Rakkiyappan R, Sivaranjani R, Velmurugan G, Cao Jinde
Department of Mathematics, Bharathiar University, Coimbatore - 641 046, Tamil Nadu, India.
Department of Mathematics, and Research Center for Complex Systems and Network Sciences, Southeast University, Nanjing 210096, China.
Neural Netw. 2016 May;77:51-69. doi: 10.1016/j.neunet.2016.01.007. Epub 2016 Jan 21.
In this paper, the problem of the global O(t(-α)) stability and global asymptotic periodicity for a class of fractional-order complex-valued neural networks (FCVNNs) with time varying delays is investigated. By constructing suitable Lyapunov functionals and a Leibniz rule for fractional differentiation, some new sufficient conditions are established to ensure that the addressed FCVNNs are globally O(t(-α)) stable. Moreover, some sufficient conditions for the global asymptotic periodicity of the addressed FCVNNs with time varying delays are derived, showing that all solutions converge to the same periodic function. Finally, numerical examples are given to demonstrate the effectiveness and usefulness of our theoretical results.
本文研究了一类具有时变时滞的分数阶复值神经网络（FCVNNs）的全局(O(t^{-\alpha}))稳定性和全局渐近周期性问题。通过构造合适的Lyapunov泛函和分数阶导数的莱布尼茨法则，建立了一些新的充分条件，以确保所研究的FCVNNs是全局(O(t^{-\alpha}))稳定的。此外，还推导了所研究的具有时变时滞的FCVNNs全局渐近周期性的一些充分条件，表明所有解都收敛到同一个周期函数。最后，给出了数值例子来证明我们理论结果的有效性和实用性。
