Global asymptotic stability of fractional-order complex-valued neural networks with probabilistic time-varying delays

Stability and synchronization for complex-valued neural networks with stochastic parameters and mixed time delays

In this paper, a class of complex-valued neural networks (CVNNs) with stochastic parameters and mixed time delays are proposed. The random fluctuation of system parameters is considered in order to describe the implementation of CVNNs more practically. Mixed time delays including distributed delays and time-varying delays are also taken into account in order to reflect the influence of network loads and communication constraints. Firstly, the stability problem is investigated for the CVNNs. In virtue of Lyapunov stability theory, a sufficient condition is deduced to ensure that CVNNs are asymptotically stable in the mean square. Then, for an array of coupled identical CVNNs with stochastic parameters and mixed time delays, synchronization issue is investigated. A set of matrix inequalities are obtained by using Lyapunov stability theory and Kronecker product and if these matrix inequalities are feasible, the addressed CVNNs are synchronized. Finally, the effectiveness of the obtained theoretical results is demonstrated by two numerical examples.

Quasi-Synchronization and Quasi-Uniform Synchronization of Caputo Fractional Variable-Parameter Neural Networks with Probabilistic Time-Varying Delays

Owing to the symmetry between drive–response systems, the discussions of synchronization performance are greatly significant while exploring the dynamics of neural network systems. This paper investigates the quasi-synchronization (QS) and quasi-uniform synchronization (QUS) issues between the drive–response systems on fractional-order variable-parameter neural networks (VPNNs) including probabilistic time-varying delays. The effects of system parameters, probability distributions and the order on QS and QUS are considered. By applying the Lyapunov–Krasovskii functional approach, Hölder’s inequality and Jensen’s inequality, the synchronization criteria of fractional-order VPNNs under controller designs with constant gain coefficients and time-varying gain coefficients are derived. The obtained criteria are related to the probability distributions and the order of the Caputo derivative, which can greatly avoid the situation in which the upper bound of an interval with time delay is too large yet the probability of occurrence is very small, and information such as the size of time delay and probability of occurrence is fully considered. Finally, two examples are presented to further confirm the effectiveness of the algebraic criteria under different probability distributions.