Search results for: globally exponential stability.

Authors: J.H. Park, S. Lakshmanan, H.Y. Jung, S.M. Lee

Abstract:

This paper is concerned with the delay-distributiondependent stability criteria for bidirectional associative memory (BAM) neural networks with time-varying delays. Based on the Lyapunov-Krasovskii functional and stochastic analysis approach, a delay-probability-distribution-dependent sufficient condition is derived to achieve the globally asymptotically mean square stable of the considered BAM neural networks. The criteria are formulated in terms of a set of linear matrix inequalities (LMIs), which can be checked efficiently by use of some standard numerical packages. Finally, a numerical example and its simulation is given to demonstrate the usefulness and effectiveness of the proposed results.

Keywords: BAM neural networks, Probabilistic time-varying delays, Stability criteria.

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Authors: Xia Zhou, Shouming Zhong

Abstract:

The problem of delay-range-dependent exponential synchronization is investigated for Lur-e master-slave systems with delay feedback control and Markovian switching. Using Lyapunov- Krasovskii functional and nonsingular M-matrix method, novel delayrange- dependent exponential synchronization in mean square criterions are established. The systems discussed in this paper is advanced system, and takes all the features of interval systems, Itˆo equations, Markovian switching, time-varying delay, as well as the environmental noise, into account. Finally, an example is given to show the validity of the main result.

Keywords: Synchronization, delay-range-dependent, Markov chain, generalized Itō's formula, brownian motion, M-matrix.

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Authors: C. E. Madubueze, S. C. Madubueze, S. Ajama

Abstract:

Cholera is a disease that is predominately common in developing countries due to poor sanitation and overcrowding population. In this paper, a deterministic model for the dynamics of cholera is developed and control measures such as health educational message, therapeutic treatment, and vaccination are incorporated in the model. The effective reproduction number is computed in terms of the model parameters. The existence and stability of the equilibrium states, disease free and endemic equilibrium states are established and showed to be locally and globally asymptotically stable when R0 < 1 and R0 > 1 respectively. The existence of backward bifurcation of the model is investigated. Furthermore, numerical simulation of the model developed is carried out to show the impact of the control measures and the result indicates that combined control measures will help to reduce the spread of cholera in the population.

Keywords: Backward bifurcation, cholera, equilibrium, dynamics, stability.

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Authors: M. Kidouche, H. Habbi, M. Zelmat

Abstract:

In this paper, the decomposition-aggregation method is used to carry out connective stability criteria for general linear composite system via aggregation. The large scale system is decomposed into a number of subsystems. By associating directed graphs with dynamic systems in an essential way, we define the relation between system structure and stability in the sense of Lyapunov. The stability criteria is then associated with the stability and system matrices of subsystems as well as those interconnected terms among subsystems using the concepts of vector differential inequalities and vector Lyapunov functions. Then, we show that the stability of each subsystem and stability of the aggregate model imply connective stability of the overall system. An example is reported, showing the efficiency of the proposed technique.

Keywords: Composite system, Connective stability, Lyapunovfunctions.

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Authors: Nam Lethanh, Bryan T. Adey

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In this paper, the potential use of an exponential hidden Markov model to model a hidden pavement deterioration process, i.e. one that is not directly measurable, is investigated. It is assumed that the evolution of the physical condition, which is the hidden process, and the evolution of the values of pavement distress indicators, can be adequately described using discrete condition states and modeled as a Markov processes. It is also assumed that condition data can be collected by visual inspections over time and represented continuously using an exponential distribution. The advantage of using such a model in decision making process is illustrated through an empirical study using real world data.

Keywords: Deterioration modeling, Exponential distribution, Hidden Markov model, Pavement management

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Authors: C. M. De Marco Muscat-Fenech, A.M. Grech La Rosa

Abstract:

The application of stability theory has led to detailed studies of different types of vessels; however, the shortage of information relating to multihull vessels demanded further investigation. This study shows that the position of the hulls has a very influential effect on both the transverse and longitudinal stability of the tricore. HSC stability code is applied for the optimisation of the hull configurations. Such optimization criteria would undoubtedly aid the performance of the vessel for both commercial or leisure purposes

Keywords: Stability, Multihull, Tricore

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Authors: Ksenija Dumičić, Anita Čeh Časni, Berislav Žmuk

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The aim of this paper is to select the most accurate forecasting method for predicting the future values of the unemployment rate in selected European countries. In order to do so, several forecasting techniques adequate for forecasting time series with trend component, were selected, namely: double exponential smoothing (also known as Holt`s method) and Holt-Winters` method which accounts for trend and seasonality. The results of the empirical analysis showed that the optimal model for forecasting unemployment rate in Greece was Holt-Winters` additive method. In the case of Spain, according to MAPE, the optimal model was double exponential smoothing model. Furthermore, for Croatia and Italy the best forecasting model for unemployment rate was Holt-Winters` multiplicative model, whereas in the case of Portugal the best model to forecast unemployment rate was Double exponential smoothing model. Our findings are in line with European Commission unemployment rate estimates.

