In this paper, we consider the uniform asymptotic stability, global asymptotic stability and global exponential stability of the equilibrium point of discrete Hopfield neural networks with delays. Some new stability criteria for system are derived by using the Lyapunov functional method and the linear matrix inequality approach, for estimating the upper bound of Lyapunov functional derivative. ...

‎In this paper we focus on the Cauchy problem for the generalized‎ ‎IBq equation with damped term in $n$-dimensional space‎. ‎We establish the global existence and decay estimates of solution with $L^q(1leq qleq 2)$ initial value‎, ‎provided that the initial value is suitably small‎. ‎Moreover‎, ‎we also show that the solution is asymptotic to the solution $u_L$ to the corresponding linear equa...

The Small Subgraph Conditioning Method has been used to study the almost sure existence and the asymptotic distribution of the number of regular spanning subgraphs of various types in random d -regular graphs. In this paper we use the method to determine the asymptotic distribution of the number of 3-star factors in random d -regular graphs for d ≥ 4.

We present a systematic approach for the design of change detection and model validation algorithms for dynamical systems. We show bow to associate to any identification algorithm a change detection and a model validation procedure, which are optimal in some asymptotic sense. The foundations of our method go back to the asymptotic local approach in statistics, and our method generalizes this ap...

This article summarizes the results of a series of Monte Carlo simulations of persistent spins or \survivors" in the triangular Q-state Potts model. It is shown that the fraction F(t) of survivors decays algebraically in time t, with nontrivial exponents depending on Q but not on temperature T. At zero temperature , asymptotic exponents have been calculated for the whole range of Q = 3 to 1. In...

This work concernes the contrast difference test and its asymptotic properties for non linear auto-regressive models. Our approach is based on an application of the parametric bootstrap method. It is a re-sampling method based on the estimate parameters of the models. The resulting methodology is illustrated by simulations of multilayer perceptron models, and an asymptotic justification is give...

The method of modi®ed equations is studied as a technique for the analysis of ®nite di€erence equations. The non-uniqueness of the modi®ed equation of a di€erence method is stressed and three kinds of modi®ed equations are introduced. The ®rst modi®ed or equivalent equation is the natural pseudo-di€erential operator associated to the original numerical method. Linear and nonlinear combinations ...

We suggest a new method to compute the asymptotic fitness distribution in the Bak–Sneppen model of biological evolution. As applications we derive the full asymptotic distribution in the four-species model, and give an explicit linear recurrence relation for a set of coefficients determining the asymptotic distribution in the five-species model.

We develop a generalized version of the Hardy-Ramanujan “circle method” in order to derive asymptotic series expansions for the products of modular forms and mock theta functions. Classical asymptotic methods (including the circle method) do not work in this situation because such products are not modular, and in fact, the “error integrals” that occur in the transformations of the mock theta fu...