Analysis of global O(t−α)O(t−α) stability and global asymptotical periodicity for a class of fractional-order complex-valued neural networks with time varying delays

In this paper, the problem of the global O(t−α)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)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.