Abstract:
We derive a new criterion for checking the global stability of periodic oscillation of bidirectional associative memory (BAM) neural networks with periodic coefficients and distributed delay, and find that the criterion relies on the Lipschitz constants of the signal transmission functions, weights of the neural network, and delay kernels. The proposed model transforms the original interacting network into matrix analysis problem which is easy to check, thereby significantly reducing the computational complexity and making analysis of periodic oscillation for even large-scale networks.

Abstract:
We derive a new criterion for checking the global stability of periodic oscillation of bidirectional associative memory (BAM) neural networks with periodic coefficients and distributed delay, and find that the criterion relies on the Lipschitz constants of the signal transmission functions, weights of the neural network, and delay kernels. The proposed model transforms the original interacting network into matrix analysis problem which is easy to check, thereby significantly reducing the computational complexity and making analysis of periodic oscillation for even large-scale networks.

In this paper, based on the theory of fractional-order calculus, we obtain some
sufficient conditions for the uniform stability of fractional-order fuzzy BAM
neural networks with delays in the leakage terms. Moreover, the existence,
uniqueness and stability of its equilibrium point are also proved. A numerical
example is presented to demonstrate the validity and feasibility of the proposed
results.

Abstract:
This paper considers the delay-dependent exponential stability for discrete-time BAM neural networks with time-varying delays. By constructing the new Lyapunov functional, the improved delay-dependent exponential stability criterion is derived in terms of linear matrix inequality (LMI). Moreover, in order to reduce the conservativeness, some slack matrices are introduced in this paper. Two numerical examples are presented to show the effectiveness and less conservativeness of the proposed method.

Abstract:
把不确定性因素考虑到双向联想记忆神经网络(BAM)中, 得到一类带Brown运动的随机时滞双向联想记忆神经网络(BAM)模型. 在激活函数有界的条件下, 研究了随机时滞BAM神经网络的全局散逸性. 通过Lyapunov泛函、Jensen不等式和It 公式等, 讨论了随机时滞BAM神经网络系统均方散逸的充分条件, 给出了该系统散逸的吸引集. 通过数值例子对所给出的结论进行了验证. ： Considering the randomness, which is one of the uncertain factors in the bidirectional associative memory(BAM) neural networks system, it is obtained that a class of stochastic bidirectional associative memory(BAM) neural networks with time delay and Brownian motion. Under the condition of the bounded activation function of the equation, it discusses the global dissipativity for stochastic bidirectional associative memory (BAM) networks with time delay. By using Lyapunov functions, Jensen's inequality and It's formula,it provides the sufficient condition for the global dissipativity in the mean square of such stochastic bidirectional associative memory (BAM) neural networks;it also gives the attractive set of the system. Finally, the numerical example is provided to demonstrate the effectiveness of the conclusion. The conclusion is a generalization of the existing literature in the paper

Abstract:
This paper concerns the exponential convergence of bidirectional associative memory (BAM) neural networks with unbounded distributed delays. Sufficient conditions are derived by exploiting the exponentially fading memory property of delay kernel functions. The method is based on comparison principle of delay differential equations and does not need the construction of any Lyapunov functions.

Abstract:
本文介绍了一类分数阶模糊时滞神经网络模型.利用压缩映射原理,讨论了带时滞的分数阶神经网络模型解的存在性和唯一性,并根据Gronwall不等式结合分数阶微分方程的性质,证明了分数阶神经网络模型平衡点的有限时间稳定性,给出了有限时间稳定性的判断准则.最后,给出数值仿真说明了理论结果的正确性. In this paper, we introduce a class of fractional-order fuzzy neutral network system. According to Gronwall inequality, contraction mapping principle and the properties of fractional diffierential equation, the existence, uniqueness and finite time stability of fractional-order fuzzy neural networks with delay are researched. Finally, the numerical simulation is studied to illustrate the theory

