动态神经网络的输入2状态稳定性分析

针对非自治的动态神经网络系统，建立了动态神经网络的数学模型．并将其等效成一个非线性仿射控制系统．深入分析了该系统平衡点的存在性、唯一性和全局渐近稳定性，给出了系统输入-状态稳定的充分条件，构建了ISS-Lyapunov函数，并应用该函数确保了系统的全局渐近稳定性．     

非线性耦合统一混沌系统的同步

研究非线性耦合的两个统一混沌系统的同步问题．首先利用线性时变系统的稳定性理论,推出当两个统一混沌系统的误差系统渐近稳定时,耦合函数的参数选择范围,从而得出两个统一混沌系统全局渐近同步的充分条件．然后基于Routh-Hurwitz稳定性判别方法,同样得出了混沌系统同步的一个充分条件．通过数值仿真发现,根据第1种方法选择的参数能使混沌系统全局渐近同步;而依据第2种方法选择的参数,即使误差系统系数矩阵的瞬间特征值具有负实部,也会出现混沌同步失去的情况,从而表明了该分析方法的有效性．     

时滞切换不确定神经网络系统的指数稳定性

本文研究了具有无穷时滞切换不确定细胞神经网络(UCNNs)系统任意切换下的指数稳定性.利用同胚映射和M-矩阵理论,得到UCNNs系统平衡点存在性,唯一性和指数稳定性的充分条件;利用Lyapunov泛函方法,研究了时滞切换UCNNs系统任意切换下的鲁棒指数稳定性,并得到确保系统全局指数稳定的充分条件.     

一类推广的二元神经网络的稳定性分析

利用不动点定理和微分不等式的分析技巧,引入多个变时滞,去掉对激活函数光滑性与有界性的假设,研究了一类推广的二元神经网络的平衡点的存在性,得到了系统存在平衡点和全局指数稳定性的新的充分条件．     

具反映扩散有限连续分布时滞细胞神经网络的全局指数稳定性

研究了具反应扩散有限连续分布细胞神经网络的平衡点的存在性及全局指数稳定性问题,提出了新的比较原理,在对神经元的激励函数的较宽松的条件下,利用同伦不变性原理获得了该系统的平衡点的存在性,利用所得的比较原理获得了该系统全局指数渐近稳定性的充分条件,而且这些条件容易检验,并举了一个数值实例以说明结论的有效性．     

区间时变细胞神经网络的全局鲁棒指数稳定性

研究了一类区间时变扰动、变时滞细胞神经网络的全局鲁棒指数稳定性问题．利用Leibniz-Newton公式对原系统进行模型变换,并分析了变换模型和原始模型的等价性．基于变换模型,运用线性矩阵不等式的方法,通过选择适当的Lyapunov-Krasovskii泛函,推导了该系统全局鲁棒指数稳定的时滞相关的充分条件．通过数值实例将所得结果与前人的结果相比较,表明了本文所提出的稳定判据具有更低的保守性．     

Hopfield神经网络系统的全局稳定性分析

研究一类Hopfield神经网络系统的平衡状态的存在性、唯一性与全局稳定性, 这类系统放弃了以前对激励函数的有界性、单调性和可微性要求. 利用M矩阵理论, 通过构造适当的Lyapunov函数, 得到了系统全局渐近稳定的充分条件.     

非线性采样系统指数稳定的新条件

研究了非线性采样系统的稳定性问题. 对以采样周期为参数的离散时间系统族, 证明了全局指数稳定的Lyapunov定理和逆定理. 分别基于系统的一般近似模型和Euler近似模型, 给出了闭环系统全局指数稳定的新条件. 与现有结果相比, 取消了Lyapunov函数全局Lipschitz连续的假设, 减弱了闭环系统全局指数稳定的充分条件.     

一般Brusselator系统解的稳定性和存在性分析

研究了一般Brusselator系统在Neumann边界条件下解的性质。利用稳定性理论讨论了其常数解的稳定性。以u的扩散系数θ为分歧参数,利用分歧理论分析了由常数解产生的局部和全局分歧情况,给出了局部分歧解存在的充分条件以及分歧解的全局走向。     

具有m个开关系统的渐近稳定性

研究了一类具有m个开关系统的渐近稳定性,借助于多重Lyapunov函数,给出了该系统全局渐近稳定的充分条件,部分地改进了前人的结果。     

Permanence and global attractivity of the discrete Gilpin–Ayala type population model

In this paper, we propose a discrete Gilpin–Ayala competition model and a discrete Gilpin–Ayala type multispecies competition–predator model. For general nonautonomous case, sufficient conditions which ensure the permanence and the global stability of the system are obtained; For periodic case, sufficient conditions which ensure the existence of an unique globally stable positive periodic solution of the system are obtained. An example together with its numeric simulations shows the feasibility of the main results.     

Stability and stabilization of discrete-time periodic linear systems with actuator saturation

This paper is concerned with the problems of stability and stabilization for discrete-time periodic linear systems subject to input saturation. Both local results and global results are obtained. For local stability and stabilization, the so-called periodic invariant set is used to estimate the domain of attraction. The conditions for periodic invariance of an ellipsoid can be expressed as linear matrix inequalities (LMIs) which can be used for both enlarging the domain of attraction with a given controller and synthesizing controllers. The periodic enhancement technique is introduced to reduce the conservatism in the methods. As a by-product, less conservative results for controller analysis and design for discrete-time time-invariant systems with input saturation are obtained. For global stability, by utilizing the special properties of the saturation function, a saturation dependent periodic Lyapunov function is constructed to derive sufficient conditions for guaranteeing the global stability of the system. The corresponding conditions are expressed in the form of LMIs and can be efficiently solved. Several numerical and practical examples are given to illustrate the theoretical results proposed in the paper.     

