共查询到20条相似文献,搜索用时 46 毫秒
1.
该文研究Hopfield神经网络概周期解的存在性和全局吸性,获得了该网络存在唯一概周期解的充分条件和所有解收敛于此概周期解的充分条件。 相似文献
2.
《Nonlinear Analysis: Real World Applications》2008,9(2):663-673
This paper is devoted to the existence and globally exponential stability of almost periodic solution for a class of Cohen–Grossberg neural networks with variable coefficients. By using Banach fixed point theorem and applying inequality technique, we give some sufficient conditions ensuring the existence and globally exponential stability of almost periodic solution. These results have important leading significance in designs and applications of Cohen–Grossberg neural networks. Finally, two examples with their numerical simulations are provided to show the correctness of our analysis. 相似文献
3.
In this paper, by using the contraction principle and Gronwall–Bellman’s inequality, some sufficient conditions are obtained for checking the existence and exponential stability of almost periodic solution for shunting inhibitory cellular neural networks (SICNNs) with impulse. Our results are essentially new. It is the first time that the existence of almost periodic solutions for the impulsive neural networks are obtained. 相似文献
4.
LU Wenlian & CHEN Tianping Key Laboratory of Nonlinear Mathematics Science of Ministry of Education Fudan University Shanghai China 《中国科学A辑(英文版)》2005,48(8):1015-1026
Research on delayed neural networks with variable self-inhibitions, interconnection weights, and inputs is an important issue. In this paper, we discuss a large class of delayed dynamical systems with almost periodic self-inhibitions, inter-connection weights, and inputs. This model is universal and includes delayed systems with time-varying delays, distributed delays as well as combination of both. We prove that under some mild conditions, the system has a unique almost periodic solution, which is globally exponentially stable. We propose a new approach, which is independent of existing theory concerning with existence of almost periodic solution for dynamical systems. 相似文献
5.
利用Banach空间压缩不动点定理和微分不等式的分析技巧,研究一类具分布时滞的Hopfield神经网络模型的概周期解的存在性和稳定性。得到了系统存在概周期和全局指数稳定的新的充分条件。所得结果改进和推广了相关文献的结论。 相似文献
6.
Xiang Hongjun Wang Jinhua Chen Anping 《Annals of Differential Equations》2005,21(4):604-615
In this paper, a class of two-dimensional shunting inhibitory cellular neural networks with distributed delays and variable coefficients system is studied. By using the Schauder's fixed point theorem and Lyapunov function, we obtain some sufficient conditions about the existence and attractivity of almost periodic solutions to the above system, and all its solutions converge to such almost periodic solution. An example is given to illustrate that the conditions of our results are feasible. 相似文献
7.
This paper discusses a class of the bidirectional associative memories(BAM) type neural networks with impulse.By using the Banach fixed point theory and some analysis technology,we obtain the existence of almost periodic solution and stability under some sufficient conditions. 相似文献
8.
《Communications in Nonlinear Science & Numerical Simulation》2014,19(10):3857-3879
In this paper, we investigate the almost periodic dynamical behaviors for a class of general Cohen–Grossberg neural networks with discontinuous right-hand sides, time-varying and distributed delays. By means of retarded differential inclusions theory and nonsmooth analysis theory with generalized Lyapunov approach, we obtain the existence, uniqueness and global stability of almost periodic solution to the neural networks system. It is worthy to pointed out that, without assuming the boundedness or monotonicity of the discontinuous neuron activation functions, our results will also be valid. Finally, we give some numerical examples to show the applicability and effectiveness of our main results. 相似文献
9.
Almost periodic solutions of recurrent neural networks with continuously distributed delays 总被引:2,自引:0,他引:2
In this paper, a class of recurrent neural networks with continuously distributed delays is discussed. Without resorting to the theory of exponential dichotomy, several new sufficient conditions are obtained ensuring the existence of an almost periodic solution for this model based on a special functional and analysis technique. Moreover, by constructing suitable Lyapunov functions, the attractivity and exponential stability of the almost periodic solution are also considered for the system. The results obtained are helpful to design globally stable almost periodic oscillatory neural networks. A numerical example is given to show the feasibility of the results obtained. 相似文献
10.
