GLOBAL ATTRACTIVITY AND GLOBAL EXPONENTIAL STABILITY FOR DELAYED HOPFIELD NEURAL NETWORK MODELS
蒲志林; 徐道义
2001-01-01
Some global properties such as global attractivity and global exponential stability for delayed Hopfield neural networks model, under the weaker assumptions on nonlinear activation functions, are concerned. By constructing suitable Liapunov function, some simpler criteria for global attractivity and global exponential stability for Hopfield continuous neural networks with time delays are presented.
Global Exponential Stability Analysis of a Class of Dynamical Neural Networks
Jin-Liang Shao; Ting-Zhu Huang
2009-01-01
The problem of the global exponential stability of a class of Hopfield neural networks is considered. Based on nonnegative matrix theory, a sufficient condition for the existence, uniqueness and global exponential stability of the equilibrium point is presented. And the upper bound for the degree of exponential stability is given. Moreover, a simulation is given to show the effectiveness of the result.
Hao Chen
2015-01-01
Full Text Available This paper concerns the problem of the globally exponential stability of neural networks with discrete and distributed delays. A novel criterion for the globally exponential stability of neural networks is derived by employing the Lyapunov stability theory, homomorphic mapping theory, and matrix theory. The proposed result improves the previously reported global stability results. Finally, two illustrative numerical examples are given to show the effectiveness of our results.
Global stabilizer of a general class of feedback nonlinear systems and its exponential convergence
Runing MA; Jundi DIAN
2005-01-01
We discuss the global stabilization procedure which renders a general class of feedback nonlinear systems exponential convergent. Our stabilizer consists of a nested saturation function, which is a nonlinear combination of satrration functions. Here we prove the exponential convergence of the stabilizer for the first time and give numerical examples to illustrate the efficiency of the result given above.
无
2007-01-01
In this paper, global exponential stability of almost periodic solution of cellular neural networks with time-varing delays (CNNVDs) is considered. By using the methods of the topological degree theory and generalized Halanay inequality, a few new applicable criteria are established for the existence and global exponential stability of almost periodic solution. Some previous results are improved and extended in this letter and one example is given to illustrate the effectiveness of the new results.
Global exponential stability of mixed discrete and distributively delayed cellular neural network
Yao Hong-Xing; Zhou Jia-Yan
2011-01-01
This paper concernes analysis for the global exponential stability of a class of recurrent neural networks with mixed discrete and distributed delays. It first proves the existence and uniqueness of the balance point, then by employing the Lyapunov-Krasovskii functional and Young inequality, it gives the sufficient condition of global exponential stability of cellular neural network with mixed discrete and distributed delays, in addition, the example is provided to illustrate the applicability of the result.
A new result on global exponential robust stability of neural networks with time-varying delays
Jinliang SHAO; Tingzhu HUANG
2009-01-01
In this paper,the global exponential robust stability of neural networks with time-varying delays is investigated.By using nonnegative matrix theory and the Halanay inequality,a new sufficient condition for global exponential robust stability is presented.It is shown that the obtained result is different from or improves some existing ones reported in the literatures.Finally,some numerical examples and a simulation are given to show the effectiveness of the obtained result.
Global exponential stability conditions for generalized state-space systems with time-varying delays
Yu, K.-W. [Department of Marine Engineering, National Kaohsiung Marine University, Kaohsiung 811, Taiwan (China)], E-mail: kwyu@mail.nkmu.edu.tw; Lien, C.-H. [Department of Marine Engineering, National Kaohsiung Marine University, Kaohsiung 811, Taiwan (China)], E-mail: chlien.ee@msa.hinet.net
2008-05-15
A unified approach is proposed to deal with the exponential stability for generalized state-space systems with time-varying delays. Many systems models can be regarded as special cases of the considered systems; such as neutral time-delay systems and delayed cellular neural networks. Delay-dependent stability criteria are proposed to guarantee the global exponential stability for generalized state-space systems with two cases of uncertainties. Two numerical examples are given to show the effectiveness of our method.
Analysis of global exponential stability for a class of bi—directional associative memory networks
王宏霞; 何晨
2003-01-01
In real-time applications of bi-directional associative memory (BAM) networks.a global exponentially stable equilibrium is highly desired.The existence,uniqueness and global exponential stability for a class of BAM networks are studied in this paper,the signal function of neurons is assumed to be piece-wise linear from the engineering point of view.A very concise condition for the equilbrium of such a network being globally exponentially stable is derived.which makes the pactical design of this kind of networks an easy job.
Analysis of global exponential stability for a class of bi-directional associative memory networks
王宏霞; 何晨
2003-01-01
In real-time applications of bi-directional associative memory (BAM) networks, a global exponentially stable equilibrium is highly desired. The existence, uniqueness and global exponential stability for a class of BAM networks are studied in this paper, the signal function of neurons is assumed to be piece-wise linear from the engineering point of view. A very concise condition for the equilibrium of such a network being globally exponentially stable is derived,which makes the practical design of this kind of networks an easy job.
