Periodic bidirectional associative memory neural networks with distributed delays

Some sufficient conditions are obtained for the existence and global exponential stability of a periodic solution to the general bidirectional associative memory (BAM) neural networks with distributed delays by using the continuation theorem of Mawhin's coincidence degree theory and the Lyapunov functional method and the Young's inequality technique. These results are helpful for designing a globally exponentially stable and periodic oscillatory BAM neural network, and the conditions can be easily verified and be applied in practice. An example is also given to illustrate our results.     

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.     

时变时滞BAM神经网络系统的指数稳定性分析

利用Lyapunov稳定性理论和线性矩阵不等式技术,得到了保证时变时滞BAM神经网络系统指数稳定性的时滞依赖稳定性准则.所给的准则可用Matlab中的LMI控制工具箱进行验证.仿真实例进一步说明了结果的有效性.     

Functional differential inclusions and dynamic behaviors for memristor-based BAM neural networks with time-varying delays

In this paper, we formulate and investigate a class of memristor-based BAM neural networks with time-varying delays. Under the framework of Filippov solutions, the viability and dissipativity of solutions for functional differential inclusions and memristive BAM neural networks can be guaranteed by the matrix measure approach and generalized Halanay inequalities. Then, a new method involving the application of set-valued version of Krasnoselskii’ fixed point theorem in a cone is successfully employed to derive the existence of the positive periodic solution. The dynamic analysis in this paper utilizes the theory of set-valued maps and functional differential equations with discontinuous right-hand sides of Filippov type. The obtained results extend and improve some previous works on conventional BAM neural networks. Finally, numerical examples are given to demonstrate the theoretical results via computer simulations.     

非自治分布时滞BAM神经网络的绝对指数稳定性

利用Brouwer不动点理论和不等式技巧, 讨论了非自治分布时滞BAM神经网络的绝对指数稳定性, 给出了实用有效的判定条件,仅要求激活函数满足局部Lipschitz条件,所得结果更容易验证。 例子说明结果的有效性。     

Cohen-Grossberg-type BAM神经网络吸引集和不变集(英文)

利用矩阵理论和不等式分析技巧,讨论了一类具分布时滞的Cohen-Grossberg型BAM神经网络的不变集和吸引集,获得了一些最新结果,并给出一个实例说明我们结果的可行性.     

时滞BAM神经网络的全局稳定性

利用李雅普诺夫泛函方法并结合一些分析技巧获得了时滞BAM神经网络平衡点全局渐近稳定和全局指数稳定的充分条件，这些条件对设计全局渐近稳定的BAM神经网络和全局指数稳定的BAM神经网络具有重要意义．     

随机时滞BAM神经网络的全局散逸性

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.     

具有双时滞的分数阶BAM神经网络模型的动力学行为

本文研究了一类具有双时滞的五神经元分数阶BAM神经网络模型的动力学行为。通过将时滞之和作为参数,利用分数阶微分方程稳定性理论和分支理论,得到了系统零平衡点稳定性和产生Hopf分支的充分条件,并通过仿真模拟,验证了理论分析的正确性。