Existence and global exponential stability of almost periodic solutions for BAM neural networks with distributed leakage delays on time scales

In this paper, we deal with a class of BAM neural networks with distributed leakage delays on time scales. Some sufficient conditions which ensure the existence and exponential stability of almost periodic solutions for such class of BAM neural networks are obtained by applying the exponential dichotomy of linear differential equations, Lapunov functional method and contraction mapping principle. An example is given to illustrate the effectiveness of the theoretical predictions. The obtained results in this paper are completely new and complement the previously known publications.     

Existence and exponential stability of almost periodic solutions for neutral‐type BAM neural networks with distributed leakage delays

This paper is concerned with a class of neutral‐type BAM neural networks with distributed leakage delays. By applying the exponential dichotomy of linear differential equations, Lyapunov functional method and contraction mapping principle, we establish some sufficient conditions which ensure the existence and exponential stability of almost periodic solutions for such BAM neural networks. An example is given to illustrate the effectiveness of the theoretical findings. The results obtained in this article are completely new and complement the previously known studies. Copyright © 2016 John Wiley & Sons, Ltd.     

Exponential stability and periodic solution for fuzzy BAM Neural networks with time varying delays

In this paper, a class of fuzzy BAM neural networks with time varying delays is discussed. By using the properties of M-matrix, Linear Matrix Inequality（LMI） approach and general Lyapunov-Krasovskii functional, some new sufficient conditions are derived to ensure the existence of periodic solutions and the global exponential stability of the fuzzy BAM neural networks with time varying delays. These results have important significance in the design of global exponential stable BAM networks with delays. Moreover, an example is given to illustrate that the conditions of the results in the paper are feasible.     

Anti-synchronization control of a class of memristive recurrent neural networks

In this paper, we formulate and investigate a class of memristive recurrent neural networks. Two different types of anti-synchronization algorithms are derived to achieve the exponential anti-synchronization of the coupled systems based on drive–response concept, differential inclusions theory and Lyapunov functional method. The proposed anti-synchronization algorithms are simple and can be easily realized. The analysis in the paper employs results from the theory of differential equations with discontinuous right-hand side as introduced by Filippov. The obtained results extend some previous works on conventional recurrent neural networks.     

Multiple Hopf bifurcations of symmetric BAM neural network model with delay

A symmetric BAM neural network model with delay is considered. Some results of Hopf bifurcations occurring at the zero equilibrium as the delay increases are exhibited. The existence of multiple periodic solutions is established using a symmetric Hopf bifurcation result of Wu [J. Wu, Symmetric functional differential equations and neural networks with memory, Transactions of the American Mathematical Society 350 (12) (1998) 4799–4838].     

Stability analysis for periodic solution of BAM neural networks with discontinuous neuron activations and impulses

In this paper, we present a general class of BAM neural networks with discontinuous neuron activations and impulses. By using the fixed point theorem in differential inclusions theory, we investigate the existence of periodic solution for this neural network. By constructing the suitable Lyapunov function, we give a sufficient condition which ensures the uniqueness and global exponential stability of the periodic solution. The results of this paper show that the Forti’s conjecture is true for BAM neural networks with discontinuous neuron activations and impulses. Further, a numerical example is given to demonstrate the effectiveness of the results obtained in this paper.     

变时滞BAM神经网络的全局指数稳定性

研究一类变时滞BAM神经网络平衡点的全局指数稳定性问题.在不要求激励函数全局Lipschitz条件下,通过构造合适的Lyapunov泛函,并结合Young不等式,得到了BAM神经网络模型在一定条件下全局指数稳定的一些充分条件,推广和改进了前人的相关结论,为综合设计指数稳定的时滞BAM神经网络提供了依据.     