RONG LIBIN; LU WENLIAN; CHEN TIANPING
2004-01-01
Without assuming the boundedness, strict monotonicity and differentiability of the activation functions, the authors utilize the Lyapunov functional method to analyze the global convergence of some delayed models. For the Hopfield neural network with time delays, a new sufficient condition ensuring the existence, uniqueness and global exponential stability of the equilibrium point is derived. This criterion concerning the signs of entries in the connection matrix imposes constraints on the feedback matrix independently of the delay parameters. From a new viewpoint, the bidirectional associative memory neural network with time delays is investigated and a new global exponential stability result is given.
On global exponential stability of positive neural networks with time-varying delay.
Hien, Le Van
2017-03-01
This paper presents a new result on the existence, uniqueness and global exponential stability of a positive equilibrium of positive neural networks in the presence of bounded time-varying delay. Based on some novel comparison techniques, a testable condition is derived to ensure that all the state trajectories of the system converge exponentially to a unique positive equilibrium. The effectiveness of the obtained results is illustrated by a numerical example.
GLOBAL EXPONENTIAL STABILITY OF HOPFIELD NEURAL NETWORKS WITH VARIABLE DELAYS AND IMPULSIVE EFFECTS
YANG Zhi-chun; XU Dao-yi
2006-01-01
A class of Hopfield neural network with time-varying delays and impulsive effects is concerned. By applying the piecewise continuous vector Lyapunov function some sufficient conditions were obtained to ensure the global exponential stability of impulsive delay neural networks. An example and its simulation are given to illustrate the effectiveness of the results.
ZHU Qing; LIANG Fang; ZHANG Qing
2009-01-01
In this paper, the Cohen-Grossberg neural networks with time-varying delays and impulses are considered. New sufficient conditions for the existence and global exponential stability of a unique equilibrium point are established by using the fixed point theorem and Lyapunov functional. An example is given to demonstrate the effectiveness of our results.
J. Thipcha
2013-01-01
Full Text Available The global exponential stability for bidirectional associative memory neural networks with time-varying delays is studied. In our study, the lower and upper bounds of the activation functions are allowed to be either positive, negative, or zero. By constructing new and improved Lyapunov-Krasovskii functional and introducing free-weighting matrices, a new and improved delay-dependent exponential stability for BAM neural networks with time-varying delays is derived in the form of linear matrix inequality (LMI. Numerical examples are given to demonstrate that the derived condition is less conservative than some existing results given in the literature.
Global exponential stability analysis of cellular neural networks with multiple time delays
Zhanshan WANG; Huaguang ZHANG
2007-01-01
Global exponential stability problems are investigated for cellular neural networks (CNN) with multiple time-varying delays. Several new criteria in linear matrix inequality form or in algebraic form are presented to ascertain the uniqueness and global exponential stability of the equilibrium point for CNN with multiple time-varying delays and with constant time delays. The proposed method has the advantage of considering the difference of neuronal excitatory and inhibitory effects, which is also computationally efficient as it can be solved numerically using the recently developed interior-point algorithm or be checked using simple algebraic calculation. In addition, the proposed results generalize and improve upon some previous works. Two numerical examples are used to show the effectiveness of the obtained results.
Global exponential stability of Cohen-Grossberg neural networks with variable delays
ZHANG Li-juan; SHI Bao
2009-01-01
A class of generalized Cohen-Grossberg neural networks(CGNNs) with variable delays are investigated. By introducing a new type of Lyapunov functional and applying the homeomorphism theory and inequality technique, some new conditions are derived ensuring the existence and uniqueness of the equilibrium point and its global exponential stability for CGNNs. These results obtained are independent of delays, develop the existent outcome in the earlier literature and are very easily checked in practice.
Liu, Xiwei; Chen, Tianping
2016-03-01
In this paper, we investigate the global exponential stability for complex-valued recurrent neural networks with asynchronous time delays by decomposing complex-valued networks to real and imaginary parts and construct an equivalent real-valued system. The network model is described by a continuous-time equation. There are two main differences of this paper with previous works: 1) time delays can be asynchronous, i.e., delays between different nodes are different, which make our model more general and 2) we prove the exponential convergence directly, while the existence and uniqueness of the equilibrium point is just a direct consequence of the exponential convergence. Using three generalized norms, we present some sufficient conditions for the uniqueness and global exponential stability of the equilibrium point for delayed complex-valued neural networks. These conditions in our results are less restrictive because of our consideration of the excitatory and inhibitory effects between neurons; so previous works of other researchers can be extended. Finally, some numerical simulations are given to demonstrate the correctness of our obtained results.
Wu, Ailong; Zeng, Zhigang
2015-03-01
Modeling and related characterization of memristive neurodynamic systems becomes a critical pathway towards neuromorphic system designs. This paper presents a general class of memristive neural networks with time-varying delays. Some improved algebraic criteria for global exponential stability of memristive neural networks are obtained. The criteria improve some previous results and are easy to be verified with the physical parameters of system itself. The proposed framework for theoretical analysis of memristive neurodynamic systems may be useful in developing nanoscale memristor device as synapse in neuromorphic computing architectures.
