scholarly journals Robustness of Hopfield Neural Networks Described by Differential Algebraic Systems of Index-1 under the Conditions of Deviation Argument and Stochastic Disturbance

2021 ◽  
Vol 2021 ◽  
pp. 1-15
Author(s):  
Qing Liu ◽  
Ping Li ◽  
Zuqiao Yang ◽  
Zhibing Liu
Keyword(s):  
Noise Intensity ◽  
Hopfield Neural Network ◽  
Interval Length ◽  
Theory Method ◽  
Stochastic Disturbances ◽  
Deviation Function ◽  
Algebraic Systems ◽  
Stochastic Disturbance ◽  
Exponentially Stable ◽  
First Time

Robustness refers to the ability of a system to maintain its original state under a continuous disturbance conditions. The deviation argument (DA) and stochastic disturbances (SDs) are enough to disrupt a system and keep it off course. Therefore, it is of great significance to explore the interval length of the deviation function and the intensity of noise to make a system remain exponentially stable. In this paper, the robust stability of Hopfield neural network (VPHNN) models based on differential algebraic systems (DAS) is studied for the first time. By using integral inequalities, expectation inequalities, and the basic control theory method, the upper bound of the interval of the deviation function and the noise intensity are found, and the system is guaranteed to remain exponentially stable under these disturbances. It is shown that as long as the deviation and disturbance of a system are within a certain range, there will be no unstable consequences. Finally, several simulation examples are used to verify the effectiveness of the approach and are described below.

Subspace identification for a stochastic model of plague

2016 ◽  
Vol 09 (05) ◽  
pp. 1650069 ◽  
Author(s):  
Miao Yu ◽  
Jianchang Liu
Keyword(s):  
Stochastic Model ◽  
Discrete Model ◽  
Noise Intensity ◽  
Classical Model ◽  
Least Square Method ◽  
Least Square ◽  
Subspace Identification ◽  
Stochastic Disturbances

In this paper, a stochastic model of plague is first studied by subspace identification. First, the discrete model of plague is obtained based on the classical model. The corresponding stochastic model is proposed for the existence of stochastic disturbances. Second, for the model, the parameter matrices and noise intensity are obtained. Finally, the simulations of the model show that the subspace identification is more precise than least square method.

IMPROVED SUFFICIENT CONDITIONS FOR GLOBAL EXPONENTIAL STABILITY OF RECURRENT NEURAL NETWORKS WITH DISTRIBUTED DELAYS

2008 ◽  
Vol 18 (07) ◽  
pp. 2029-2037
Author(s):  
WEI WU ◽  
BAO TONG CUI ◽  
ZHIGANG ZENG
Keyword(s):  
Neural Network ◽  
Neural Networks ◽  
Exponential Stability ◽  
Recurrent Neural Networks ◽  
Sufficient Conditions ◽  
Hopfield Neural Network ◽  
Cellular Neural Network ◽  
Distributed Delays ◽  
Globally Exponential Stability ◽  
Exponentially Stable

In this paper, the globally exponential stability of recurrent neural networks with continuously distributed delays is investigated. New theoretical results are presented in the presence of external stimuli. It is shown that the recurrent neural network is globally exponentially stable, and the estimated location of the equilibrium point can be obtained. As typical representatives, the Hopfield neural network (HNN) and the cellular neural network (CNN) are examined in detail. Comparison between our results and the previous results admits the improvement of our results.

scholarly journals LMI-Based Stability Criterion for Impulsive CGNNs via Fixed Point Theory

2015 ◽  
Vol 2015 ◽  
pp. 1-10 ◽  
Author(s):  
Xiongrui Wang ◽  
Ruofeng Rao ◽  
Shouming Zhong
Keyword(s):  
Fixed Point ◽  
Contraction Mapping ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Contraction Mapping Theorem ◽  
Related Literature ◽  
Variation Range ◽  
Exponentially Stable ◽  
The Stability ◽  
First Time

Linear matrices inequalities (LMIs) method and the contraction mapping theorem were employed to prove the existence of globally exponentially stable trivial solution for impulsive Cohen-Grossberg neural networks (CGNNs). It is worth mentioning that it is the first time to use the contraction mapping theorem to prove the stability for CGNNs while only the Leray-Schauder fixed point theorem was applied in previous related literature. An example is given to illustrate the effectiveness of the proposed methods due to the large allowable variation range of impulse.