线性离散周期奇异系统的可解性与渐近稳定性

讨论了线性离散周期奇异系统初值问题的可解性和渐近稳定性问题.首先分析总结了线性离散变系数奇异系统可解性及其广义状态解的一般概念.在此基础上,定义了线性离散变系数奇异系统的一致渐近稳定性,并通过增加系统维数把线性离散周期奇异系统转化为线性定常奇异系统,从而得到了线性离散周期奇异系统可解和一致渐近稳定的充要条件.     

Existence and global asymptotic stability of periodic solution for discrete and distributed time-varying delayed neural networks with discontinuous activations

In this paper, we study a general class of neural networks with discrete and distributed time-varying delays, whose neuron activations are discontinuous and may be unbounded or nonmonotonic. By using the Leray-Schauder alternative theorem in multivalued analysis, matrix theory and generalized Lyapunov-like approach, we obtain some sufficient conditions ensuring the existence, uniqueness and global asymptotic stability of the periodic solution. Moreover, when all the variable coefficients and time delays are real constants, we discuss the global convergence in finite time of the neural network dynamical system. Our results extend previous works not only on discrete and distributed time-varying delayed neural networks with continuous or even Lipschitz continuous activations, but also on discrete and distributed time-varying delayed neural networks with discontinuous activations. Two numerical examples are given to illustrate the effectiveness of our main results.     

Periodic Solution for Fuzzy Cohen–Grossberg BAM Neural Networks with Both Time-Varying and Distributed Delays and Variable Coefficients

In this paper, we investigate the existence and global exponential stability of periodic solution for a general class of fuzzy Cohen–Grossberg bidirectional associative memory (BAM) neural networks with both time-varying and (finite or infinite) distributed delays and variable coefficients. Some novel sufficient conditions for ascertaining the existence, uniqueness, global attractivity and exponential stability of the periodic solution to the considered system are obtained by applying matrix theory, inequality analysis technique and contraction mapping principle. The results remove the usual assumption that the activation functions are bounded and/or continuously differentiable. It is believed that these results are significant and useful for the design and applications of fuzzy Cohen–Grossberg BAM neural networks. Moreover, an example is employed to illustrate the effectiveness and feasibility of the results obtained here.     

The numerical simulation of periodic solutions for a predator–prey system

In this article, the existence and global stability of periodic solutions for a semi-ratio-dependent predator–prey system with Holling IV functional response and time delays are investigated. Using coincidence degree theory and Lyapunov method, sufficient conditions for the existence and global stability of periodic solutions are obtained. A numerical simulation is given to illustrate the results.     

Stability and existence of periodic solutions in inertial BAM neural networks with time delay

In this paper, the global exponential stability and existence of periodic solutions for inertial BAM neural networks are investigated. The system is transformed to first-order differential equation with chosen variable substitution. Then, some new sufficient conditions that ensure the existence and exponential stability of periodic solutions for the system are obtained by constructing suitable Lyapunov function, using Weierstrass criteria and boundedness of solutions. Finally, an example is given to illustrate the effectiveness of the results.     

Exponential stability and periodic oscillatory solution in BAMnetworks with delays

Both exponential stability and periodic oscillatory solution of bidirectional associative memory (BAM) networks with axonal signal transmission delays are considered by constructing suitable Lyapunov functional and some analysis techniques. Some simple sufficient conditions are given ensuring the global exponential stability and the existence of periodic oscillatory solutions of BAM with delays. These conditions are presented in terms of system parameters and have important leading significance in the design and applications of globally exponentially stable and periodic oscillatory neural circuits for BAM with delays. In addition, two examples are given to illustrate the results.     

Uniform global asymptotic stabilisation of bilinear non-homogeneous periodic systems with stable free dynamics

We study the problem of uniform global asymptotic stabilisation of the origin for bilinear non-homogeneous control systems with periodic coefficients by means of state feedback. We assume that the free dynamic system is Lyapunov stable. We obtain new controllability-like rank conditions, which are sufficient for uniform global asymptotic stabilisation of the periodic bilinear systems. The proof is based on the use of the Krasovsky–La Salle invariance principle for periodic systems. A stabilising feedback control law is quadratic in the state variable and periodic in the time variable. Consequences derived for linear and homogeneous bilinear systems. Under some assumptions, the controllability-like rank condition for linear and homogeneous bilinear systems coincides correspondingly with the property of complete controllability and consistency.     

参数摄动混杂离散系统的鲁棒稳定性

采用线性矩阵不等式(LMI)方法研究离散事件状态转移条件为状态依赖的参数摄动线性混杂离散系统的鲁棒稳定性问题, 提出此类系统全局鲁棒渐近稳定性判定定理, 基于分段Lyapunov函数给出了一般混杂离散系统在Lyapunov意义下局部稳定的判定定理, 该定理可将线性混杂离散系统的稳定性问题转化为LMI问题, 在此基础上提出了参数摄动线性混杂离散系统在Lyapunov意义下局部鲁棒稳定的充分条件.