In this paper, firstly, we propose a complex dynamical network model, which is always uniformly asymptotically stable about its equilibrium. Then, we give theoretical analysis of its uniform asymptotical stability by using Lyapunov stability theory. Finally, we show a numerical example to verify our theoretical result. r 2006 Elsevier B.V. All rights reserved.

We obtain sufficient conditions for oscillation of solutions, and for asymptotical stability of the positive equilibrium, of the scalar nonlinear delay differential equation dN dt = r(t)N(t) [ a− ( m ∑ k=1 bkN(gk(t)) )γ] ,

Wang proposed a gradient-based neural network (GNN) to solve online matrix-inverses. Global asymptotical convergence was shown for such a neural network when applied to inverting nonsingular matrices. As compared to the previously-presented asymptotical convergence, this paper investigates more desirable properties of the gradient-based neural network; e.g., global exponential convergence for n...

We consider scalar delay differential equations x′(t) = −δx(t)+f(t, xt) (∗) with nonlinear f satisfying a sort of negative feedback condition combined with a boundedness condition. The well-known Mackey–Glass-type equations, equations satisfying the Yorke condition, and equations with maxima all fall within our considerations. Here, we establish a criterion for the global asymptotical stability...

Based on optimal theory, Kelly model realizes the bandwidth allocation on network with proportional fairness and has asymptotical stability. However, the primal algorithm of Kelly model leads to the packet accumulation in the queue of the bottleneck link. By using heuristic fuzzy rules, this paper designs a fuzzy controller to adjust the additive increase parameter of the primal algorithm dynam...

Many practical engineering problems can be modelled as such a class of hybrid dynamic systems, where N plants are controlled by a central controller in sharing time manner. Event feedback strategy is used as the real-time scheduling policy such that one and only one plant among N plants is chosen to be controlled at any time. In this paper, the asymptotical and exponential stability of this cla...

The concept of asymptotical stability is fundamental in the theory of ordinary and partial differential equations. In this way the stability theory leads to the real world applications. The recent advances of stability theory interact with spectral theory, harmonic analysis, modern topics of complex functions theory and also with control theory. This note begins with the following simple remark...

In this paper, we analyze the stability and convergence of a one-layer neural network proposed by Gao and Wang, which is designed to solve a class of horizontal linear complementarity problems. The globally asymptotical stability and globally exponential stability of this network are proved strictly under mild conditions, respectively. Meanwhile, this network is applied to solve a transportatio...

I n this short paper, some globally asymptotical stability criteria for the equilibrium states of a class of discrete-time dynamic neural networks with continuous states and asymmetrical weight matrices are presented. The resulting stability criteria are represented by either the existence of the positive daagonal solutions of the Lyapunov equations or some inequalities. Finally, some examples ...

The dynamics of SEIR epidemic model with saturated incidence rate and saturated treatment function are explored in this paper. The basic reproduction number that determines disease extinction and disease survival is given. The existing threshold conditions of all kinds of the equilibrium points are obtained. Sufficient conditions are established for the existence of backward bifurcation. The lo...