共查询到20条相似文献，搜索用时 15 毫秒
1.
Qiankun Song 《Journal of The Franklin Institute》2008,345(1):39-59
In this paper, the discrete-time fuzzy cellular neural network with variable delays and impulses is considered. Based on M-matrix theory and analytic methods, several simple sufficient conditions checking the global exponential stability and the existence of periodic solutions are obtained for the neural networks. Moreover, the estimation for exponential convergence rate index is proposed. The obtained results show that the stability and periodic solutions still remain under certain impulsive perturbations for the neural network with stable equilibrium point and periodic solutions. Some examples with simulations are given to show the effectiveness of the obtained results. 相似文献
2.
Chaouki Aouiti Imen Ben Gharbia Jinde Cao Ahmed Alsaedi 《Journal of The Franklin Institute》2019,356(4):2294-2324
In this letter, the existence and the global exponential stability of piecewise pseudo almost periodic solutions (PAPT) for bidirectional associative memory neural networks (BAMNNs) with time-varying delay in leakage (or forgetting) terms and impulsive are investigated by applying contraction mapping fixed point theorem, the exponential dichotomy of linear differential equations and differential inequality techniques. Furthermore, we give an explanatory example to illustrate the efficiency of the theoretical predictions. 相似文献
3.
In this paper, a discrete-time interval general BAM bidirectional associative memory neural networks model is considered. By employing the theory of coincidence degree and using Halanay-type inequality technique we establish new sufficient conditions ensuring the existence and global exponential stability of periodic solutions for the discrete-time interval general BAM bidirectional neural networks. The results obtained generalize and improve known results in [23]. An example is provided to show the correctness of our analysis. 相似文献
4.
C. Maharajan R. Raja Jinde Cao G. Rajchakit 《Journal of The Franklin Institute》2018,355(11):4727-4754
In this paper, the global robust exponential stability problem for a class of uncertain inertial-type BAM neural networks with both time-varying delays is focused through Lagrange sense. The existence of time-varying delays in discrete and distributed terms is explored with the availability of lower and upper bounds of time-varying delays. Firstly, we transform the proposed inertial BAM neural networks to usual one. Secondly, by the aid of LKF, stability theory, integral inequality, some novel sufficient conditions for the global robust exponential stability of the addressed neural networks are obtained in terms of linear matrix inequalities, which can be easily tested in practice by utilizing LMI control toolbox in MATLAB software. Furthermore, many comparisons of proposed work are listed with some existing literatures to get less conservatism. Finally, two numerical examples are provided to demonstrate the advantages and superiority of our theoretical outcomes. 相似文献
5.
Fanchao Kong Quanxin Zhu Kai Wang Juan J. Nieto 《Journal of The Franklin Institute》2019,356(18):11605-11637
In the paper, we are concerned with a class of discontinuous BAM neural networks with hybrid time-varying delays and D operator. Based on the concept of Filippov solution, by means of the differential inclusions theory and the non-smooth analysis theory with Lyapunov-like approach, some new and novel sufficient conditions are derived to guarantee the existence, uniqueness and global exponential stability of almost-periodic solution of our proposed neural network model. To the authors’ knowledge, the results established in the paper are the only available results on the BAM neural networks, connecting the three main characteristics, i.e., discontinuous activation functions, hybrid time-varying delays and D operator. Some previous works in the literature are significantly extend and complement. Finally, two topical simulation examples are given to show the effectiveness of the established main results. 相似文献
6.
In this paper, we investigate the problem of global exponential stability analysis for a class of delayed recurrent neural networks. This class includes Hopfield neural networks and cellular neural networks with interval time-delays. Improved exponential stability condition is derived by employing new Lyapunov-Krasovskii functional and the integral inequality. The developed stability criteria are delay dependent and characterized by linear matrix inequalities (LMIs). The developed results are less conservative than previous published ones in the literature, which are illustrated by representative numerical examples. 相似文献
7.
In this paper, some sufficient conditions are obtained for existence and global exponential stability of a unique equilibrium point of competitive neural networks with different time scales and multiple delays by using nonlinear Lipschitz measure (NLM) method and constructing suitable Lyapunov functional. The results of this paper are new and they complete previously known results. 相似文献
8.