Dissipative differential inclusions,set-valued energy storage and supply rate maps,and stability of discontinuous feedback systems

In this paper, we develop dissipativity notions for dynamical systems with discontinuous vector fields. Specifically, we consider dynamical systems with Lebesgue measurable and locally essentially bounded vector fields characterized by differential inclusions involving Filippov set-valued maps specifying a set of directions for the system velocity and admitting Filippov solutions with absolutely continuous curves. In particular, we introduce a generalized definition of dissipativity for discontinuous dynamical systems in terms of set-valued supply rate maps and set-valued storage maps consisting of locally Lebesgue integrable supply rates and Lipschitz continuous storage functions, respectively. In addition, we introduce the notion of a set-valued available storage map and a set-valued required supply map, and show that if these maps have closed convex images they specialize to single-valued maps corresponding to the smallest available storage and the largest required supply of the differential inclusion, respectively. Furthermore, we show that all system storage functions are bounded from above by the largest required supply and bounded from below by the smallest available storage, and hence, a dissipative differential inclusion can deliver to its surroundings only a fraction of its generalized stored energy and can store only a fraction of the generalized work done to it. Moreover, extended Kalman–Yakubovich–Popov conditions, in terms of the discontinuous system dynamics, characterizing dissipativity via generalized Clarke gradients and locally Lipschitz continuous storage functions are derived. Finally, these results are then used to develop feedback interconnection stability results for discontinuous systems thereby providing a generalization of the small gain and positivity theorems to systems with discontinuous vector fields.     

Existence and global exponential stability of periodic solution for impulsive Cohen-Grossberg-type BAM neural networks with continuously distributed delays

This paper is concerned with the existence and global exponential stability of periodic solution for a class of impulsive Cohen-Grossberg-type BAM neural networks with continuously distributed delays. Some sufficient conditions ensuring the existence and global exponential stability of periodic solution are derived by constructing a suitable Lyapunov function and a new differential inequality. The proposed method can also be applied to study the impulsive Cohen-Grossberg-type BAM neural networks with finite distributed delays. The results in this paper extend and improve the earlier publications. Finally, two examples with numerical simulations are given to demonstrate the obtained results.     

Filippov solutions in the analysis of piecewise linear models describing gene regulatory networks

We study some properties of piecewise linear differential systems describing gene regulatory networks, where the dynamics are governed by sigmoid-type nonlinearities which are close to or coincide with the step functions. To overcome the difficulty of describing the dynamics of the system near singular stationary points (belonging to the discontinuity set of the system) we use the concept of Filippov solutions. It consists in replacing discontinuous differential equations with differential inclusions. The global existence and some other basic properties of the Filippov solutions such as continuous dependence on parameters are studied. We also study the uniqueness and non-uniqueness of the Filippov solutions in singular domains. The concept of Filippov stationary point is extensively exploited in the paper. We compare two ways of defining the singular stationary points: one is based on the Filippov theory and the other consists in replacing step functions with steep sigmoids and investigating the smooth systems thus obtained. The results are illustrated by a number of examples.     

Global asymptotic stability of BAM neural networks with mixed delays and impulses

In this paper, BAM neural networks with mixed delays and impulses are considered. A new set of sufficient conditions are derived by constructing suitable Lyapunov functional with matrix theory for the global asymptotic stability of BAM neural networks with mixed delays and impulses. Moreover, an example is also provided to illustrate the effectiveness of the results.     

NEW CRITERIA OF EXPONENTIAL STABILITY FOR BAM NEURAL NETWORKS WITH DELAYS

In this Letter,a novel Lyapunov functional is constructed to investigate the exponential stability of the BAM neural networks.New sufficient conditions of the uniqueness and global exponential stability for the equilibrium of BAM neural networks with delays are obtained.The results improve those existing ones.     

Functional differential inclusions generated by functional differential equations with discontinuities

Given a functional differential equation with a discontinuity, a construction of its extension in the shape of a functional differential inclusion is offered. This construction can be regarded as a generalization of the famous Filippov approach to study ordinary differential equations with discontinuities. Some basic properties of the solutions of the introduced functional differential inclusions are studied. The developed approach is applied to analysis of gene regulatory networks with general delays.     

