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Abstract: To overcome the staircasing effects and simultaneously avoid edge blurring, this paper describes a fourth-order partial differential equation based edge-preserving regularization filter for noise removal. This technique is closely related to the nonlinear anisotropic diffusion. Compared results distinctly demonstrate the superiority of our proposed scheme over the LLT model, in terms of removing noise while sharply maintaining the edge features. [Copyright &y& Elsevier]

Abstract: The asymptotic behavior of the bounded solutions of the delayed system is investigated, where is a given constant, , , is strictly increasing on , and either for all or for all . It is shown that every bounded solution of the system tends to a constant vector as . The result obtained extends the existing ones in the literature. [Copyright &y& Elsevier]

Abstract: Consider the Liénard equation with a deviating argument where and are continuous functions on is a bounded continuous function on , and is a bounded continuous function on . We obtain some new sufficient conditions for all solutions and their derivatives to be bounded, which substantially extend and improve some important results from the literature. [Copyright &y& Elsevier]

Abstract: In this work, we use the coincidence degree theory to establish new results on the existence and uniqueness of -periodic solutions for a kind of Liénard equation with a deviating argument of the form [Copyright &y& Elsevier]

Abstract: In this paper, cellular neural networks with complex deviating arguments are considered. Sufficient conditions for the existence of the periodic solutions are established by using the coincidence degree theorem. The results of this paper are new and complement previously known results. [Copyright &y& Elsevier]

Abstract: In this paper the shunting inhibitory cellular neural networks (SICNNs) with time-varying delays are considered. Without assuming the global Lipschitz and bounded conditions of activation functions, sufficient conditions for the existence of the almost periodic solutions are established by using a fixed point theorem. The results of this paper are new and complement previously known results. [Copyright &y& Elsevier]

Abstract: This work focuses on the asymptotic behavior of solutions for a class of neutral delay difference equations, which are discrete analogues of a generalization of J.R. Haddock’s conjecture. It is shown that every bounded solution of the equations converges to a constant. Our results improve some known results from the literature. [Copyright &y& Elsevier]

Abstract: It is known that the complete stability of cellular neural networks with delays is very important in applications such as processing of a moving image. In this work, we utilize the Lyapunov functional method to analyse complete stability of cellular neural networks with delay. Our result is an improvement on that in [P.P. Civalleri, M. Gilli, L. Pandolfi, On stability of cellular neural networks with delay, IEEE Trans. Circuits Syst. I 40 (1993) 157–165]. [Copyright &y& Elsevier]

Abstract: This paper is concerned with a delay differential system Such a differential system can be regarded as a model of a two-neuron artificial neural network with delayed feedback. Some interesting results are obtained for the existence and exponential stability of the periodic solution for the system. Our approach is based on the continuation theorem of the coincidence degree, a priori estimates, and differential inequalities. [Copyright &y& Elsevier]

Abstract: In this paper, by employing comparison technique and invariance properties of a positively limited set, we investigate the convergence of precompact orbits of a class of discrete-time semiflows. In particular, we consider the convergence of precompact orbits of discrete-time semiflows generated by some monotone mapping. We then apply these abstract results to a class of difference systems to obtain the large-time behavior of solutions. Our results improve and extend some existing ones. [Copyright &y& Elsevier]

In this work, we investigate the global dynamics of a controlled discontinuous diffusive SIR epidemic system under Neumann boundary conditions. We first establish the conditions for the existence of the solution and obtain the boundedness of the solution for the controlled discontinuous diffusive system. Then, under the framework of differential inclusion, we study the existence of constant equilibria of the controlled diffusive epidemic system. Furthermore, we discuss the global dynamical behaviour of the controlled discontinuous diffusive epidemic system. [ABSTRACT FROM AUTHOR]

Abstract: We consider a discrete-time system modelling a network of two neurons. The situationwith self-connections is addressed in terms of stability and bifurcation analysis. Choosing an appropriate bifurcation parameter, we prove that the Neimark-Sacker bifurcation occurs when the bifurcation parameter exceeds a critical value. The direction and stability of bifurcation are determined by the normal form theory and center manifold theorem. Results of some computer simulations are displayed graphically. [Copyright &y& Elsevier]

Abstract: The stability of stochastic delayed Hopfield neural networks (DHNN) is investigated in this paper. Under the help of suitable Lyapunov function and the semimartingale convergence theorem, we obtain some sufficient criteria to check the almost sure exponential stability of the DHNN. [Copyright &y& Elsevier]