《Journal of The Franklin Institute》2021,358(16):8656-8677
In this paper, a class of nonlocal Hopfield neural networks with random initial data is introduced, where the randomness may be of probability uncertainty. Sufficient conditions are derived to ensure the existence and globally exponential convergence of periodic solution for the addressed system in the frame of nonlinear expectation and linear expectation, respectively. Moreover, numerical examples are given to show the effectiveness of the obtained results. 相似文献
9.
In this paper, the exponential stability of a class of delayed neural networks described by nonlinear delay differential equations of the neutral type has been studied. By constructing appropriate Lyapunov functional and using the linear matrix inequality (LMI) optimization approach, a series of sufficient criteria is obtained ensuring the existence, uniqueness and global exponential stability of an equilibrium point of such a kind of delayed neural networks. These conditions are dependent on the size of the time delay and the measure of the space, which is usually less conservative than delay-independent and space-independent ones. And, these networks are generalized without assuming the boundedness and differentiability of the activate functions. The proposed LMI condition can be checked easily by recently developed algorithms. The results are new and improve the earlier work. Examples are provided to demonstrate the effectiveness and applicability of the proposed criteria. 相似文献
10.
In this paper, we investigate the problem of global exponential dissipativity of neural networks with variable delays and impulses. The impulses are classified into three classes: input disturbances, stabilizing and “neutral” type—the impulses are neither helpful for stabilizing nor destabilizing the neural networks. We handle the three types of impulses in a uniform way by using the excellent ideology introduced recently. To this end, we propose new techniques which coupled with more general Lyapunov functions to realize the ideology and it is shown that they are more effective. Exponential dissipativity conditions are established in terms of linear matrix inequalities (LMIs) and these conditions can be straightforwardly reduced to exponential stability conditions. Numerical results are given to show that the obtained conditions are effective and less conservative than the existing ones. 相似文献
11.
This paper deals with the problem of the global robust asymptotic stability of the class of dynamical neural networks with multiple time delays. We propose a new alternative sufficient condition for the existence, uniqueness and global asymptotic stability of the equilibrium point under parameter uncertainties of the neural system. We first prove the existence and uniqueness of the equilibrium point by using the Homomorphic mapping theorem. Then, by employing a new Lyapunov functional, the Lyapunov stability theorem is used to establish the sufficient condition for the asymptotic stability of the equilibrium point. The obtained condition is independent of time delays and relies on the network parameters of the neural system only. Therefore, the equilibrium and stability properties of the delayed neural network can be easily checked. We also make a detailed comparison between our result and the previous corresponding results derived in the previous literature. This comparison proves that our result is new and improves some of the previously reported robust stability results. Some illustrative numerical examples are given to show the applicability and advantages of our result. 相似文献
12.
In this paper, we consider the stability of a class of stochastic delay Hopfield neural networks driven by G-Brownian motion. Under a sublinear expectation framework, we give the definition of exponential stability in mean square and construct some conditions such that the stochastic system is exponentially stable in mean square. Moreover, we also consider the stability of the Euler numerical solution of such equation. Finally, we give an example and its numerical simulation to illustrate our results. 相似文献
13.
Qiankun Song 《Journal of The Franklin Institute》2006,343(7):705-719
In this paper, the global exponential robust stability is investigated for Cohen-Grossberg neural network with time-varying delays and reaction-diffusion terms, this neural network contains time-invariant uncertain parameters whose values are unknown but bounded in given compact sets. Neither the boundedness and differentiability on the activation functions nor the differentiability on the time-varying delays are assumed. By using general Halanay inequality and M-matrix theory, several new sufficient conditions are obtained to ensure the existence, uniqueness, and global exponential robust stability of equilibrium point for Cohen-Grossberg neural network with time-varying delays and reaction-diffusion terms. Several previous results are improved and generalized, and three examples are given to show the effectiveness of the obtained results. 相似文献
14.
This paper is concerned with a class of neutral delay BAM neural networks with time-varying delays in leakage terms. Some sufficient conditions are established to ensure the existence and exponential stability for such class of neural networks by employing the exponential dichotomy of linear differential equations, fixed point theorems and differential inequality techniques. An example is provided to show the effectiveness of the theoretical results. The results of this paper are completely new and complementary to the previously known results. 相似文献
15.