Keywords: European Union countries, exponential smoothing methods, forecast accuracy unemployment rate.

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Authors: Amjad Abdullah, Amjad Yahya, Bushra Aljohani, Amani S. Alghamdi

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Change point detection is an important part of data analysis. The presence of a change point refers to a significant change in the behavior of a time series. In this article, we examine the detection of multiple change points of parameters of the exponential Lomax distribution, which is broad and flexible compared with other distributions while fitting data. We used the Schwarz information criterion and binary segmentation to detect multiple change points in publicly available data on the average temperature in the ozone layer. The change points were successfully located.

Keywords: Binary segmentation, change point, exponential Lomax distribution, information criterion.

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Authors: Mustafa Bayram Gücen, Coşkun Yakar

Abstract:

In this study, we have investigated the strict stability of fuzzy differential systems and we compare the classical notion of strict stability criteria of ordinary differential equations and the notion of strict stability of fuzzy differential systems. In addition that, we present definitions of stability and strict stability of fuzzy differential equations and also we have some theorems and comparison results. Strict Stability is a different stability definition and this stability type can give us an information about the rate of decay of the solutions. Lyapunov’s second method is a standard technique used in the study of the qualitative behavior of fuzzy differential systems along with a comparison result that allows the prediction of behavior of a fuzzy differential system when the behavior of the null solution of a fuzzy comparison system is known. This method is a usefull for investigating strict stability of fuzzy systems. First of all, we present definitions and necessary background material. Secondly, we discuss and compare the differences between the classical notion of stability and the recent notion of strict stability. And then, we have a comparison result in which the stability properties of the null solution of the comparison system imply the corresponding stability properties of the fuzzy differential system. Consequently, we give the strict stability results and a comparison theorem. We have used Lyapunov second method and we have proved a comparison result with scalar differential equations.

Keywords: Fuzzy systems, fuzzy differential equations, fuzzy stability, strict stability.

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Authors: Changjin Xu, Peiluan Li

Abstract:

In this paper, we study the stability of a fractional order delayed predator-prey model. By using the Laplace transform, we introduce a characteristic equation for the above system. It is shown that if all roots of the characteristic equation have negative parts, then the equilibrium of the above fractional order predator-prey system is Lyapunov globally asymptotical stable. An example is given to show the effectiveness of the approach presented in this paper.

Keywords: Fractional predator-prey model, laplace transform, characteristic equation.

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Authors: Nur Zakiah Mohd Saat, Abdul Aziz Jemain

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Saddlepoint approximations is one of the tools to obtain an expressions for densities and distribution functions. We approximate the densities of the observed gaps between the hypopnea events using the Huzurbazar saddlepoint approximation. We demonstrate the density of a maximum likelihood estimator in exponential families.

Keywords: Exponential, maximum likehood estimators, observed gap, Saddlepoint approximations.

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Authors: A. Thomas, B. John Oommen

Abstract:

Although the field of parametric Pattern Recognition (PR) has been thoroughly studied for over five decades, the use of the Order Statistics (OS) of the distributions to achieve this has not been reported. The pioneering work on using OS for classification was presented in [1] for the Uniform distribution, where it was shown that optimal PR can be achieved in a counter-intuitive manner, diametrically opposed to the Bayesian paradigm, i.e., by comparing the testing sample to a few samples distant from the mean. This must be contrasted with the Bayesian paradigm in which, if we are allowed to compare the testing sample with only a single point in the feature space from each class, the optimal strategy would be to achieve this based on the (Mahalanobis) distance from the corresponding central points, for example, the means. In [2], we showed that the results could be extended for a few symmetric distributions within the exponential family. In this paper, we attempt to extend these results significantly by considering asymmetric distributions within the exponential family, for some of which even the closed form expressions of the cumulative distribution functions are not available. These distributions include the Rayleigh, Gamma and certain Beta distributions. As in [1] and [2], the new scheme, referred to as Classification by Moments of Order Statistics (CMOS), attains an accuracy very close to the optimal Bayes’ bound, as has been shown both theoretically and by rigorous experimental testing.

