scholarly journals On the Global Dissipativity of a Class of Cellular Neural Networks with Multipantograph Delays

2011 ◽  
Vol 2011 ◽  
pp. 1-7 ◽  
Author(s):  
Liqun Zhou
Keyword(s):  
Neural Networks ◽  
Sufficient Conditions ◽  
Cellular Neural Networks ◽  
Variable Coefficients ◽  
The Other ◽  
Algebraic Methods ◽  
Lyapunov Functionals ◽  
The One ◽  
Delay Dependent ◽  
First Time

For the first time the global dissipativity of a class of cellular neural networks with multipantograph delays is studied. On the one hand, some delay-dependent sufficient conditions are obtained by directly constructing suitable Lyapunov functionals; on the other hand, firstly the transformation transforms the cellular neural networks with multipantograph delays into the cellular neural networks with constant delays and variable coefficients, and then constructing Lyapunov functionals, some delay-independent sufficient conditions are given. These new sufficient conditions can ensure global dissipativity together with their sets of attraction and can be applied to design global dissipative cellular neural networks with multipantograph delays and easily checked in practice by simple algebraic methods. An example is given to illustrate the correctness of the results.

scholarly journals Global Stability of Almost Periodic Solution of a Class of Neutral-Type BAM Neural Networks

2012 ◽  
Vol 2012 ◽  
pp. 1-18
Author(s):  
Tetie Pan ◽  
Bao Shi ◽  
Jian Yuan
Keyword(s):  
Neural Networks ◽  
Periodic Solution ◽  
Neutral Type ◽  
Sufficient Conditions ◽  
Variable Coefficients ◽  
Almost Periodic Solution ◽  
Bam Neural Networks ◽  
Almost Periodic ◽  
Globally Exponential Stability ◽  
First Time

A class of BAM neural networks with variable coefficients and neutral delays are investigated. By employing fixed-point theorem, the exponential dichotomy, and differential inequality techniques, we obtain some sufficient conditions to insure the existence and globally exponential stability of almost periodic solution. This is the first time to investigate the almost periodic solution of the BAM neutral neural network and the results of this paper are new, and they extend previously known results.

Global exponential stability of cellular neural networks with multi-proportional delays

2015 ◽  
Vol 08 (06) ◽  
pp. 1550071 ◽  
Author(s):  
Liqun Zhou ◽  
Yanyan Zhang
Keyword(s):  
Neural Networks ◽  
Exponential Stability ◽  
Global Exponential Stability ◽  
Sufficient Conditions ◽  
Cellular Neural Networks ◽  
Varying Coefficients ◽  
Proportional Delays ◽  
Time Varying Coefficients ◽  
Delay Differential ◽  
Delay Dependent

In this paper, a class of cellular neural networks (CNNs) with multi-proportional delays is studied. The nonlinear transformation yi(t) = xi( e t) transforms a class of CNNs with multi-proportional delays into a class of CNNs with multi-constant delays and time-varying coefficients. By applying Brouwer fixed point theorem and constructing the delay differential inequality, several delay-independent and delay-dependent sufficient conditions are derived for ensuring the existence, uniqueness and global exponential stability of equilibrium of the system and the exponentially convergent rate is estimated. And several examples and their simulations are given to illustrate the effectiveness of obtained results.

GLOBAL EXPONENTIAL STABILITY CONDITIONS FOR DELAYED PARABOLIC NEURAL NETWORKS WITH VARIABLE COEFFICIENTS

2007 ◽  
Vol 17 (12) ◽  
pp. 4409-4415
Author(s):  
XUYANG LOU ◽  
BAOTONG CUI
Keyword(s):  
Neural Networks ◽  
Exponential Stability ◽  
Differential Inequality ◽  
Global Exponential Stability ◽  
Sufficient Conditions ◽  
Variable Coefficients ◽  
Lyapunov Functionals ◽  
The Stability ◽  
Delay Differential ◽  
Delay Differential Inequality

In this paper, we present a class of delayed parabolic neural networks (DPNN) with variable coefficients. Some sufficient conditions for the global exponential stability of the DPNN with variable coefficients are derived by a method based on delay differential inequality. The method, which does not make use of Lyapunov functionals, is simple and effective for the stability analysis of DPNN with variable coefficients.