Global exponential robust stability of static interval neural networks with S-type distributed delays 总被引：1，自引：0，他引：1
The authors in [7] obtained the global asymptotical stability for static interval neural networks with S-type distributed delays by using the Razumikhin theorem. The aim of our paper is to investigate the global exponential robust stability by using the Lyapunov functional methods, and we will improve the proof methods more concise. A theorem and a corollary were obtained in which the boundedness, monotonicity and differentiability conditions on the activation functions are not required. So we generalize the results of related literature [7]. As an application, an example to demonstrate our results is given. 相似文献
16.
通过构造V函数法及细致的分析得到系统的一致持续性,在种群一致持续性前提下,利用Brouwer不动点定理证明系统至少存在一个正周期解,并通过构造Lyapunov泛函和运用微分不等式,稳定性理论及Barbalat’s引理得到了判定正周期解的全局渐近稳定性和全局吸引的充分条件。 相似文献
17.
In this paper, an auxiliary model-based nonsingular M-matrix approach is used to establish the global exponential stability of the zero equilibrium, for a class of discrete-time high-order Cohen–Grossberg neural networks (HOCGNNs) with time-varying delays, connection weights and impulses. A new impulse-free discrete-time HOCGNN with time-varying delays and connection weights is firstly constructed, and the relationship between the solutions of original systems and new HOCGNNs is indicated by a technical lemma. From which, the global exponential stability criteria for the zero equilibrium are derived by using an inductive idea and the properties of nonsingular M-matrices. The effectiveness of the obtained stability criteria is illustrated by numerical examples. Compared with the previous results, this paper has three advantages: (i) The Lyapunov–Krasovskii functional is not required; (ii) The obtained global exponential stability criteria are applied to check whether a matrix is a nonsingular M-matrix, which can be conveniently tested; (iii) The proposed approach applies to most of discrete-time system models with impulses and delays. 相似文献
18.
This paper considers existence, uniqueness and the global asymptotic stability of fuzzy cellular neural networks with mixed delays. The mixed delays include constant delay in the leakage term (i.e., “leakage delay”), time-varying delays and continuously distributed delays. Based on the Lyapunov method and the linear matrix inequality (LMI) approach, some sufficient conditions ensuring global asymptotic stability of the equilibrium point are derived, which are dependent on both the discrete and distributed time delays. These conditions are expressed in terms of LMI and can be easily checked by MATLAB LMI toolbox. In addition, two numerical examples are given to illustrate the feasibility of the result. 相似文献
19.
This paper investigates the pth moment exponential stability of impulsive stochastic functional differential equations. Some sufficient conditions are obtained to ensure the pth moment exponential stability of the equilibrium solution by the Razumikhin method and Lyapunov functions. Based on these results, we further discuss the pth moment exponential stability of generalized impulsive delay stochastic differential equations and stochastic Hopfield neural networks with multiple time-varying delays from the impulsive control point of view. The results derived in this paper improve and generalize some recent works reported in the literature. Moreover, we see that impulses do contribute to the stability of stochastic functional differential equations. Finally, two numerical examples are provided to demonstrate the efficiency of the results obtained. 相似文献
20.
R. Raja U. Karthik Raja R. Samidurai A. Leelamani 《Journal of The Franklin Institute》2013,350(10):3217-3247
This paper addresses the problem of global exponential dissipativity for a class of uncertain discrete-time BAM stochastic neural networks with time-varying delays, Markovian jumping and impulses. By constructing a proper Lyapunov–Krasovskii functional and combining with linear matrix inequality (LMI) technique, several sufficient conditions are derived for verifying the global exponential dissipativity in the mean square of such stochastic discrete-time BAM neural networks. The derived conditions are established in terms of linear matrix inequalities, which can be easily solved by some available software packages. One important feature presented in our paper is that without employing model transformation and free-weighting matrices our obtained result leads to less conservatism. Additionally, three numerical examples with simulation results are provided to show the effectiveness and usefulness of the obtained result. 相似文献