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Wei Xing Zheng - One of the best experts on this subject based on the ideXlab platform.

  • Stability analysis of multiple equilibria for Recurrent Neural Networks with discontinuous Mexican-hat-type activation function
    2015 IEEE International Symposium on Circuits and Systems (ISCAS), 2015
    Co-Authors: Wei Xing Zheng, Jinhu Lü
    Abstract:

    This paper is concerned with stability analysis of multiple equilibria for Recurrent Neural Networks. A new type of activation function, namely, discontinuous Mexican-hat-type activation function, is proposed for Recurrent Neural Networks. Then with the aid of the fixed point theorem, some sufficient conditions for coexistent multiple equilibria are obtained to guarantee that such n-neuron Recurrent Neural Networks can have at least 4n equilibria. In view of the theory of strict diagonal dominance matrix, further stability analysis reveals that 3n equilibria are locally exponentially stable. The new results considerably improve the existing multistability results in the literature.

  • Stability analysis of multiple equilibria for Recurrent Neural Networks with time-varying delays
    2013 IEEE International Symposium on Circuits and Systems (ISCAS), 2013
    Co-Authors: Zhigang Zeng, Wei Xing Zheng
    Abstract:

    The problem of stability of multiple equilibria is studied in this paper for two kinds of Recurrent Neural Networks with time-varying delays and activation functions symmetrical with respect to the origin on the phase plane. Some sufficient conditions are obtained to ensure that two kinds of Recurrent Neural Networks can have (2m + 1)n equilibrium points and (m + 1)n of them are locally exponentially stable. The derived conditions are valuable extensions to the existing results on stability of multiple equilibria for Recurrent Neural Networks with time-varying delays in the literature.

  • A study of asymptotic stability for delayed Recurrent Neural Networks
    2009 IEEE International Symposium on Circuits and Systems, 2009
    Co-Authors: Chunwei Song, Wei Xing Zheng
    Abstract:

    This paper addresses the problem of asymptotic stability for discrete-time Recurrent Neural Networks with time-varying delay. The analysis starts with a general assumption that the time-varying delay may be expressed as the lower bound plus the length of an interval over which the delay varies. Then the delay partitioning technique is used to establish a new delay-dependent sufficient condition under which the asymptotic stability of Recurrent Neural Networks with time-varying delay can be guaranteed. The new stability criterion takes the form of linear matrix inequalities, thus lending itself to being readily checkable by the available software package. The obtained theoretical result is further illustrated by numerical results, including their superiority over the existing results on asymptotic stability of delayed Recurrent Neural Networks.

Zhigang Zeng - One of the best experts on this subject based on the ideXlab platform.

  • Stability analysis of multiple equilibria for Recurrent Neural Networks with time-varying delays
    2013 IEEE International Symposium on Circuits and Systems (ISCAS), 2013
    Co-Authors: Zhigang Zeng, Wei Xing Zheng
    Abstract:

    The problem of stability of multiple equilibria is studied in this paper for two kinds of Recurrent Neural Networks with time-varying delays and activation functions symmetrical with respect to the origin on the phase plane. Some sufficient conditions are obtained to ensure that two kinds of Recurrent Neural Networks can have (2m + 1)n equilibrium points and (m + 1)n of them are locally exponentially stable. The derived conditions are valuable extensions to the existing results on stability of multiple equilibria for Recurrent Neural Networks with time-varying delays in the literature.

  • dynamic behaviors of memristor based Recurrent Neural Networks with time varying delays
    Neural Networks, 2012
    Co-Authors: Ailong Wu, Zhigang Zeng
    Abstract:

    The paper introduces a general class of memristor-based Recurrent Neural Networks with time-varying delays. Conditions on the nondivergence and global attractivity are established by using local inhibition, respectively. Moreover, exponential convergence of the Networks is studied by using local invariant sets. The analysis in the paper employs results from the theory of differential equations with discontinuous right-hand sides as introduced by Filippov. The obtained results extend some previous works on conventional Recurrent Neural Networks.

Jun Wang - One of the best experts on this subject based on the ideXlab platform.

  • global stability of complex valued Recurrent Neural Networks with time delays
    IEEE Transactions on Neural Networks, 2012
    Co-Authors: Jin Hu, Jun Wang
    Abstract:

    Since the last decade, several complex-valued Neural Networks have been developed and applied in various research areas. As an extension of real-valued Recurrent Neural Networks, complex-valued Recurrent Neural Networks use complex-valued states, connection weights, or activation functions with much more complicated properties than real-valued ones. This paper presents several sufficient conditions derived to ascertain the existence of unique equilibrium, global asymptotic stability, and global exponential stability of delayed complex-valued Recurrent Neural Networks with two classes of complex-valued activation functions. Simulation results of three numerical examples are also delineated to substantiate the effectiveness of the theoretical results.

  • Global exponential stability and periodicity of Recurrent Neural Networks with time delays
    IEEE Transactions on Circuits and Systems I: Regular Papers, 2005
    Co-Authors: Jun Wang
    Abstract:

    In this paper, the global exponential stability and periodicity of a class of Recurrent Neural Networks with time delays are addressed by using Lyapunov functional method and inequality techniques. The delayed Neural network includes the well-known Hopfield Neural Networks, cellular Neural Networks, and bidirectional associative memory Networks as its special cases. New criteria are found to ascertain the global exponential stability and periodicity of the Recurrent Neural Networks with time delays, and are also shown to be different from and improve upon existing ones.