Fei Yu
2009-01-01
Full Text Available Based on the theory of calculus on time scales, the homeomorphism theory, Lyapunov functional method, and some analysis techniques, sufficient conditions are obtained for the existence, uniqueness, and global exponential stability of the equilibrium point of Cohen-Grossberg bidirectional associative memory (BAM neural networks with distributed delays and impulses on time scales. This is the first time applying the time-scale calculus theory to unify the discrete-time and continuous-time Cohen-Grossberg BAM neural network with impulses under the same framework.
Zhou, Liqun; Zhang, Yanyan
2016-01-01
In this paper, a class of recurrent neural networks with multi-proportional delays is studied. The nonlinear transformation transforms a class of recurrent neural networks with multi-proportional delays into a class of recurrent neural networks with constant delays and time-varying coefficients. By constructing Lyapunov functional and establishing the delay differential inequality, several delay-dependent and delay-independent sufficient conditions are derived to ensure global exponential periodicity and stability of the system. And several examples and their simulations are given to illustrate the effectiveness of obtained results.
Song, Qiankun; Yan, Huan; Zhao, Zhenjiang; Liu, Yurong
2016-07-01
In this paper, the global exponential stability of complex-valued neural networks with both time-varying delays and impulsive effects is discussed. By employing Lyapunov functional method and using matrix inequality technique, several sufficient conditions in complex-valued linear matrix inequality form are obtained to ensure the existence, uniqueness and global exponential stability of equilibrium point for the considered neural networks. Moreover, the exponential convergence rate index is estimated, which depends on the system parameters. The proposed stability results are less conservative than some recently known ones in the literatures, which is demonstrated via two examples with simulations.
秦玉明; 李海燕
2014-01-01
This article is devoted to the study of global existence and exponential stability of solutions to an initial-boundary value problem of the quasilinear thermo-diffusion equations with second sound by means of multiplicative techniques and energy method provided that the initial data are close to the equilibrium and the relaxation kernel is strongly positive definite and decays exponentially.
Song, Qiankun; Yan, Huan; Zhao, Zhenjiang; Liu, Yurong
2016-09-01
This paper investigates the stability problem for a class of impulsive complex-valued neural networks with both asynchronous time-varying and continuously distributed delays. By employing the idea of vector Lyapunov function, M-matrix theory and inequality technique, several sufficient conditions are obtained to ensure the global exponential stability of equilibrium point. When the impulsive effects are not considered, several sufficient conditions are also given to guarantee the existence, uniqueness and global exponential stability of equilibrium point. Two examples are given to illustrate the effectiveness and lower level of conservatism of the proposed criteria in comparison with some existing results.
Bo Zhou; Jianda Han; Xianzhong Dai
2011-01-01
While the nonholonomic robots with no-slipping constraints are studied extensively nowadays, the slipping effect is inevitable in many practical applications and should be considered necessarily to achieve autonomous navigation and control purposes especially in outdoor environments. In this paper the robust point stabilization problem of a tracked mobile robot is discussed in the presence of track slipping, which can be treated as model perturbation that violates the pure nonholonomic constraints. The kinematic model of the tracked vehicle is created, in which the slipping is assumed to be a time-varying parameter under certain assumptions of track-soil interaction. By transforming the original system to the special chained form of nonholonomic system, the integrator backstepping procedure with a state-scaling technique is used to construct the controller to stabilize the system at the kinematic level. The global exponential stability of the final system can be guaranteed by Lyapunov theory. Simulation results with different initial states and slipping parameters demonstrate the fast convergence, robustness and insensitivity to the initial state of the proposed method.
Liang, X B; Si, J
2001-01-01
This paper investigates the existence, uniqueness, and global exponential stability (GES) of the equilibrium point for a large class of neural networks with globally Lipschitz continuous activations including the widely used sigmoidal activations and the piecewise linear activations. The provided sufficient condition for GES is mild and some conditions easily examined in practice are also presented. The GES of neural networks in the case of locally Lipschitz continuous activations is also obtained under an appropriate condition. The analysis results given in the paper extend substantially the existing relevant stability results in the literature, and therefore expand significantly the application range of neural networks in solving optimization problems. As a demonstration, we apply the obtained analysis results to the design of a recurrent neural network (RNN) for solving the linear variational inequality problem (VIP) defined on any nonempty and closed box set, which includes the box constrained quadratic programming and the linear complementarity problem as the special cases. It can be inferred that the linear VIP has a unique solution for the class of Lyapunov diagonally stable matrices, and that the synthesized RNN is globally exponentially convergent to the unique solution. Some illustrative simulation examples are also given.
Gong, Weiqiang; Liang, Jinling; Cao, Jinde
2015-10-01
In this paper, based on the matrix measure method and the Halanay inequality, global exponential stability problem is investigated for the complex-valued recurrent neural networks with time-varying delays. Without constructing any Lyapunov functions, several sufficient criteria are obtained to ascertain the global exponential stability of the addressed complex-valued neural networks under different activation functions. Here, the activation functions are no longer assumed to be derivative which is always demanded in relating references. In addition, the obtained results are easy to be verified and implemented in practice. Finally, two examples are given to illustrate the effectiveness of the obtained results.
Global exponential stability for switched memristive neural networks with time-varying delays.