Keywords: Classification using Order Statistics (OS), Exponential family, Moments of OS

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Authors: Sajjad Farashi

Abstract:

Neurons in the nervous system communicate with each other by producing electrical signals called spikes. To investigate the physiological function of nervous system it is essential to study the activity of neurons by detecting and sorting spikes in the recorded signal. In this paper a method is proposed for considering the spike sorting problem which is based on the nonlinear modeling of spikes using exponential autoregressive model. The genetic algorithm is utilized for model parameter estimation. In this regard some selected model coefficients are used as features for sorting purposes. For optimal selection of model coefficients, self-organizing feature map is used. The results show that modeling of spikes with nonlinear autoregressive model outperforms its linear counterpart. Also the extracted features based on the coefficients of exponential autoregressive model are better than wavelet based extracted features and get more compact and well-separated clusters. In the case of spikes different in small-scale structures where principal component analysis fails to get separated clouds in the feature space, the proposed method can obtain well-separated cluster which removes the necessity of applying complex classifiers.

Keywords: Exponential autoregressive model, Neural data, spike sorting, time series modeling.

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Authors: Lianglin Xiong, Yun Zhao, Tao Jiang

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In this paper, we study the stability of n-dimensional linear fractional neutral differential equation with time delays. By using the Laplace transform, we introduce a characteristic equation for the above system with multiple time delays. We discover that if all roots of the characteristic equation have negative parts, then the equilibrium of the above linear system with fractional order is Lyapunov globally asymptotical stable if the equilibrium exist that is almost the same as that of classical differential equations. An example is provided to show the effectiveness of the approach presented in this paper.

Keywords: Fractional neutral differential equation, Laplace transform, characteristic equation.

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Authors: Maryam Khazaei Pool, Lori Lewis

Abstract:

This is a summary of articles based on higher order B-splines methods and the variation of B-spline methods such as Quadratic B-spline Finite Elements Method, Exponential Cubic B-Spline Method Septic B-spline Technique, Quintic B-spline Galerkin Method, and B-spline Galerkin Method based on the Quadratic B-spline Galerkin method (QBGM) and Cubic B-spline Galerkin method (CBGM). In this paper we study the B-spline methods and variations of B-spline techniques to find a numerical solution to the Burgers’ equation. A set of fundamental definitions including Burgers equation, spline functions, and B-spline functions are provided. For each method, the main technique is discussed as well as the discretization and stability analysis. A summary of the numerical results is provided and the efficiency of each method presented is discussed. A general conclusion is provided where we look at a comparison between the computational results of all the presented schemes. We describe the effectiveness and advantages of these methods.

Keywords: Burgers’ Equation, Septic B-spline, Modified Cubic B-Spline Differential Quadrature Method, Exponential Cubic B-Spline Technique, B-Spline Galerkin Method, and Quintic B-Spline Galerkin Method.

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Authors: K. P. Vishwanath, A. Kandasamy

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The present work deals with analyses of the effects of bearing curvature and non-Newtonian characteristics on the load capacity of an exponential rectangular squeeze film bearing using Bingham fluids as lubricants. Bingham fluids are characterized by an yield value and hence the formation of a “rigid" core in the region between the plates is justified. The flow is confined to the region between the core and the plates. The shape of the core has been identified through numerical means. Further, numerical solutions for the pressure distribution and load carrying capacity of the bearing for various values of Bingham number and curvature parameter have been obtained. The effects of bearing curvature and non-Newtonian characteristics of the lubricant on the bearing performances have been discussed.

Keywords: rheodynamic lubrication, yield stress, non-Newtonianfluid, Bingham fluid, exponential squeeze film.

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Authors: Haowei Chen, Kaiqi Xiong

Abstract:

We have developed a better model for understanding the dynamics of malware spread in WMNs in this paper. The suggested model provides an insight into how viral propagation with energy exhaustion and various dispersed node densities might function. Based on a theoretical examination of the suggested model, we conclude that the threshold parameter could be used to identify the dynamics of viral spread globally. When the threshold is less than 1, the virus may be contained, but if it is greater than 1, a pandemic may result. Lastly, we discuss the various viral propagation strategies in relation to the distributed node densities and communication radii in WMNs. The aforementioned numerical simulation findings could serve as a guarantee of the theoretical analyses’ correctness.

Keywords: Bluetooth Security, Malware Propagation, Wireless Mesh Networks, Stability Analysis.

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Authors: Meftah Ali

Abstract:

This article aims to analyze the static stability and pseudostatic slope by using different methods such as: Bishop method, Junbu, Ordinary, Morgenstern-price and GLE. The two dimensional modeling of slope stability under various loading as: the earthquake effect, the water level and road mobile charges. The results show that the slope is stable in the static case without water, but in other cases, the slope lost its stability and give unstable. The calculation of safety factor is to evaluate the stability of the slope using the limit equilibrium method despite the difference between the results obtained by these methods that do not rely on the same assumptions. In the end, the results of this study illuminate well the influence of the action of water, moving loads and the earthquake on the stability of the slope.

