Synchronization for a class of generalized neural networks with interval time-varying delays and reaction-diffusion terms

Abstract

In this paper, the synchronization problem for a class of generalized neural networks with interval time-varying delays and reaction-diffusion terms is investigated under Dirichlet boundary conditions and Neumann boundary conditions, respectively. Based on Lyapunov stability theory, both delay-derivative-dependent and delay-range-dependent conditions are derived in terms of linear matrix inequalities (LMIs), whose solvability heavily depends on the information of reaction-diffusion terms. The proposed generalized neural networks model includes reaction-diffusion local field neural networks and reaction-diffusion static neural networks as its special cases. The obtained synchronization results are easy to check and improve upon the existing ones. In our results, the assumptions for the differentiability and monotonicity on the activation functions are removed. It is assumed that the state delay belongs to a given interval, which means that the lower bound of delay is not restricted to be zero. Finally, the feasibility and effectiveness of the proposed methods is shown by simulation examples.

Event-triggered synchronization of uncertain delayed generalized RDNNs

“…In this section, our event triggering scheme can ensure the stability of the closed-loop system (25). The following novel criteria can guarantee synchronous of the master system (1) and slave system (3) with 0 A B C       via the event trigger scheme (12).…”

“…Remark3. In recent years, a great number of research investigations have analyzed interval-delayed NNs [6][7][8][9][12][13][14][18][19][20]. Development of delay-dependent stability or synchronization conditions has received increasing attention from research communities, which have become important topics of research.…”

“…Development of delay-dependent stability or synchronization conditions has received increasing attention from research communities, which have become important topics of research. Recently, many effective methods and techniques including the delay-partitioning method [45],reciprocally convex combination method [9], free-weighting matrix approach [12,18] and augmented Lyapunov-Krasovskii functionals approach [14] have been utilized to derive much less conservative results. For interval-delayed NNs, the authors in [9,45,46] have found the admissible maximum upper bound  of time varying delay   t  for guaranteeing stability of system considered by giving different values of scalar  .…”

“…Hence, static network models and local field network models are never identical. Recently, some researchers have studied new unified NNs called generalized NNs (GNNs) to combine these two NN models and provided some criteria with a unified frame suitable for both local field NNs and static NNs [7][8][9]12]. Time delays are frequently encountered in hardware installations of NNs and many biological systems, which are ubiquitous in nature because of the finite signal communication time , switching speed of amplifiers and memory effects, and they may induce instability, poor performance and oscillation of systems [1][2][3][4].…”

“…new less conservative delay-dependent stability conditions for generalized neural networks with interval time-varying delays are established by constructing a suitable Lyapunov-Krasovskii functional and applying the linear matrix inequality formulation. The authors in [12] investigated the synchronization for a class of GNNs based on Lyapunov stability theory and obtained both delay-derivative-dependent and delay-range-dependent conditions in terms of linear matrix inequalities. In addition, parameter uncertainties are unavoidable when modeling and implementing real NNs owing to measure errors, the parameter fluctuation and external disturbance, etc.…”