Event-based master-slave synchronization of complex-valued neural networks via pinning impulsive control

The dynamics of octonion-valued neutral type high-order Hopfield neural networks with D operator

In this paper, the existence, uniqueness and global exponential stability of pseudo almost periodic solutions for a class of octonion-valued neutral type high-order Hopfield neural network models with D operator are established by using the Banach fixed point theorem and differential inequality techniques. Compared with most existing models, in this class of networks, all connection weights and activation functions are assumed to be octonion-valued functions except for time delays. And unlike most of the existing methods of studying octonion-valued neural networks, our method is a non-decomposition method, that is, the method of directly studying octonion-valued systems. The results and methods in this paper are new. In addition, an example and its numerical simulation are given to illustrate the feasibility of our results.

Non-fragile output-feedback synchronization for delayed discrete-time complex-valued neural networks with randomly occurring uncertainties

This paper is step forward to establish an exponential synchronization criterion for discrete-time complex-valued neural networks (CVNNs) having time-varying delays subject to randomly occurring uncertain weighting parameters, in order to overcome the fluctuation when the output-feedback controller imposes on its dynamics. To achieve this, Jensen's weighted summation inequalities (WSIs) and an extended reciprocal convex matrix inequality (ERCMI) are extended into the domain of complex field. By introducing some augmented vectors, a Lyapunov-Krasovskii functional (LKF) is constructed to attain an improved delay-dependent linear matrix inequalities (LMIs) constraint for the exponential synchronization phenomenon of the desired master-slave neuronal system model. For instance, the upper bound of the quadratic summation terms occurred in the finite difference of the LKF have been obtained from its linearization that has been made by the developed complex-valued WSIs and complex-valued ERCMI. The proposed results are less restrictive with the minimum number of decision variables than those obtained using existing inequalities. The designed output-feedback control gain has been determined by solving a set of complex-valued LMIs and it has been enforced with a prescribed exponential decay rate. Finally, in sight of MATLAB software, the established results have been examined via a numerical example supported by the simulation results.