Abstract:
This paper is concerned with the finite-time stability of Caputo fractional neural networks with distributed delay. The factors of such systems including Caputo’s fractional derivative and distributed delay are taken into account synchronously. For the Caputo fractional neural network model, a finite-time stability criterion is established by using the theory of fractional calculus and generalized Gronwall-Bellman inequality approach. Both the proposed criterion and an illustrative example show that the stability performance of Caputo fractional distributed delay neural networks is dependent on the time delay and the order of Caputo’s fractional derivative over a finite time. 1. Introduction It is well known that the fractional calculus is a generalization and extension of the traditional integer-order differential and integral calculus. The fractional calculus has gained importance in both theoretical and engineering applications of several branches of science and technology. It draws a great application in nonlinear oscillations of earthquakes and many physical phenomena such as seepage flow in porous media and in fluid dynamic traffic models. Many practical systems in interdisciplinary fields can be described through fractional derivative formulation. For more details on fractional calculus theory, one can see the monographs of Miller and Ross [1], Podlubny [2], Diethelm [3], and Kilbas et al. [4]. In the last few years, there has been a surge in the study of the theory of fractional dynamical systems. Some recent works the theory of fractional differential systems can be seen in [5–10] and references therein. In particular, for the first time, Lazarevi？ [7] investigated the finite-time stability of fractional time-delay systems. In [8], Lazarevi？ and Spasi？ further introduced the Gronwall’s approach to discuss the finite-time stability of fractional-order dynamic systems. Compared with the classical integer-order derivatives, fractional-order derivatives provide an excellent approach for the description of memory and hereditary properties of various processes. Therefore, it may be more accurate to model by fractional-order derivatives than integer-order ones. In [11–13], fractional operators were introduced into artificial neural network, and the fractional-order formulations of artificial neural network models were also proposed in research works about biological neurons. Recently, there has been an increasing interest in the investigation of the fractional-order neural networks, and some important and interesting results were obtained [13–19], due

Abstract:
By using Mawhins's continuation theorem of coincidence degree theory and constructing some suitable Lyapunov functions, the periodicity and the exponential stability for a class of bidirectional associative memory (BAM) high-order Hopfield neural networks with impulses and delays on time scales are investigated. An example illustrates our results.

Abstract:
A fractional-order two-neuron Hopfield neural network with delay is proposed based on the classic well-known Hopfield neural networks, and further, the complex dynamical behaviors of such a network are investigated. A great variety of interesting dynamical phenomena, including single-periodic, multiple-periodic, and chaotic motions, are found to exist. The existence of chaotic attractors is verified by the bifurcation diagram and phase portraits as well. 1. Introduction Fractional calculus, which mainly deals with derivatives and integrals of arbitrary order, was firstly introduced 300 years ago. However, it is only in recent decades that fractional calculus is applied to physics and engineering [1–3]. The main advantage of fractional-order models in comparison with its integer-order counterparts is that fractional derivatives provide an excellent tool in the description of memory and hereditary properties of various processes. In fractional calculus, a generalized capacitor, called “fractance,” is often considered to be the main operator. It is actually an electrical circuit in which its voltage and current are related by the fractional-order differential equation [4]. Chaos theory has been extensively investigated in various fields of research after the first observation of chaotic attractors in Lorenz system. Recently, study on the complex dynamical behaviors of fractional-order systems has become a hot research topic due to the fact that fractional-order systems show higher nonlinearity and more degrees of freedom in the models, and therefore fractional-order chaotic systems are considered to have the potential ability of improving the security of chaotic communication systems [5]. It has been known that chaos in many well-known integer-order chaotic systems will remain when the orders become fractional, and a great number of fractional-order chaotic systems have been proposed as a consequence [6–14]. Moreover, chaotic behaviors have also been found to exist in some discontinuous systems with fractional derivatives [15]. However, it is worthwhile to note that none of the aforementioned fractional-order chaotic systems are time-delayed systems. On the other hand, the dynamics of delayed neural networks (DNNs) with traditional integer-order derivatives have been extensively studied both in theory and applications. [16–25]. It has been reported that DNNs can really display quite rich dynamical behaviors. For instance, Lu studied the complex dynamics of a DNN of Hopfield-type with two neurons and concluded that for a certain set of system parameters