Xin, Youming; Li, Yuxia; Cheng, Zunshui; Huang, Xia
2016-08-01
This paper considers the problem of exponential stability for switched memristive neural networks (MNNs) with time-varying delays. Different from most of the existing papers, we model a memristor as a continuous system, and view switched MNNs as switched neural networks with uncertain time-varying parameters. Based on average dwell time technique, mode-dependent average dwell time technique and multiple Lyapunov-Krasovskii functional approach, two conditions are derived to design the switching signal and guarantee the exponential stability of the considered neural networks, which are delay-dependent and formulated by linear matrix inequalities (LMIs). Finally, the effectiveness of the theoretical results is demonstrated by two numerical examples.
Global exponential stability of Hopfield-type neural network and its applications
梁学斌; 吴立德
1995-01-01
If the matrix measure of connection weight of Hopfield-type continuous feedback neural network is less than the reciprocal of maximal product of resistance and gain constants, then the network system is globally and exponentially stable. The above reciprocal is a sharp upper bound of matrix measure of connection weight which guarantees that the above conclusion holds. The above result answers partially the open problem proposed by Vidyasagar recently, i. e whether neural network with "nearly" symmetric connection weight can exhibit limit cycles. The relation between the network time constant and the global exponential convergence rate is pointed out, and application to optimization computation of our results is also given.
Manivannan, R; Samidurai, R; Cao, Jinde; Alsaedi, Ahmed; Alsaadi, Fuad E
2017-03-01
This paper investigates the problems of exponential stability and dissipativity of generalized neural networks (GNNs) with time-varying delay signals. By constructing a novel Lyapunov-Krasovskii functionals (LKFs) with triple integral terms that contain more advantages of the state vectors of the neural networks, and the upper bound on the time-varying delay signals are formulated. We employ a new integral inequality technique (IIT), free-matrix-based (FMB) integral inequality approach, and Wirtinger double integral inequality (WDII) technique together with the reciprocally convex combination (RCC) approach to bound the time derivative of the LKFs. An improved exponential stability and strictly (Q,S,R)-γ-dissipative conditions of the addressed systems are represented by the linear matrix inequalities (LMIs). Finally, four interesting numerical examples are developed to verify the usefulness of the proposed method with a practical application to a biological network. Copyright © 2016 Elsevier Ltd. All rights reserved.
Zhang, Wei; Huang, Tingwen; He, Xing; Li, Chuandong
2017-11-01
In this study, we investigate the global exponential stability of inertial memristor-based neural networks with impulses and time-varying delays. We construct inertial memristor-based neural networks based on the characteristics of the inertial neural networks and memristor. Impulses with and without delays are considered when modeling the inertial neural networks simultaneously, which are of great practical significance in the current study. Some sufficient conditions are derived under the framework of the Lyapunov stability method, as well as an extended Halanay differential inequality and a new delay impulsive differential inequality, which depend on impulses with and without delays, in order to guarantee the global exponential stability of the inertial memristor-based neural networks. Finally, two numerical examples are provided to illustrate the efficiency of the proposed methods. Copyright © 2017 Elsevier Ltd. All rights reserved.
Li, Bing; Li, Yongkun; Zhang, Xuemei
2016-01-01
In this paper, by using the existence of the exponential dichotomy of linear dynamic equations on time scales and the theory of calculus on time scales, we study the existence and global exponential stability of periodic solutions for a class of n-dimensional neutral dynamic equations on time scales. We also present an example to illustrate the feasibility of our results. The results of this paper are completely new and complementary to the previously known results even in both the case of differential equations (time scale [Formula: see text]) and the case of difference equations (time scale [Formula: see text]).
Global Exponential Stability of Discrete-Time Neural Networks with Time-Varying Delays
S. Udpin
2013-01-01
Full Text Available This paper presents some global stability criteria of discrete-time neural networks with time-varying delays. Based on a discrete-type inequality, a new global stability condition for nonlinear difference equation is derived. We consider nonlinear discrete systems with time-varying delays and independence of delay time. Numerical examples are given to illustrate the effectiveness of our theoretical results.
Zhong, Kai; Zhu, Song; Yang, Qiqi
2016-11-01
In recent years, the stability problems of memristor-based neural networks have been studied extensively. This paper not only takes the unavoidable noise into consideration but also investigates the global exponential stability of stochastic memristor-based neural networks with time-varying delays. The obtained criteria are essentially new and complement previously known ones, which can be easily validated with the parameters of system itself. In addition, the study of the nonlinear dynamics for the addressed neural networks may be helpful in qualitative analysis for general stochastic systems. Finally, two numerical examples are provided to substantiate our results.
Hu, Jin; Wang, Jun
2015-06-01
In recent years, complex-valued recurrent neural networks have been developed and analysed in-depth in view of that they have good modelling performance for some applications involving complex-valued elements. In implementing continuous-time dynamical systems for simulation or computational purposes, it is quite necessary to utilize a discrete-time model which is an analogue of the continuous-time system. In this paper, we analyse a discrete-time complex-valued recurrent neural network model and obtain the sufficient conditions on its global exponential periodicity and exponential stability. Simulation results of several numerical examples are delineated to illustrate the theoretical results and an application on associative memory is also given.