Keywords: Slope stability, pseudo static, safety factor, limit equilibrium.

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Authors: Hamid R. S. Mojaveri, Seyed S. Mousavi, Mojtaba Heydar, Ahmad Aminian

Abstract:

The aim of this paper is to present a methodology in three steps to forecast supply chain demand. In first step, various data mining techniques are applied in order to prepare data for entering into forecasting models. In second step, the modeling step, an artificial neural network and support vector machine is presented after defining Mean Absolute Percentage Error index for measuring error. The structure of artificial neural network is selected based on previous researchers' results and in this article the accuracy of network is increased by using sensitivity analysis. The best forecast for classical forecasting methods (Moving Average, Exponential Smoothing, and Exponential Smoothing with Trend) is resulted based on prepared data and this forecast is compared with result of support vector machine and proposed artificial neural network. The results show that artificial neural network can forecast more precisely in comparison with other methods. Finally, forecasting methods' stability is analyzed by using raw data and even the effectiveness of clustering analysis is measured.

Keywords: Artificial Neural Networks (ANN), bullwhip effect, demand forecasting, Support Vector Machine (SVM).

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Authors: Pyone Lai Swe, Wanna Swe, Kyaw Myo Lin

Abstract:

Voltage stability has become an important issue to many power systems around the world due to the weak systems and long line on power system networks. In this paper, MATLAB load flow program is applied to obtain the weak points in the system combined with finding the voltage stability limit. The maximum permissible loading of a system, within the voltage stability limit, is usually determined. The methods for varying tap ratio (using tap changing transformer) and applying different values of shunt capacitor injection to improve the voltage stability within the limit are also provided.

Keywords: Load flow, Voltage stability, Tap changingtransformer, Shunt capacitor injection, Voltage stability limit

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Authors: Lili Wang, Meng Hu

Abstract:

In this paper, based on almost periodic functional hull theory and M-matrix theory, some sufficient conditions are established for the existence and uniqueness of positive almost periodic solution for a class of BAM neural networks with time-varying delays. An example is given to illustrate the main results.

Keywords: Delayed BAM neural networks, Hull theorem, Mmatrix, Almost periodic solution, Global exponential stability.

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Authors: Changchun Shen, Shouming Zhong

Abstract:

This paper investigates the problem of absolute stability and robust stability of a class of Lur-e systems with neutral type and time-varying delays. By using Lyapunov direct method and linear matrix inequality technique, new delay-dependent stability criteria are obtained and formulated in terms of linear matrix inequalities (LMIs) which are easy to check the stability of the considered systems. To obtain less conservative stability conditions, an operator is defined to construct the Lyapunov functional. Also, the free weighting matrices approach combining a matrix inequality technique is used to reduce the entailed conservativeness. Numerical examples are given to indicate significant improvements over some existing results.

Keywords: Lur'e system, linear matrix inequalities, Lyapunov, stability.

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Authors: Naiqin Feng, Yuhui Qiu, Yingshan Zhang, Fang Wang

Abstract:

A logic model for analyzing complex systems- stability is very useful to many areas of sciences. In the real world, we are enlightened from some natural phenomena such as “biosphere", “food chain", “ecological balance" etc. By research and practice, and taking advantage of the orthogonality and symmetry defined by the theory of multilateral matrices, we put forward a logic analysis model of stability of complex systems with three relations, and prove it by means of mathematics. This logic model is usually successful in analyzing stability of a complex system. The structure of the logic model is not only clear and simple, but also can be easily used to research and solve many stability problems of complex systems. As an application, some examples are given.

Keywords: Complex system, logic model, relation, stability.

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Authors: Gabriel I. Loaiza O., Carlos A. Cadavid M., Juan C. Arango P.

Abstract:

It is known that the Riemannian manifold determined by the family of inverse Gaussian distributions endowed with the Fisher metric has negative constant curvature κ = −1/2 , as does the family of usual Gaussian distributions. In the present paper, firstly we arrive at this result by following a different path, much simpler than the previous ones. We first put the family in exponential form, thus endowing the family with a new set of parameters, or coordinates, θ1, θ2; then we determine the matrix of the Fisher metric in terms of these parameters; and finally we compute this matrix in the original parameters. Secondly, we define the Inverse q−Gaussian distribution family (q < 3), as the family obtained by replacing the usual exponential function by the Tsallis q−exponential function in the expression for the Inverse Gaussian distribution, and observe that it supports two possible geometries, the Fisher and the q−Fisher geometry. And finally, we apply our strategy to obtain results about the Fisher and q−Fisher geometry of the Inverse q−Gaussian distribution family, similar to the ones obtained in the case of the Inverse Gaussian distribution family.

