Search

This manuscript studies the stability for a class of Cohen-Grossberg neural networks (CGNNs) with variable delays. By practicing the scheme of Lyapunov function (LF), M-matrix (MM) theory, homeomorphism theory and nonlinear measure (NM) method, a new sufficient condition is obtained to ensure the existence, uniqueness and global exponential stability (GES) of equilibrium point (EP) for the studied network. As the condition is independent to delay, it can be applied to networks with large delays. The result generalises and improves the earlier publications. Finally, an example is supplied to exhibit the power of the results and less conservativeness over some earlier publications.

This paper deals with global synchronisation in arrays of delayed chaotic neural networks with nonlinear hybrid coupling. By constructing a new Lyapunov-Krasovskii functional, a novel synchronisation criterion is presented in terms of matrix inequalities based on Chen's integral inequalities and reciprocal convex technique. These established conditions are heavily dependent on the bounds of both time-delay and its derivative. Through employing Matlab Toolbox and adjusting some matrix parameters in the derived results, the design and applications of the generalised networks can be realised. The effectiveness and applicability of the proposed methods is demonstrated by a numerical example with simulations.

This paper investigates the quartic non-diagonal algebraic Hermite-Padé approximation to the exponential function. Explicit formulas and differential equations are obtained for the polynomial coefficients. An exact asymptotic expression is obtained for the error function. As an application, a class of local analytical difference schemes based on quartic Padé approximation for diffusion-convection equation with constant coefficients are proposed. A numerical example is provided to demonstrate the effectiveness of the theoretical results.

This paper investigates the globally stochastic synchronisation problem for a class of neutral-type chaotic neural networks with Markovian jumping parameters under impulsive perturbations in mean square. By virtue of drive-response concept and time-delay feedback control techniques, by using the Lyapunov functional method, vector Wirtinger-type inequality, a novel reciprocal convex lemma and the free-weight matrix method, a novel sufficient condition is derived to ensure the asymptotic synchronisation of two identical Markovian jumping chaotic delayed neural networks with impulsive perturbation. The proposed results, which do not require the differentiability and monotonicity of the activation functions, can be easily checked via MATLAB software. Finally, a numerical example with simulations is provided to illustrate the effectiveness of the presented synchronisation scheme.

The existence, uniqueness and globally exponential stability is investigated for a class of discrete-time recurrent neural networks with discrete and bounded distributed delays. The activation functions are required to be neither bounded nor monotonic. By introducing triple-sum terms, a new Lyapunov-Krasovskii functional is constructed. After using the homeomorphism mapping principle, discrete Jensen inequality and generalised discrete Jensen inequality, a linear matrix inequality (LMI) approach is developed to establish delay-dependent sufficient conditions for exponential stability of the discrete-time neural networks. As the obtained conditions are expressed in terms of LMIs, the feasibility can be easily checked by using the numerically efficient MATLAB LMI toolbox. Two numerical examples are also given to show the effectiveness of our results.

The globally exponential stabilization problem is investigated for a general class of stochastic Cohen-Grossberg neural networks with both Markovian jumping parameters and mixed mode-dependent time-delays. The mixed time-delays consist of both discrete and distributed delays. This paper aims to design a memoryless state feedback controller such that the closed-loop system is stochastically exponentially stable in the mean square sense. By introducing a new Lyapunov-Krasovskii functional that accounts for the mode-dependent mixed delays, stochastic analysis is conducted in order to derive delay-dependent criteria for the exponential stabilization problem. Three numerical examples are carried out to demonstrate the feasibility of our delay-dependent stabilization criteria.