Zhang, Jianlin
2017-04-01
In this paper, we study a large time behavior of the global spherically or cylindrically symmetric solutions in H 1 for the compressible viscous radiative and reactive gas in multi-dimension with large initial data. Precisely, if the initial data are spherically symmetric or cylindrically symmetric, the smallness of initial data is not needed. The main concern of the present paper is to investigate the exponential stability of a solution toward the stationary solution as time goes to infinity. We obtain the uniform positive lower and upper bounds of the density by using different methods.
Li, Hongfei; Jiang, Haijun; Hu, Cheng
2016-03-01
In this paper, we investigate a class of memristor-based BAM neural networks with time-varying delays. Under the framework of Filippov solutions, boundedness and ultimate boundedness of solutions of memristor-based BAM neural networks are guaranteed by Chain rule and inequalities technique. Moreover, a new method involving Yoshizawa-like theorem is favorably employed to acquire the existence of periodic solution. By applying the theory of set-valued maps and functional differential inclusions, an available Lyapunov functional and some new testable algebraic criteria are derived for ensuring the uniqueness and global exponential stability of periodic solution of memristor-based BAM neural networks. The obtained results expand and complement some previous work on memristor-based BAM neural networks. Finally, a numerical example is provided to show the applicability and effectiveness of our theoretical results.
Yanke Du
2013-01-01
Full Text Available A class of interval Cohen-Grossberg neural networks with time-varying delays and infinite distributed delays is investigated. By employing H-matrix and M-matrix theory, homeomorphism techniques, Lyapunov functional method, and linear matrix inequality approach, sufficient conditions are established for the existence, uniqueness, and global robust exponential stability of the equilibrium point and the periodic solution to the neural networks. Our results improve some previously published ones. Finally, numerical examples are given to illustrate the feasibility of the theoretical results and further to exhibit that there is a characteristic sequence of bifurcations leading to a chaotic dynamics, which implies that the system admits rich and complex dynamics.
Exponential Stabilization of Underactuated Vehicles
Pettersen, K.Y.
1996-12-31
Underactuated vehicles are vehicles with fewer independent control actuators than degrees of freedom to be controlled. Such vehicles may be used in inspection of sub-sea cables, inspection and maintenance of offshore oil drilling platforms, and similar. This doctoral thesis discusses feedback stabilization of underactuated vehicles. The main objective has been to further develop methods from stabilization of nonholonomic systems to arrive at methods that are applicable to underactuated vehicles. A nonlinear model including both dynamics and kinematics is used to describe the vehicles, which may be surface vessels, spacecraft or autonomous underwater vehicles (AUVs). It is shown that for a certain class of underactuated vehicles the stabilization problem is not solvable by linear control theory. A new stability result for a class of homogeneous time-varying systems is derived and shown to be an important tool for developing continuous periodic time-varying feedback laws that stabilize underactuated vehicles without involving cancellation of dynamics. For position and orientation control of a surface vessel without side thruster a new continuous periodic feedback law is proposed that does not cancel any dynamics, and that exponentially stabilizes the origin of the underactuated surface vessel. A further issue considered is the stabilization of the attitude of an AUV. Finally, the thesis discusses stabilization of both position and attitude of an underactuated AUV. 55 refs., 28 figs.
Wang, Dongshu; Huang, Lihong
2014-03-01
In this paper, we investigate the 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 the fixed point theorem of multi-valued maps, the existence of periodic solutions for the neural networks is obtained. After that, we derive some sufficient conditions for the global exponential stability and convergence of the neural networks, in terms of nonsmooth analysis theory with generalized Lyapunov approach. Without assuming the boundedness (or the growth condition) and monotonicity of the discontinuous neuron activation functions, our results will also be valid. Moreover, our results extend previous works not only on discrete time-varying and distributed delayed neural networks with continuous or even Lipschitz continuous activations, but also on discrete time-varying and distributed delayed neural networks with discontinuous activations. We give some numerical examples to show the applicability and effectiveness of our main results.
Guo, Zhenyuan; Wang, Jun; Yan, Zheng
2013-12-01
This paper addresses the global exponential dissipativity of memristor-based recurrent neural networks with time-varying delays. By constructing proper Lyapunov functionals and using M-matrix theory and LaSalle invariant principle, the sets of global exponentially dissipativity are characterized parametrically. It is proven herein that there are 2(2n(2)-n) equilibria for an n-neuron memristor-based neural network and they are located in the derived globally attractive sets. It is also shown that memristor-based recurrent neural networks with time-varying delays are stabilizable at the origin of the state space by using a linear state feedback control law with appropriate gains. Finally, two numerical examples are discussed in detail to illustrate the characteristics of the results. Copyright © 2013 Elsevier Ltd. All rights reserved.
Xu, Lijun; Jiang, Qi; Gu, Guodong
2016-01-01
A kind of neutral-type Cohen-Grossberg shunting inhibitory cellular neural networks with distributed delays and impulses is considered. Firstly, by using the theory of impulsive differential equations and the contracting mapping principle, the existence and uniqueness of the almost periodic solution for the above system are obtained. Secondly, by constructing a suitable Lyapunov functional, the global exponential stability of the unique almost periodic solution is also investigated. The work in this paper improves and extends some results in recent years. As an application, an example and numerical simulations are presented to demonstrate the feasibility and effectiveness of the main results.