Research on Optimal CDMA Multiuser Detection Based on Stochastic Hopfield Neural Network

2019 ◽  
Vol 12 (3) ◽  
pp. 233-240
Author(s):  
Tongke Fan
Keyword(s):  
Neural Network ◽  
Local Convergence ◽  
High Speed ◽  
Hopfield Neural Network ◽  
Communication Model ◽  
State Variables ◽  
Stochastic Disturbance ◽  
Detection Techniques ◽  
The Neural Network ◽  
Searching Ability

Background: Most of the common multi-user detection techniques have the shortcomings of large computation and slow operation. For Hopfield neural networks, there are some problems such as high-speed searching ability and parallel processing, but there are local convergence problems. Objective: The stochastic Hopfield neural network avoids local convergence by introducing noise into the state variables and then achieves the optimal detection. Methods: Based on the study of CDMA communication model, this paper presents and models the problem of multi-user detection. Then a new stochastic Hopfield neural network is obtained by introducing a stochastic disturbance into the traditional Hopfield neural network. Finally, the problem of CDMA multi-user detection is simulated. Conclusion: The results show that the introduction of stochastic disturbance into Hopfield neural network can help the neural network to jump out of the local minimum, thus achieving the minimum and improving the performance of the neural network.

GUARANTEED ATTRACTIVITY OF EQUILIBRIUM POINTS IN A CLASS OF DELAYED NEURAL NETWORKS

2006 ◽  
Vol 16 (09) ◽  
pp. 2737-2743 ◽  
Author(s):  
XIAOFAN YANG ◽  
XIAOFENG LIAO ◽  
YUANYAN TANG ◽  
DAVID J. EVANS
Keyword(s):  
Neural Networks ◽  
Stable Equilibrium ◽  
Equilibrium Points ◽  
Practical Importance ◽  
Activation Functions ◽  
Qualitative Properties ◽  
Domains Of Attraction ◽  
Delayed Neural Networks ◽  
Exponentially Stable ◽  
First Time

This paper addresses qualitative properties of equilibrium points in a class of delayed neural networks. We derive a sufficient condition for the local exponential stability of equilibrium points, and give an estimate on the domains of attraction of locally exponentially stable equilibrium points. Our condition and estimate are formulated in terms of the network parameters, the neurons' activation functions and the associated equilibrium point; hence, they are easily checkable. Another advantage of our results is that they neither depend on monotonicity of the activation functions nor on symmetry of the interconnection matrix. Our work has practical importance in evaluating the performance of the related associative memory. To our knowledge, this is the first time to present an estimate on the domains of attraction of equilibrium points for delayed neural networks.

scholarly journals Stable bounded value analysis of disturbance in stochastic linear power systems

2020 ◽  
pp. 002029402095910
Author(s):  
Jie Xu ◽  
Zhanbei Tong ◽  
Wengen Gao
Keyword(s):  
Stability Analysis ◽  
Power Systems ◽  
Power System ◽  
Numerical Solution ◽  
Stochastic Disturbances ◽  
Value Analysis ◽  
Stochastic Disturbance ◽  
Infinite Systems ◽  
Analysis Process ◽  
The Stability

Stochastic disturbances play a profound problem in the power system, which have an important impact on the stability of the power system. The paper proposes the stability analysis of stochastic disturbance bounded value of linear power system, and presents that the stability of power system has bounded value under stochastic disturbance and additional disturbance, and gives the analysis process in combination with stochastic differentiation. The equation theory proposes a numerical solution based on mean stability to calculate the boundedness of infinite systems under the influence of stochastic disturbance and additional disturbance. The results show that the system has bounded value stability under the disturbance.