Keywords: Base of Changes, Information Geometry, Inverse Gaussian distribution, Inverse q-Gaussian distribution, Statistical Manifolds.

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Authors: Nasrin Eghbali

Abstract:

In this paper we consider the approximate Jordan maps and boundedness of these maps. Also we investigate the stability of approximate Jordan maps and prove some stability properties for approximate Jordan maps.

Keywords: Approximate Jordan map, stability.

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Authors: R.Guzman-Martinez, Oscar Garcia-Olalla, R.Alaiz-Rodriguez

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Feature selection plays an important role in applications with high dimensional data. The assessment of the stability of feature selection/ranking algorithms becomes an important issue when the dataset is small and the aim is to gain insight into the underlying process by analyzing the most relevant features. In this work, we propose a graphical approach that enables to analyze the similarity between feature ranking techniques as well as their individual stability. Moreover, it works with whatever stability metric (Canberra distance, Spearman's rank correlation coefficient, Kuncheva's stability index,...). We illustrate this visualization technique evaluating the stability of several feature selection techniques on a spectral binary dataset. Experimental results with a neural-based classifier show that stability and ranking quality may not be linked together and both issues have to be studied jointly in order to offer answers to the domain experts.

Keywords: Feature Selection Stability, Spectral data, Data visualization

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Authors: Xiuyong Ding, Lan Shu

Abstract:

This paper addresses the stability of the switched systems with discrete and distributed time delays. By applying Lyapunov functional and function method, we show that, if the norm of system matrices Bi is small enough, the asymptotic stability is always achieved. Finally, a example is provided to verify technically feasibility and operability of the developed results.

Keywords: Switched system, stability, Lyapunov function, Lyapunov functional, delays.

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Authors: Mohammed Amroune, Hadi Sebaa, Tarek Bouktir

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Reactive power limit of power system is one of the major causes of voltage instability. The only way to save the system from voltage instability is to reduce the reactive power load or add additional reactive power to reaching the point of voltage collapse. In recent times, the application of FACTS devices is a very effective solution to prevent voltage instability due to their fast and very flexible control. In this paper, voltage stability assessment with SVC and TCSC devices is investigated and compared in the modified IEEE 30-bus test system. The fast voltage stability indicator (FVSI) is used to identify weakest bus and to assess the voltage stability of power system.

Keywords: SVC, TCSC, Voltage stability, Fast Voltage Stability Index (FVSI), Reactive power.

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Authors: Rajkumar Verma, Bhu Dev Sharma

Abstract:

Entropy is a key measure in studies related to information theory and its many applications. Campbell for the first time recognized that the exponential of the Shannon’s entropy is just the size of the sample space, when distribution is uniform. Here is the idea to study exponentials of Shannon’s and those other entropy generalizations that involve logarithmic function for a probability distribution in general. In this paper, we introduce a measure of sample space, called ‘entropic measure of a sample space’, with respect to the underlying distribution. It is shown in both discrete and continuous cases that this new measure depends on the parameters of the distribution on the sample space - same sample space having different ‘entropic measures’ depending on the distributions defined on it. It was noted that Campbell’s idea applied for R`enyi’s parametric entropy of a given order also. Knowing that parameters play a role in providing suitable choices and extended applications, paper studies parametric entropic measures of sample spaces also. Exponential entropies related to Shannon’s and those generalizations that have logarithmic functions, i.e. are additive have been studies for wider understanding and applications. We propose and study exponential entropies corresponding to non additive entropies of type (α, β), which include Havard and Charvˆat entropy as a special case.

Keywords: Sample space, Probability distributions, Shannon’s entropy, R`enyi’s entropy, Non-additive entropies .

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Authors: Hong Li, Shou-ming Zhong, Hou-biao Li

Abstract:

In this paper, some brief sufficient conditions for the stability of FO-LTI systems dαx(t) dtα = Ax(t) with the fractional order are investigated when the matrix A and the fractional order α are uncertain or both α and A are uncertain, respectively. In addition, we also relate the stability of a fractional-order system with order 0 < α ≤ 1 to the stability of its equivalent fractional-order system with order 1 ≤ β < 2, the relationship between α and β is presented. Finally, a numeric experiment is given to demonstrate the effectiveness of our results.

Keywords: Interval fractional-order systems, linear matrix inequality (LMI), asymptotical stability.

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