Xiaoping Xue

Impulsive functional differential inclusions and fuzzy population models

In this paper we shall establish some existence results for the impulsive functional differential inclusion and the fuzzy impulsive functional differential equation with some conditions, and study the properties of the solution set and the attainable set. Finally, the results will be used to fuzzy population models.

Global exponential stability of almost periodic solution of delayed neural networks with discontinuous activations

In this paper, we study the existence, uniqueness and stability of almost periodic solution for the class of delayed neural networks. The neural network considered in this paper employs the activation functions which are discontinuous monotone increasing and (possibly) unbounded. Under a new sufficient condition, we prove that the neural network has a unique almost periodic solution, which is globally exponentially stable. Moreover, the obtained conclusion is applied to prove the existence and stability of periodic solution (or equilibrium point) for delayed neural networks with periodic coefficients (or constant coefficients). We also give some illustrative numerical examples to show the effectiveness of our results.

A project neural network for solving degenerate convex quadratic program

This paper develops a project neural network for solving degenerate quadratic programming problems with general linear constraints. Compared with the existing neural networks for solving strict convex quadratic program, the proposed neural networks for solving degenerate convex quadratic program has a wider domain for implementation. In the theoretical aspects, the proposed neural network is shown to have complete convergence and finite-time convergence. Moreover, the nonsingular part of the output trajectory respect to Q has an exponentially convergent rate. Furthermore, through any equilibrium point of the proposed neural network, the information that whether the objective function can reach its minimum of R^n within the constraint conditions can be obtained easily. Illustrative examples further show the correctness of the results in this paper, and the good performance of the proposed neural network.

Two-point boundary value problems of undamped uncertain dynamical systems

In this paper we study two-point boundary value problems of a class of uncertain dynamical systems, i.e., undamped uncertain dynamical systems. We introduce the concept of large solutions and small solutions for two-point boundary value problems of undamped uncertain dynamical systems, and under some conditions establish the existence and uniqueness of large solutions and small solutions and settle the relationship between large solutions and small solutions.

Asymptotic Stability Analysis of a Kind of Switched Positive Linear Discrete Systems

This note studies the asymptotic stability of switched positive linear discrete systems whose subsystems are (sp) matrices. Such a matrix is the character of a kind of asymptotically stable linear systems and it is very easy to test. A new definition of (sp) matrix is given by means of graph theory. Based on an approaching using partially ordered semigroups and Lie algebras, we present several new criteria for asymptotic stability. We also derive an algebraic condition and discuss a kind of higher order difference equation. Our results have a robustness property to some extent.

Global Exponential Stability and Global Convergence in Finite Time of Neural Networks with Discontinuous Activations

In this paper, we consider a general class of neural networks, which have arbitrary constant delays in the neuron interconnections, and neuron activations belonging to the set of discontinuous monotone increasing and (possibly) unbounded functions. Based on the topological degree theory and Lyapunov functional method, we provide some new sufficient conditions for the global exponential stability and global convergence in finite time of these delayed neural networks. Under these conditions the uniqueness of initial value problem (IVP) is proved. The exponential convergence rate can be quantitatively estimated on the basis of the parameters defining the neural network. These conditions are easily testable and independent of the delay. In the end some remarks and examples are discussed to compare the present results with the existing ones.

The oscillation of delay differential inclusions and fuzzy biodynamics models

In this paper, some basic oscillatory and nonoscillatory properties of the delay differential inclusions are established, which are used to study fuzzy generalized Hutchinsons biodynamics models.

Periodic problems of first order uncertain dynamical systems

It is well known that there are no periodic solutions to fuzzy differential equations in the sense of Hukuhara derivatives, i.e. H-derivatives, so fuzzy differential equations in the sense of H-derivatives cannot be used to describe periodic phenomena in the real world. To overcome this disadvantage, this paper studies periodic problems of first order fuzzy differential equations in the sense of differential inclusions, i.e., periodic problems of first order uncertain dynamical systems, and obtains the existence of periodic solutions for first order uncertain dynamical systems.

Convergence and attractivity of memristor-based cellular neural networks with time delays

This paper presents theoretical results on the convergence and attractivity of memristor-based cellular neural networks (MCNNs) with time delays. Based on a realistic memristor model, an MCNN is modeled using a differential inclusion. The essential boundedness of its global solutions is proven. The state of MCNNs is further proven to be convergent to a critical-point set located in saturated region of the activation function, when the initial state locates in a saturated region. It is shown that the state convergence time period is finite and can be quantitatively estimated using given parameters. Furthermore, the positive invariance and attractivity of state in non-saturated regions are also proven. The simulation results of several numerical examples are provided to substantiate the results.

A new one-layer recurrent neural network for nonsmooth pseudoconvex optimization

Abstract This paper proposes a one-layer recurrent neural network for solving nonlinear nonsmooth pseudoconvex optimization problem subject to linear equality constraints. We first prove that the equilibrium point set of the proposed neural network is equivalent to the optimal solution of the original optimization problem, even though the objective function is pseudoconvex. Then, it is proved that the state of the proposed neural network is stable in the sense of Lyapunov, and globally convergent to an exact optimal solution of the original optimization. In the end, some illustrative examples are given to demonstrate the effectiveness of the proposed neural network.