Functional derivatives for the critical magnetic field of Pb

1978 ◽  
Vol 56 (9) ◽  
pp. 1248-1254 ◽  
Author(s):  
J. M. Daams ◽  
J. P. Carbotte
Keyword(s):  
Magnetic Field ◽  
Critical Temperature ◽  
Critical Field ◽  
Coulomb Repulsion ◽  
Critical Magnetic Field ◽  
Deviation Function ◽  
Functional Derivatives ◽  
First Time ◽  
Reduced Temperature ◽  
Good Agreement

We have calculated for superconducting Pb in the dirty (isotropic) limit the following functional derivatives: δTc/δα2F(ω), δHc(0)/δα2F(ω), δD(t)/δα2F(ω), ∂Tc/∂μ*, ∂Hc(0)/∂μ*, and ∂D(t)/∂μ*, where Tc, Hc(0), D(t), t, α2(ω)F(ω), and μ* are, respectively, the critical temperature, critical field at T = 0, deviation function for the critical field, reduced temperature T/Tc, electron–phonon spectral density, and Coulomb repulsion parameter. Our values for the first two functional derivatives are in good agreement with previous work by Rainer and Bergmann. We present the others here for the first time to relate the observed changes in Tc, Hc(0), and D(t) under hydrostatic pressure to the change in α2(ω)F(ω) and μ*.

scholarly journals Exploration on Robustness of Exponentially Global Stability of Recurrent Neural Networks with Neutral Terms and Generalized Piecewise Constant Arguments

2021 ◽  
Vol 2021 ◽  
pp. 1-13
Author(s):  
Wenxiao Si ◽  
Tao Xie ◽  
Biwen Li
Keyword(s):  
Global Stability ◽  
Signal Transmission ◽  
Original System ◽  
Interval Length ◽  
Piecewise Constant Arguments ◽  
Piecewise Constant ◽  
Compression Coefficient ◽  
Transmission Process ◽  
Exponentially Stable ◽  
The Given

With a view to the interference of piecewise constant arguments (PCAs) and neutral terms (NTs) to the original system and the significant applications in the signal transmission process, we explore the robustness of the exponentially global stability (EGS) of recurrent neural network (RNN) with PCAs and NTs (NPRNN). The following challenges arise: what the range of PCAs and the scope of NTs can NPRNN tolerate to be exponentially stable. So we derive two important indicators: maximum interval length of PCAs and the scope of neutral term (NT) compression coefficient here for NPRNN to be exponentially stable. Additionally, we theoretically proved that if the interval length of PCAs and the bound of NT compression coefficient are all lower than the given results herein, the disturbed NPRNN will still remain global exponential stability. Finally, there are two numerical examples to verify the deduced results’ effectiveness here.

scholarly journals Robust Exponential Stability of Recurrent Neural Networks with Deviating Argument and Stochastic Disturbance

2020 ◽  
Vol 13 (4) ◽  
pp. 794-806
Author(s):  
Zha Mingxin ◽  
Si Wenxiao ◽  
Xie Tao
Keyword(s):  
Neural Networks ◽  
Exponential Stability ◽  
Recurrent Neural Networks ◽  
Robust Exponential Stability ◽  
Stochastic Disturbance ◽  
Deviating Argument ◽  
Know How ◽  
Exponentially Stable ◽  
The Stability ◽  
Upper Boundary

It is well known that deviating argument and stochastic disturbance may derail the stability of recurrent neural networks (RNNs). This paper discusses the robustness of global exponential stability (GES) of RNNs accompanied with deviating argument and stochastic disturbance. For a given global exponentially stable RNNs, it is interesting to know how much the length of the interval of piecewise function and the interference intensity so that the disturbed system may still be exponentially stable. The available upper boundary of the range of piecewise variables and the interference intensity in the disturbed RNNs to keep GES are the solutions of some transcendental equations. Finally, some examples are provided to demonstrate the efficacy of the inferential results.

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