properties and initial value conditions,we divide the definition field[0,+∞)of into two intervals according to the time-varying delaysτ_(ij)(t)of the system:[0,τ_(ij)(t)]and[τ_(ij)(t),+∞),,and then we deduce the relationship between the fractional integrals of the state function x_(i)(t-τ_(ij)(t)when t is in[0,τ_(ij)(t)]andτ_(ij)(t),+∞).By introducing the Mittag-Leffler function,with the help of finite increment formula of Lagrange mean-value theorem and Arzela-Ascoli theorem that when the function sequence is equi-continuous and uniform,there is a uniformly convergent subsequence,we get the sufficient conditions to determine the global Mittag-Leffler stability and global asymptotic ω-periodicity.Finally,we give numerical simulation examples to verify the effectiveness of the theoretical results.