NOVEL STABILITY CONDITIONS FOR CELLULAR NEURAL NETWORKS WITH TIME DELAY

2001 ◽  
Vol 11 (07) ◽  
pp. 1853-1864 ◽  
Author(s):  
XIAOFENG LIAO ◽  
KWOK-WO WONG ◽  
JUEBANG YU
Keyword(s):  
Neural Networks ◽  
Time Delay ◽  
Asymptotic Stability ◽  
Global Asymptotic Stability ◽  
Research Work ◽  
Sufficient Conditions ◽  
Cellular Neural Networks ◽  
Lyapunov Functionals ◽  
Time Varying ◽  
Time Varying Delay

In this paper, the global asymptotic stability of cellular neural networks with time delay is discussed using some novel Lyapunov functionals. Novel sufficient conditions for this type of stability are derived. They are less restrictive and more practical than those currently used. As a result, the design of cellular neural networks with time delay is refined. Our work can also be generalized to cellular neural networks with time-varying delay, a topic on which little research work has been done. By means of several different Lyapunov functionals, some sufficient conditions related to the global asymptotic stability for cellular neural networks with perturbations of time-varying delays are derived.

scholarly journals Existence and Global Uniform Asymptotic Stability of Almost Periodic Solutions for Cellular Neural Networks with Discrete and Distributed Delays

2013 ◽  
Vol 2013 ◽  
pp. 1-6 ◽  
Author(s):  
Zongyi Hou ◽  
Hongying Zhu ◽  
Chunhua Feng
Keyword(s):  
Differential Equation ◽  
Neural Networks ◽  
Asymptotic Stability ◽  
Periodic Solutions ◽  
Sufficient Conditions ◽  
Cellular Neural Networks ◽  
Lyapunov Functionals ◽  
Almost Periodic Solutions ◽  
Almost Periodic ◽  
Uniform Asymptotic Stability

This paper discusses the existence and global uniform asymptotic stability of almost periodic solutions for cellular neural networks (CNNS). By utilizing the theory of the almost periodic differential equation and the Lyapunov functionals method, some sufficient conditions are obtained to ensure the existence and global uniform asymptotic stability. An example is given to illustrate the effectiveness of the main results.

scholarly journals Existence and exponential stability of a periodic solution for fuzzy cellular neural networks with time-varying delays

2011 ◽  
Vol 21 (4) ◽  
pp. 649-658 ◽  
Author(s):  
Qianhong Zhang ◽  
Lihui Yang ◽  
Daixi Liao
Keyword(s):  
Neural Networks ◽  
Periodic Solution ◽  
Exponential Stability ◽  
Differential Inequality ◽  
Sufficient Conditions ◽  
Coincidence Degree ◽  
Cellular Neural Networks ◽  
Time Varying ◽  
Fuzzy Cellular Neural Networks ◽  
Inequality Technique

Existence and exponential stability of a periodic solution for fuzzy cellular neural networks with time-varying delays Fuzzy cellular neural networks with time-varying delays are considered. Some sufficient conditions for the existence and exponential stability of periodic solutions are obtained by using the continuation theorem based on the coincidence degree and the differential inequality technique. The sufficient conditions are easy to use in pattern recognition and automatic control. Finally, an example is given to show the feasibility and effectiveness of our methods.

scholarly journals An LMI Approach for Dynamics of Switched Cellular Neural Networks with Mixed Delays

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Chuangxia Huang ◽  
Hanfeng Kuang ◽  
Xiaohong Chen ◽  
Fenghua Wen
Keyword(s):  
Neural Networks ◽  
Sufficient Conditions ◽  
Average Dwell Time ◽  
Cellular Neural Networks ◽  
Linear Matrix ◽  
Mixed Delays ◽  
Ultimate Boundedness ◽  
Globally Exponential Stability ◽  
Average Dwell Time Method ◽  
Uniformly Ultimate Boundedness

This paper considers the dynamics of switched cellular neural networks (CNNs) with mixed delays. With the help of the Lyapnnov function combined with the average dwell time method and linear matrix inequalities (LMIs) technique, some novel sufficient conditions on the issue of the uniformly ultimate boundedness, the existence of an attractor, and the globally exponential stability for CNN are given. The provided conditions are expressed in terms of LMI, which can be easily checked by the effective LMI toolbox in Matlab in practice.