Lijun Xu
2016-01-01
Full Text Available A kind of neutral-type Cohen-Grossberg shunting inhibitory cellular neural networks with distributed delays and impulses is considered. Firstly, by using the theory of impulsive differential equations and the contracting mapping principle, the existence and uniqueness of the almost periodic solution for the above system are obtained. Secondly, by constructing a suitable Lyapunov functional, the global exponential stability of the unique almost periodic solution is also investigated. The work in this paper improves and extends some results in recent years. As an application, an example and numerical simulations are presented to demonstrate the feasibility and effectiveness of the main results.
Circuit design and exponential stabilization of memristive neural networks.
Wen, Shiping; Huang, Tingwen; Zeng, Zhigang; Chen, Yiran; Li, Peng
2015-03-01
This paper addresses the problem of circuit design and global exponential stabilization of memristive neural networks with time-varying delays and general activation functions. Based on the Lyapunov-Krasovskii functional method and free weighting matrix technique, a delay-dependent criteria for the global exponential stability and stabilization of memristive neural networks are derived in form of linear matrix inequalities (LMIs). Two numerical examples are elaborated to illustrate the characteristics of the results. It is noteworthy that the traditional assumptions on the boundness of the derivative of the time-varying delays are removed.
Exponential Stabilization of an Underactuated Surface Vessel
Kristin Y. Pettersen
1997-07-01
Full Text Available The paper shows that a large class of underactuated vehicles cannot be asymptotically stabilized by either continuous or discontinuous state feedback. Furthermore, stabilization of an underactuated surface vessel is considered. Controllability properties of the surface vessels is presented, and a continuous periodic time-varying feedback law is proposed. It is shown that this feedback law exponentially stabilizes the surface vessel to the origin, and this is illustrated by simulations.
Exponential stability for uncertain neutral systems with Markov jumps
Shuping HE; Fei LIU
2009-01-01
This paper deals with the global exponential stability problems for stochastic neutral Markov jump sys-tems(MJSs) with uncertain parameters and multiple time-delays,The delays are respectively considered as constant and time varying cases,and the uncertainties are assumed to be norm bounded.By selecting appropriate Lyapunov-Krasovskii functions,it gives the sufficient condition such that the uncertain neutral MJSs are globally exponentially stochastically stable for all admissible uncertainties.The stability criteria are formulated in the form of linear matrix inequalities(LMIs),which can be easily checked in practice.Finally,two numerical examples are exploited to illustrate the effectiveness of the developed techniques.
Exponential Stability Criteria for Nonautonomous Difference Systems
Rigoberto Medina
2014-01-01
Full Text Available The aim of this paper is to characterize the exponential stability of linear systems of difference equations with slowly varying coefficients. Our approach is based on the generalization of the freezing method for difference equations combined with new estimates for the norm of bounded linear operators. The main novelty of this work is that we use estimates for the absolute values of entries of a matrix-valued function, instead of bounds on its eigenvalues. By this method, new explicit stability criteria for linear nonautonomous systems are derived.
Generalized exponential input-to-state stability of nonlinear systems with time delay
Sun, Fenglan; Gao, Lingxia; Zhu, Wei; Liu, Feng
2017-03-01
This paper studies the general input-to-state stability problem of the nonlinear delay systems. By employing Lypaunov-Razumikhin technique, several general input-to-state stability concepts, that is generalized globally exponential integral input-to-state stability (GGE-iISS), generalized globally integral exponential integral input-to-state stability (GGIE-iISS), and eλt-weighted generalized globally integral exponential integral input-to-state stability (eλt-weighted GGIE-iISS) are studied. An example is given to illustrate the correctness of the obtained theoretical results.
Exponential Stability of Stochastic Nonlinear Dynamical Price System with Delay
Wenli Zhu
2013-01-01
Full Text Available Based on Lyapunov stability theory, Itô formula, stochastic analysis, and matrix theory, we study the exponential stability of the stochastic nonlinear dynamical price system. Using Taylor's theorem, the stochastic nonlinear system with delay is reduced to an n-dimensional semilinear stochastic differential equation with delay. Some sufficient conditions of exponential stability and corollaries for such price system are established by virtue of Lyapunov function. The time delay upper limit is solved by using our theoretical results when the system is exponentially stable. Our theoretical results show that if the classical price Rayleigh equation is exponentially stable, so is its perturbed system with delay provided that both the time delay and the intensity of perturbations are small enough. Two examples are presented to illustrate our results.
Global impulsive exponential synchronization of stochastic perturbed chaotic delayed neural networks
Zhang Hua-Guang; Ma Tie-Dong; Fu Jie; Tong Shao-Cheng
2009-01-01
In this paper,the global impulsive exponential synchronization problem of a class of chaotic delayed neural networks (DNNs) with stochastic perturbation is studied. Based on the Lyapunov stability theory,stochastic analysis approach and an efficient impulsive delay differential inequality,some new exponential synchronization criteria expressed in the form of the linear matrix inequality (LMI) are derived. The designed impulsive controUer not only can globally exponentially stabilize the error dynamics in mean square,but also can control the exponential synchronization rate. Furthermore,to estimate the stable region of the synchronization error dynamics,a novel optimization control algorithm is proposed,which can deal with the minimum problem with two nonlinear terms coexisting in LMIs effectively.Simulation results finally demonstrate the effectiveness of the proposed method.