  • Recurrent Neural Networks for Computing Pseudoinverses of Rank-Deficient Matrices
    SIAM Journal on Scientific Computing, 1997
    Co-Authors: Jun Wang
    Abstract:

    Three Recurrent Neural Networks are presented for computing the pseudoinverses of rank-deficient matrices. The first Recurrent Neural network has the dynamical equation similar to the one proposed earlier for matrix inversion and is capable of Moore--Penrose inversion under the condition of zero initial states. The second Recurrent Neural network consists of an array of neurons corresponding to a pseudoinverse matrix with decaying self-connections and constant connections in each row or column. The third Recurrent Neural network consists of two layers of neuron arrays corresponding, respectively, to a pseudoinverse matrix and a Lagrangian matrix with constant connections. All three Recurrent Neural Networks are also composed of a number of independent subNetworks corresponding to the rows or columns of a pseudoinverse. The proposed Recurrent Neural Networks are shown to be capable of computing the pseudoinverses of rank-deficient matrices.

  • Recurrent Neural Networks for synthesizing linear control systems via pole placement
    Proceedings Sixth International Conference on Tools with Artificial Intelligence. TAI 94, 1994
    Co-Authors: Jun Wang, G. Wu
    Abstract:

    Recurrent Neural Networks are proposed for synthesizing linear control systems through pole placement. The proposed Neural Networks approach uses two coupled Recurrent Neural Networks for computing feedback gain matrix. Each Neural network consists of two bidirectionally connected layers and each layer consists of an array of neurons. The proposed Recurrent Neural Networks are shown to be capable of synthesizing linear control systems in real time. The operating characteristics of the Recurrent Neural Networks and closed-loop systems are demonstrated by use of two illustrative examples.

  • Recurrent Neural Networks for solving linear matrix equations
    Computers & Mathematics With Applications, 1993
    Co-Authors: Jun Wang
    Abstract:

    Abstract Recurrent Neural Networks for solving linear matrix equations are proposed. The proposed Recurrent Neural Networks consist of two bidirectionally connected layers and each layer consists of an array of neurons. The proposed Recurrent Neural Networks are shown to be asymptotically stable in the large and capable of computing inverse matrices and solving Lyapunov matrix equations. The operating characteristics of the proposed Recurrent Neural Networks are demonstrated via several illustrative examples.

Zhanshan Wang - One of the best experts on this subject based on the ideXlab platform.

  • A Comprehensive Review of Stability Analysis of Continuous-Time Recurrent Neural Networks
    IEEE Transactions on Neural Networks and Learning Systems, 2014
    Co-Authors: Huaguang Zhang, Zhanshan Wang
    Abstract:

    Stability problems of continuous-time Recurrent Neural Networks have been extensively studied, and many papers have been published in the literature. The purpose of this paper is to provide a comprehensive review of the research on stability of continuous-time Recurrent Neural Networks, including Hopfield Neural Networks, Cohen-Grossberg Neural Networks, and related models. Since time delay is inevitable in practice, stability results of Recurrent Neural Networks with different classes of time delays are reviewed in detail. For the case of delay-dependent stability, the results on how to deal with the constant/variable delay in Recurrent Neural Networks are summarized. The relationship among stability results in different forms, such as algebraic inequality forms, M-matrix forms, linear matrix inequality forms, and Lyapunov diagonal stability forms, is discussed and compared. Some necessary and sufficient stability conditions for Recurrent Neural Networks without time delays are also discussed. Concluding remarks and future directions of stability analysis of Recurrent Neural Networks are given.

  • global asymptotic stability of Recurrent Neural Networks with multiple time varying delays
    IEEE Transactions on Neural Networks, 2008
    Co-Authors: Huaguang Zhang, Zhanshan Wang
    Abstract:

    In this paper, several sufficient conditions are established for the global asymptotic stability of Recurrent Neural Networks with multiple time-varying delays. The Lyapunov-Krasovskii stability theory for functional differential equations and the linear matrix inequality (LMI) approach are employed in our investigation. The results are shown to be generalizations of some previously published results and are less conservative than existing results. The present results are also applied to Recurrent Neural Networks with constant time delays.

Sitian Qin - One of the best experts on this subject based on the ideXlab platform.

  • Global exponential stability of uncertain memristor-based Recurrent Neural Networks with mixed time delays
    International Journal of Machine Learning and Cybernetics, 2019
    Co-Authors: Jianmin Wang, Fengqiu Liu, Sitian Qin
    Abstract:

    The global exponential stability of the equilibrium point for uncertain memristor-based Recurrent Neural Networks is studied in this paper. The memristor-based Recurrent Neural Networks considered in this paper are based on a realistic memristor model, and can be considered as the extension of some existing memristor-based Recurrent Neural Networks. By virtue of homomorphic theory, it is proved that the uncertain memristor-based Recurrent Neural Networks have a unique equilibrium point under some mild assumptions. Moreover, the unique equilibrium point is proved to be globally exponentially stable by constructing a suitable Lyapunov functional. Finally, the obtained results are applied to determine the dynamical behaviors and circuit design of the memristor-based Recurrent Neural Networks by some numerical examples.