N. Belknap's Four-Valued Logic, Belknap Computer and New Proximity Functions for Comparing Discrete Objects

2021 ◽  
Vol 1 (2 (6)) ◽  
Author(s):  
Valerii Dmitrienko ◽  
Sergey Leonov ◽  
Mykola Mezentsev
Keyword(s):  
Neural Network ◽  
Neural Networks ◽  
The Other ◽  
Proximity Function ◽  
Input Information ◽  
Proximity Measures ◽  
The One ◽  
True Values

The idea of ​​Belknap's four-valued logic is that modern computers should function normally not only with the true values ​​of the input information, but also under the conditions of inconsistency and incompleteness of true failures. Belknap's logic introduces four true values: T (true - true), F (false - false), N (none - nobody, nothing, none), B (both - the two, not only the one but also the other).  For ease of work with these true values, the following designations are introduced: (1, 0, n, b). Belknap's logic can be used to obtain estimates of proximity measures for discrete objects, for which the functions Jaccard and Needhem, Russel and Rao, Sokal and Michener, Hamming, etc. are used. In this case, it becomes possible to assess the proximity, recognition and classification of objects in conditions of uncertainty when the true values ​​are taken from the set (1, 0, n, b). Based on the architecture of the Hamming neural network, neural networks have been developed that allow calculating the distances between objects described using true values ​​(1, 0, n, b). Keywords: four-valued Belknap logic, Belknap computer, proximity assessment, recognition and classification, proximity function, neural network.

Comments on the updated recommendations of the American College of Rheumatology (ACR) for the treatment of gout. Lifestyle (part 2)

2021 ◽  
Vol 15 (2) ◽  
pp. 83-88
Author(s):  
M. S. Eliseev
Keyword(s):  
Body Weight ◽  
Food Habits ◽  
The Other ◽  
Obese Patients ◽  
American College Of Rheumatology ◽  
The Russian Federation ◽  
The One ◽  
Effective Drugs ◽  
First Time

Updated ACR recommendations for the treatment of gout concerning lifestyle are discussed. Factors related to a lifestyle, above all food habits, for many years were of leading importance in the treatment of patients with gout, even after application of effective drugs. The authors of the updated ACR recommendations for the first time offered to reconsider the role of environmental factors in the genesis of gout and objectively assess the possibility of its non-drug treatment. On the one hand, regardless of the activity of the disease, the need for restrictions of the alcohol, purine-rich products and fructose-containing beverages, as well as the decrease of body weight in obese patients and vitamin C usage unviability are confirmed. On the other hand, these recommendations are conditional. Their new version of ACR recommendations is significantly different from both its previous version and other international and national recommendations, including recommendations on the diagnosis and treatment of gout used in the Russian Federation.

scholarly journals Geographical vocabulary of the Shilan dialect of the Erzya-Mordovian language

2020 ◽  
Vol 12 (4) ◽  
pp. 358-367
Author(s):  
Nikolai V. Belenov
Keyword(s):  
Original Composition ◽  
Research Methods ◽  
Field Studies ◽  
The Other ◽  
Volga Region ◽  
The One ◽  
Xix Century ◽  
First Time ◽  
Source Materials ◽  
Made In

Introduction. The article presents the results of research of the geographical vocabulary of the Shilan dialect, one of the Erzya-Mordovian dialects of the Samara region, common among Erzya population of Shilan village in Krasnoyarsk region. The dialect belongs to rare Mordovian dialects of the Samara Volga region that were formed in the region since the middle of the XIX century, and therefore its research is of extra interest. Materials and Methods. The research methods are determined by the purpose and objectives of the study. The analysis of the geographical vocabulary of the Shilan dialect is carried out with the involvement of relevant items made in other Mordovian dialects of Samara region, adjacent territories of neighboring regions, as well as other territories of settlement of the Mordovians. Data on geographical vocabulary of the dialect introduced into research for the first time. The main source materials for the article is based on field studies in Silane village during the field seasons in 2017 and 2020, as well as in other Erzya-Mordovian and Moksha-Mordovian villages of Samara region and adjacent territories in 2015 – 2020. Results and Discussion. The study showed that the geographical vocabulary of the Shilan dialect of the Erzya-Mordovian language is significantly different from the corresponding lexical clusters in other dialects of the Mordovian region, which can be explained by natural geographical conditions surrounding Shilan village and the original composition of this lexical cluster of Erzya immigrants who founded this village. Conclusion. The analysis of the geographical vocabulary of the Shilan dialect allowed, on the one hand, to identify specific features of this cluster that distinguish it from the corresponding materials of other Mordovian dialects of the region, and, on the other hand, to identify common isoglosses between it and a number of the Erzya-Mordovian dialects of the Samara Volga region.

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