Synchronization of Stochastic Competitive Neural Networks with Different Timescales and Reaction-Diffusion Terms

Abstract

We propose a feedback controller for the synchronization of stochastic competitive neural networks with different timescales and reaction-diffusion terms. By constructing a proper Lyapunov-Krasovskii functional, as well as employing stochastic analysis theory, the LaShall-type invariance principle for stochastic differential delay equations, and a linear matrix inequality (LMI) technique, a feedback controller is designed to achieve the asymptotical synchronization of coupled stochastic competitive neural networks. A simulation example is given to show the effectiveness of the theoretical results.

Adaptive Exponential Synchronization for Stochastic Competitive Neural Networks with Time-Varying Leakage Delays and Reaction-Diffusion Terms

“…Synchronization of competitive neural networks with different timescales has attracted a great interest [2][3][4][5][6][7]. In [7], Gan et al studied the adaptive synchronization for a class of competitive neural networks with different timescales and stochastic perturbation by constructing a Lyapunov-Krasovskii functional:…”

“…The neural networks discussed in [6,7,31] are the special cases of the model in this paper. From this point, our results are more general.…”

“…Numerical simulation illustrates that the reactiondiffusion neural network (49) with boundary condition (6) and the initial condition (50) exhibits a chaotic behavior (see Figure 1).…”

Finite-time synchronization of competitive neural networks with mixed delays

“…For instance, exponential stochastic synchronization of coupled memristor-based neural networks was studied in [22], and synchronization induced by temporal delays in pulse-coupled neural networks was investigated in [9]. Recently, another kind of neural networks, called competitive neural networks (CNNs), has received increasing attention of researchers [10], [23]. In the models of [10] and [23], there are two types of state variables: the short-term memory variable describing the fast neural activity, and the long memory variable describing the slow unsupervised synaptic modifications.…”

“…Recently, another kind of neural networks, called competitive neural networks (CNNs), has received increasing attention of researchers [10], [23]. In the models of [10] and [23], there are two types of state variables: the short-term memory variable describing the fast neural activity, and the long memory variable describing the slow unsupervised synaptic modifications. In the literature, there are many results concerning synchronization of CNNs [17], [4], [8], [5], [20].…”