This paper deals with the existence and global exponential stability of almost periodic solutions for quaternion-valued high-order Hopfield neural networks with delays by a direct approach. Based on the contraction mapping principle, sufficient conditions are derived to ensure the existence and uniqueness of almost periodic solutions for the networks under consideration. By constructing a suitable Lyapunov function, the global exponential stability criterion of the almost periodic solution are derived. Finally, two numerical examples are given to illustrate the main results of this paper. 相似文献
11.
一类具有逐段常变量神经网络系统概周期解存在性与指数稳定性 总被引:1,自引:0,他引:1
利用Halanay不等式,我们得到了一类具有逐段常变量神经网络系统解全局指数稳定的一个充分条件;此外,在同样条件下,通过不动点定理,证明了这类概周期系统概周期解的存在唯一性与模包含关系. 相似文献
12.
In this paper, a class of Cohen–Grossberg neural networks with bounded and unbounded delays is discussed. Several new sufficient conditions are obtained ensuring the existence and exponential stability of the almost periodic solution for this model based on inequality analysis technique and combing the exponential dichotomy with fixed point theorem. The obtained results are helpful to design globally exponentially stable almost periodic oscillatory neural networks. Two numerical examples and simulations are also given to show the feasibility of our results. 相似文献
13.
By constructing Liapunov functions and building a new inequality, we obtain two kinds of sufficient conditions for the existence and global exponential stability of almost periodic solution for a Hopfield-type neural networks subject to almost periodic external stimuli. In this paper, we assume that the network parameters vary almost periodically with time and we incorporate variable delays in the processing part of the network architectures. 相似文献
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15.
The objective of this paper is to investigate the dynamics of a class of delayed Cohen–Grossberg neural networks with discontinuous neuron activations. By means of retarded differential inclusions, we obtain a result on the local existence of solutions, which improves the previous related results for delayed neural networks. It is shown that an M-matrix condition satisfied by the neuron interconnections, can guarantee not only the existence and uniqueness of an almost periodic solution, but also its global exponential stability. It is also shown that the M-matrix condition ensures that all solutions of the system display a common asymptotic behavior. In this paper, we prove that the existence interval of the almost periodic solution is (?∞, +∞), whereas the existence interval is only proved to be [0, +∞) in most of the literature. As special cases, we derive the results of existence, uniqueness and global exponential stability of a periodic solution for delayed neural networks with periodic coefficients, as well as the similar results of an equilibrium for the systems with constant coefficients. To the author’s knowledge, the results in this paper are the only available results on almost periodicity for Cohen–Grossberg neural networks with discontinuous activations and delays. 相似文献
16.
Syed Abbas 《Acta Appl Math》2012,119(1):57-74
In this paper we discuss the existence and global attractivity of k-pseudo almost automorphic sequence solution of a model of bidirectional cellular neural networks. We consider the corresponding
difference equation analogue of the model system using suitable discretization method and obtain certain conditions for the
existence of solution. The k-pseudo almost automorphic sequence solutions generalize the results of pseudo almost periodic, almost periodic and almost
automorphic sequences solutions. Moreover the results proved in this paper are new and compliment the existing one. 相似文献
17.
In this work, we consider a class of neutral shunting inhibitory cellular neural networks with mixed delays. We study the existence, uniqueness, and the exponential stability of the measure pseudo almost periodic (or μ-pseudo almost periodic) solutions from some models for shunting inhibitory cellular neural networks with mixed delays. An example is provided to illustrate the theory developed in this work. 相似文献
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19.
Existence and global exponential stability of almost periodic solution for CNNs with variable coefficients and delays 总被引:1,自引:0,他引:1
By using exponential dichotomy and the Banach fixed-point theory and combining Yang inequality, some sufficient conditions are derived ensuring existence and global exponential stability of almost periodic solution for CNNs with variable coefficients and delays. Without assuming the boundedness of signal function, these results obtained here can be expected to have highly important significance in designs and applications of the networks. We extend and improve previously known results. 相似文献
20.
Toka Diagana 《Journal of Mathematical Analysis and Applications》2009,350(1):18-6548
This paper is concerned with the study of weighted pseudo almost periodic solutions to some classes of hyperbolic differential equations. Upon making some suitable assumptions, the existence and uniqueness of a weighted pseudo almost periodic solution is obtained. To illustrate our main result, we study the existence of a weighted pseudo almost periodic solution to a system of partial differential equations arising in control systems described by abstract retarded functional-differential equations with feedback control. 相似文献