Stability of the Exponential Functional Equation in Riesz Algebras
Bogdan Batko
2014-01-01
Full Text Available We deal with the stability of the exponential Cauchy functional equation F(x+y=F(xF(y in the class of functions F:G→L mapping a group (G, + into a Riesz algebra L. The main aim of this paper is to prove that the exponential Cauchy functional equation is stable in the sense of Hyers-Ulam and is not superstable in the sense of Baker. To prove the stability we use the Yosida Spectral Representation Theorem.
EXPONENTIAL STABILITY OF INTERVAL DYNAMICAL SYSTEM WITH MULTIDELAY
孙继涛; 张银萍; 刘永清; 邓飞其
2002-01-01
Using the matrix measure and delay differential inequality, the sufficient conditions were obtained for exponential stability of interval dynamical system with multidelay. These conditions are an improvement and extension of the results achieved in earlier papers presented by LIAO, LIU, ZHANG, SUN, et al.
Exponential stability of dynamic equations on time scales
Raffoul Youssef N
2005-01-01
Full Text Available We investigate the exponential stability of the zero solution to a system of dynamic equations on time scales. We do this by defining appropriate Lyapunov-type functions and then formulate certain inequalities on these functions. Several examples are given.
Exponential Stability of Complex-Valued Memristive Recurrent Neural Networks.
Wang, Huamin; Duan, Shukai; Huang, Tingwen; Wang, Lidan; Li, Chuandong
2017-03-01
In this brief, we establish a novel complex-valued memristive recurrent neural network (CVMRNN) to study its stability. As a generalization of real-valued memristive neural networks, CVMRNN can be separated into real and imaginary parts. By means of M -matrix and Lyapunov function, the existence, uniqueness, and exponential stability of the equilibrium point for CVMRNNs are investigated, and sufficient conditions are presented. Finally, the effectiveness of obtained results is illustrated by two numerical examples.
Exponential Stability Analysis of Cohen-Grossberg Neural Networks with Time-varying Delays
Yi-min MENG; Li-hong HUANG; Zhao-hui YUAN
2012-01-01
In this paper,we study Cohen-Grossberg neural networks (CGNN) with time-varying delay.Based on Halanay inequality and continuation theorem of the coincidence degree,we obtain some sufficient conditions ensuring the existence,uniqueness,and global exponential stability of periodic solution.Our results complement previously known results.
New results on robust exponential stability of integral delay systems
Melchor-Aguilar, Daniel
2016-06-01
The robust exponential stability of integral delay systems with exponential kernels is investigated. Sufficient delay-dependent robust conditions expressed in terms of linear matrix inequalities and matrix norms are derived by using the Lyapunov-Krasovskii functional approach. The results are combined with a new result on quadratic stabilisability of the state-feedback synthesis problem in order to derive a new linear matrix inequality methodology of designing a robust non-fragile controller for the finite spectrum assignment of input delay systems that guarantees simultaneously a numerically safe implementation and also the robustness to uncertainty in the system matrices and to perturbation in the feedback gain.
谢惠琴; 王全义
2004-01-01
In this paper, we study the existence, uniqueness, and the global exponential stability of the periodic solution and equilibrium of hybrid bidirectional associative memory neural networks with discrete delays. By ingeniously importing real parameters di > 0 (i = 1, 2,..., n) which can be adjusted, making use of the Lyapunov functional method and some analysis techniques, some new sufficient conditions are established. Our results generalize and improve the related results in [9]. These conditions can be used both to design globally exponentially stable and periodical oscillatory hybrid bidirectional associative neural networks with discrete delays, and to enlarge the area of designing neural networks. Our work has important significance in related theory and its application.
Belleter, Dennis J.W.; Galeazzi, Roberto; Fossen, Thor Inge
2015-01-01
This paper presents a global exponential stability (GES) proof for a signalbased nonlinear wave encounter frequency estimator. The estimator under consideration is a second-order nonlinear observer designed to estimate the frequency of a sinusoid with unknown frequency, amplitude and phase. The G...
Global Exponential Projective Synchronization and Lag Synchronization of Hyperchaotic Lü System
ZHANG Qun-Jiao; LU Jun-An; JIA Zhen
2009-01-01
This paper investigates the projective synchronization and lag synchronization of a new hyperchaotic system[Physica A 364 (2006) 103]. On the basis of Lyapunov stability theory, two novel nonlinear controllers are respectively designed to guarantee the global exponential projective synchronization (including complete synchronization and anti-synchronization) and lag synchronization. Finally, numerical simulations are given to show the effectiveness of the main results.
Sun, Xifang; Chen, Weisheng; Wu, Jian
2016-12-01
In this paper, we address the global generalised exponential stabilisation problem for a class of lower-triangular systems with multiple unknown directions. Instead of the well-known Nussbaum-gain adaptive rule, a Lyapunov-based adaptive logic switching rule is proposed to seek the correct control directions for such systems. The main advantage of the proposed controller is that it can guarantee the global generalised exponential stability of closed-loop systems. Simulation examples are given to verify the effectiveness of the developed control approach.
