Robust exponential stability of discrete-time uncertain impulsive stochastic neural networks with delayed impulses

This paper is devoted to the study of the robust exponential stability (RES) of discrete-time uncertain impulsive stochastic neural networks (DTUISNNs) with delayed impulses. Using Lyapunov function methods and Razumikhin techniques, a number of sufficient conditions for mean square (RES-ms) robust exponential stability are derived. The obtained results show that the hybrid dynamic is RES-ms with regard to lower boundary of impulse interval if the discrete-time stochastic neural networks (DTSNNs) is RES-ms and that the impulsive effects are instable. Conversely, if DTSNNs is not RES-ms, impulsive effects can induce unstable neural networks (NNs) to stabilize again concerning an upper bound of the impulsive interval. The results obtained in this study have a broader scope of application than some previously existing findings. Two numerical examples were presented to verify the availability and advantages of the results.

Robust Stability of Recurrent Neural Networks With Time-Varying Delays and Input Perturbation

This paper addresses the robust stability of recurrent neural networks (RNNs) with time-varying delays and input perturbation, where the time-varying delays include discrete and distributed delays. By employing the new ψ -type integral inequality, several sufficient conditions are derived for the robust stability of RNNs with discrete and distributed delays. Meanwhile, the robust boundedness of neural networks is explored by the bounded input perturbation and L¹ -norm constraint. Moreover, RNNs have a strong anti-jamming ability to input perturbation, and the robustness of RNNs is suitable for associative memory. Specifically, when input perturbation belongs to the specified and well-characterized space, the results cover both monostability and multistability as special cases. It is revealed that there is a relationship between the stability of neural networks and input perturbation. Compared with the existing results, these conditions proposed in this paper improve and extend the existing stability in some literature. Finally, the numerical examples are given to substantiate the effectiveness of the theoretical results.

Multiple ψ -Type Stability of Cohen-Grossberg Neural Networks With Both Time-Varying Discrete Delays and Distributed Delays

In this paper, multiple ψ -type stability of Cohen-Grossberg neural networks (CGNNs) with both time-varying discrete delays and distributed delays is investigated. By utilizing ψ -type functions combined with a new ψ -type integral inequality for treating distributed delay terms, some sufficient conditions are obtained to ensure that multiple equilibrium points are ψ -type stable for CGNNs with discrete and distributed delays, where the distributed delays include bounded and unbounded delays. These conditions of CGNNs with different output functions are less restrictive. More specifically, the algebraic criteria of the generalized model are applicable to several well-known neural network models by taking special parameters, and multiple different output functions are introduced to replace some of the same output functions, which improves the diversity of output results for the design of neural networks. In addition, the estimation of relative convergence rate of ψ -type stability is determined by the parameters of CGNNs and the selection of ψ -type functions. As a result, the existing results on multistability and monostability can be improved and extended. Finally, some numerical simulations are presented to illustrate the effectiveness of the obtained results.

Existence and global exponential stability of periodic solution of a cellular neural networks difference equation with delays and impulses

A class of cellular neural networks difference equation with delays and impulses are considered. Sufficient conditions for the existence and global exponential stability of periodic solution are obtained by using contraction mapping theorem and inequality techniques. The results of this paper are completely new. A numerical example and its simulations are offered to show the effectiveness of our new results.

Sigma-delta cellular neural network for 2D modulation

Although sigma-delta modulation is widely used for analog-to-digital (A/D) converters, sigma-delta concepts are only for 1D signals. Signal processing in the digital domain is extremely useful for 2D signals such as used in image processing, medical imaging, ultrasound imaging, and so on. The intricate task that provides true 2D sigma-delta modulation is feasible in the spatial domain sigma-delta modulation using the discrete-time cellular neural network (DT-CNN) with a C-template. In the proposed architecture, the A-template is used for a digital-to-analog converter (DAC), the C-template works as an integrator, and the nonlinear output function is used for the bilevel output. In addition, due to the cellular neural network (CNN) characteristics, each pixel of an image corresponds to a cell of a CNN, and each cell is connected spatially by the A-template. Therefore, the proposed system can be thought of as a very large-scale and super-parallel sigma-delta modulator. Moreover, the spatio-temporal dynamics is designed to obtain an optimal reconstruction signal. The experimental results show the excellent reconstruction performance and capabilities of the CNN as a sigma-delta modulator.

Output convergence analysis for a class of delayed recurrent neural networks with time-varying inputs

This paper studies the output convergence of a class of recurrent neural networks with time-varying inputs. The model of the studied neural networks has different dynamic structure from that in the well known Hopfield model, it does not contain linear terms. Since different structures of differential equations usually result in quite different dynamic behaviors, the convergence of this model is quite different from that of Hopfield model. This class of neural networks has been found many successful applications in solving some optimization problems. Some sufficient conditions to guarantee output convergence of the networks are derived.

Dynamic stability conditions for Lotka-Volterra recurrent neural networks with delays

The Lotka-Volterra model of neural networks, derived from the membrane dynamics of competing neurons, have found successful applications in many "winner-take-all" types of problems. This paper studies the dynamic stability properties of general Lotka-Volterra recurrent neural networks with delays. Conditions for nondivergence of the neural networks are derived. These conditions are based on local inhibition of networks, thereby allowing these networks to possess a multistability property. Multistability is a necessary property of a network that will enable important neural computations such as those governing the decision making process. Under these nondivergence conditions, a compact set that globally attracts all the trajectories of a network can be computed explicitly. If the connection weight matrix of a network is symmetric in some sense, and the delays of the network are in L2 space, we can prove that the network will have the property of complete stability.