Global exponential stability for interval general bidirectional associative memory (BAM) neural networks with proportional delays

This paper is concerned with interval general bidirectional associative memory (BAM) neural networks with proportional delays. Using appropriate nonlinear variable transformations, the interval general BAM neural networks with proportional delays can be equivalently transformed into the interval general BAM neural networks with constant delays. The sufficient condition for the existence and uniqueness of equilibrium point of the model is established by applying Brouwer's fixed point theorem. By constructing suitable delay differential inequalities, some sufficient conditions for the global exponential stability of the model are obtained. Two examples are given to illustrate the effectiveness of the obtained results. This paper ends with a brief conclusion. Copyright © 2016 John Wiley & Sons, Ltd.     

中立型驱动反应BAM 神经网络的全局渐近同步性

针对一类具有时滞的中立型驱动反应BAM神经网络,提出全局渐近同步性问题.不使用现有文献中传统的李雅普诺夫泛函、矩阵测度和线性矩阵不等式(LMI)等已被广泛应用于研究神经网络全局渐近同步性的方法,而是通过构造2个微分不等式U 1(t)和U 1(t),利用微分不等式方程和不等式技巧解出2个不等式,得到能够确保中立型驱动反应BAM神经网络全局渐近同步的两个新的充分条件.     

Dynamics of fuzzy impulsive bidirectional associative memory neural networks with time-varying delays

Complex nonlinear systems can be represented to a set of linear sub-models by using fuzzy sets and fuzzy reasoning via ordinary Takagi-Sugeno (TS) fuzzy models. In this paper, the exponential stability of TS fuzzy bidirectional associative memory (BAM) neural networks with impulsive effect and time-varying delays is investigated. The model of fuzzy impulsive BAM neural networks with time-varying delays established as a modified TS fuzzy model is new in which the consequent parts are composed of a set of impulsive BAM neural networks with time-varying delays. Further the exponential stability for fuzzy impulsive BAM neural networks is presented by utilizing the Lyapunov-Krasovskii functional and the linear matrix inequality (LMI) technique without tuning any parameters. In addition, an example is provided to illustrate the applicability of the result using LMI control toolbox in MATLAB.     

Global asymptotic stability of stochastic Cohen-Grossberg-type BAM neural networks with mixed delays: An LMI approach

In this paper, we consider the stochastic Cohen-Grossberg-type BAM neural networks with mixed delays. By utilizing the Lyapunov-Krasovskii functional and the linear matrix inequality (LMI) approach, some sufficient LMI-based conditions are obtained to guarantee the global asymptotic stability of stochastic Cohen-Grossberg-type BAM neural networks with mixed delays. These conditions can be easily checked via the MATLAB LMI toolbox. Moreover, the obtained results extend and improve the earlier publications. Finally, a numerical example is provided to demonstrate the low conservatism and effectiveness of the proposed LMI conditions.     

时滞BAM神经网络周期解的存在性和全局指数稳定性

本文利用迭合度理论,通过构造适当的Lyapunov泛函并结合Yang不等式分析技巧,获得了具周期系数的时滞BAM神经网络周期解的存在性和全局指数稳定性的充分条件,这些结果对设计全局指数稳定的BAM神经网络与周期振荡的BAM神经网络具有重要的指导意义.     

Global exponential stability of BAM neural networks with time-varying delays: The discrete-time case

This paper deals with the problem of stability analysis for a class of discrete-time bidirectional associative memory (BAM) neural networks with time-varying delays. By employing the Lyapunov functional and linear matrix inequality (LMI) approach, a new sufficient conditions is proposed for the global exponential stability of discrete-time BAM neural networks. The proposed LMI based results can be easily checked by LMI control toolbox. Moreover, an example is also provided to demonstrate the effectiveness of the proposed method.     

Stabilization of delayed Cohen‐Grossberg BAM neural networks

This paper deals with finite‐time stabilization results of delayed Cohen‐Grossberg BAM neural networks under suitable control schemes. We propose a state‐feedback controller together with an adaptive‐feedback controller to stabilize the system of delayed Cohen‐Grossberg BAM neural networks. Stabilization conditions are derived by using Lyapunov function and some algebraic conditions. We also estimate the upper bound of settling time functional for the stabilization, which depends on the controller schemes and system parameters. Two illustrative examples and numerical simulations are given to validate the success of the derived theoretical results.