Synchronization for delayed non-autonomous reaction-diffusion fuzzy cellular neural networks

In this letter, the synchronization schemes for delayed non-autonomous reaction-diffusion fuzzy cellular neural networks is considered. Based on the simple adaptive controller, a set of sufficient conditions to guarantee the synchronization are obtained. Moreover, the asymptotic behavior of the unknown parameters can be derived in the meanwhile. At last, some examples are given to show the effectiveness of the main results.     

On the geometry of wave solutions of a delayed reaction-diffusion equation

The aim of this paper is to study the existence and the geometry of positive bounded wave solutions to a non-local delayed reaction-diffusion equation of the monostable type.     

Positive almost periodic solutions for recurrent neural networks

In this paper recurrent neural networks with time-varying delays and continuously distributed delays are considered. Sufficient conditions for the existence and exponential stability of the positive almost periodic solutions are established, which are new and complement previously known results.     

Existence and uniqueness of almost periodic solutions for a class of Hopfield neural networks with neutral delays

In this work Hopfield neural networks with neutral delays are considered. Some sufficient conditions for the existence and uniqueness of almost periodic solutions are established by using the fixed point theorem and differential inequality techniques. The results of this work are new and complement previously known results.     

Almost periodic solutions for impulsive neural networks with delay

In the present paper the problems of existence and uniqueness of almost periodic solutions for impulsive cellular neural networks with delay are considered.     

Almost periodic solutions for shunting inhibitory cellular neural networks

In this paper, shunting inhibitory cellular neural networks with continuously distributed delays are considered. Without assuming the global Lipschitz conditions of activation functions, some new sufficient conditions for the existence and exponential stability of the almost periodic solutions are established.     

New results of almost periodic solutions for recurrent neural networks

In this paper recurrent neural networks with time-varying delays and continuously distributed delays are considered. Without assuming the global Lipschitz conditions of activation functions, some sufficient conditions for the existence and local exponential stability of the almost periodic solutions are established, which are new and complement previously known results.     

Multiple periodic solutions in impulsive hybrid neural networks with delays

The existence of multiple periodic solutions and their exponential stability are investigated for impulsive hybrid Hopfield-type neural networks with both time-dependent and distributed delays, using the Leray-Schauder fixed point theorem and Lyapunov functionals. The criteria given are easily verifiable, possess many adjustable parameters, and depend on impulses, providing flexibility for the analysis and design of delayed neural networks with impulse effects. Examples are given.     

Global exponential stability for a class of generalized delayed neural networks with impulses

In this paper, by utilizing Lyapunov functional method, the quality of negative definite matrix and the linear matrix inequality approach, the global exponential stability of the equilibrium point for a class of generalized delayed neural networks with impulses is investigated. A new criterion on global exponential stability is obtained. The result is related to the size of delays and impulses. An example is given to illustrate the effectiveness of our result. Copyright © 2011 John Wiley & Sons, Ltd.     

Almost periodic solutions of recurrent neural networks with continuously distributed delays

In this paper, a class of recurrent neural networks with continuously distributed delays is discussed. Without resorting to the theory of exponential dichotomy, several new sufficient conditions are obtained ensuring the existence of an almost periodic solution for this model based on a special functional and analysis technique. Moreover, by constructing suitable Lyapunov functions, the attractivity and exponential stability of the almost periodic solution are also considered for the system. The results obtained are helpful to design globally stable almost periodic oscillatory neural networks. A numerical example is given to show the feasibility of the results obtained.     

Hopfield神经网络的周期解存在性及其全局吸引性

利用重合度理论和微分不等式分析等技巧，给出了Hopfield神经网络周期解存在性及其全局吸引性的判别准则。     

Nontrivial periodic solutions to a type of delayed resonant differential equations

In this paper, we consider a type of delayed resonant differential equations. We focus on the existence of periodic solutions. Employing the Clark dual, we provide two sets of criteria on the existence of at least one periodic solution. In fact, the periodic solutions are critical points minimizing the dual functional of the coupled Hamiltonian system on certain subspaces of a Banach space.     

Stability of spatially homogeneous periodic solutions of reaction-diffusion equations

When a certain condition is satisfied, a reaction-diffusion equation has a spatially homogeneous periodic solution, i.e. a temporally periodic solution that does not depend on spatial variables. We analyse the orbital stability of this periodic solution. A sufficient condition is given for the homogeneity breaking instability, which is stated in terms of the manner of dependency of its temporal period on a certain parameter of the system.     

Existence and exponential stability of periodic solutions for a class of Cohen–Grossberg neural networks with bounded and unbounded delays

In this paper, a class of Cohen–Grossberg neural networks with bounded and unbounded delays are considered. Without assuming the boundedness, monotonicity, and differentiability of activation functions and any symmetry of interconnections, sufficient conditions for the existence and exponential stability of the periodic solutions are established by using the coincidence degree theorem and differential inequality techniques. The results of this paper are new and they complement previously known results.     

Convergence for a class of delayed recurrent neural networks without M-matrix condition

In this paper, we investigate the asymptotic behavior of solutions to a class of recurrent neural network model with delays. Without assuming M-matrix condition, it is shown that every solution of the network tends to an equilibrium point as t→∞. Our results improve and extend some corresponding ones already known.     

Existence of periodic solutions for neutral type cellular neural networks with delays

In this paper, by using the theory of abstract continuation theorem of k contractive operator, we study the existence of periodic solutions for neutral type cellular neural networks with delays.     

Existence of periodic solutions for cellular neural networks with complex deviating arguments

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.     

Periodic solutions of a delayed,periodic logistic equation

Consider the delayed periodic logistic equation, N(t)=N(t) [a(t)-b(t)N^p(t-σ(t))-c(t)N^q(t−T(t))], which describes the evolution of a single species. The existence of a positive periodic solution is established by using the method of coincidence degree.