韩天勇
2009-01-01
本文讨论了含混合时滞和脉冲的Cohen-Grossberg神经网络的稳定性.通过应用M矩阵理论和不等式技巧,得到了含混合时滞的Cohen-Grossberg神经网络平衡态的全局指数稳定性的充分条件.相比以前同类文献,本文减弱了部分条件,推广了部分结论,并在文末给出了两个示例.本文结论对于设计和应用神经网络有一定实用价值.%In this paper,the Cohen-Grossberg neural networks with mixed delays and impulses are considered.Applying the idea of M-matrix theory and inequality technique,several new sufficient conditions are obtained to ensure global exponential stability of equilibrium point for impulsive Cohen-Grossberg neural networks with mixed delays and impulses.These results generalize a few previous known results and remove some restrictions on the neural network.Two examples are given to show the effectiveness of the obtained results.
阮锴; 蒋海军; 胡成
2014-01-01
In this paper, the existence of unique equilibrium point of neural networks with infinite distributed delays is discussed by means of Homeomorphism theory and inequality technique. Then, some useful criteria for the globally exponential stability of this model are derived by way of contradiction and the analysis technique which are different from the methods employed in correspondingly previous works. Finally, an example is provided to illustrate the applicability of the result.%通过同胚映射的理论和不等式技巧，研究了一类具有无穷分布时滞神经网络的平衡点的存在唯一性。并在此基础上，利用反证法和分析技巧给出了模型平衡点的全局指数稳定性的条件，这种方法与技巧不同于以往的文章。最后给出一个实例来验证理论结果的有效性。
施继忠; 张继业
2012-01-01
为研究车辆建模导致的随机误差对自动化公路车辆系统等关联大系统的影响,将确定性箱体理论推广到随机箱体理论,利用M-矩阵理论和随机箱体理论,构造适当的向量Lyapunov函数,通过分析相应随机微分不等式的稳定性,利用随机大系统的系数矩阵以及与大系统关联的Lyapunov矩阵方程的解构造判定矩阵,得到该类大系统全局指数稳定性的充分性判据,即当判定矩阵为M-矩阵时,大系统是全局指数稳定的.仿真结果表明:本文算法收敛速度快,在20 s内系统状态就能达到稳定.%In order to study the effects of random errors caused by vehicle modeling on interconnected large-scale systems like the automated highway vehicle system, the deterministic theory was extended to the random case theory, and a proper vector Lyapunov function was constructed using the matrix theory and the random case theory. By analyzing the stability of stochastic differential inequalities, a coefficient matrix of the random large-scale system and the solutions of the Lyapunov matrix function interconnected with large-scale system are used to construct a judgment matrix, and then obtain the sufficiency criterion for global exponential stability of the large-scale system: when the judgment matrix is a quasi-Af-matrix, the global index of the large-scale system is stable. Simulation results show that the algorithm proposed in the paper has a rapid convergence rate, and the system can achieve stability in 20 s.
Global exponential almost periodicity of a delayed memristor-based neural networks.
Chen, Jiejie; Zeng, Zhigang; Jiang, Ping
2014-12-01
In this paper, the existence, uniqueness and stability of almost periodic solution for a class of delayed memristor-based neural networks are studied. By using a new Lyapunov function method, the neural network that has a unique almost periodic solution, which is globally exponentially stable is proved. Moreover, the obtained conclusion on the almost periodic solution is applied to prove the existence and stability of periodic solution (or equilibrium point) for delayed memristor-based neural networks with periodic coefficients (or constant coefficients). The obtained results are helpful to design the global exponential stability of almost periodic oscillatory memristor-based neural networks. Three numerical examples and simulations are also given to show the feasibility of our results.
周少波; 薛明皋
2014-01-01
The paper develops exponential stability of the analytic solution and convergence in probability of the numerical method for highly nonlinear hybrid stochastic pantograph equation. The classical linear growth condition is replaced by polynomial growth conditions, under which there exists a unique global solution and the solution is almost surely exponen-tially stable. On the basis of a series of lemmas, the paper establishes a new criterion on convergence in probability of the Euler-Maruyama approximate solution. The criterion is very general so that many highly nonlinear stochastic pantograph equations can obey these conditions. A highly nonlinear example is provided to illustrate the main theory.
Robust exponential stability and stabilization of linear uncertain polytopic time-delay systems
Nam PHAN T.; Phat VU N.
2008-01-01
This paper proposes new sufficient conditions for the exponential stability and stabilization.of linear uncertain polytopic time-delay systems.The conditions for exponential stability are expressed in terms of Kharitonov-type linear matrix inequalities(LMIs)and we develop control design methods based on UMIs for solving stabilization problem.Our method consists of a combination of the LMI approach and the use of parameter-dependent Lyapunov funcfionals,which allows to compute simultaneously the two bounds that characterize the exponetial stability rate of the solution.Numerical examples illustrating the conditions are given.
Zhang, Guodong; Shen, Yi
2015-11-01
This paper is concerned with the global exponential stability on a class of delayed neural networks with state-dependent switching. Under the novel conditions, some sufficient criteria ensuring exponential stability of the proposed system are obtained. In particular, the obtained conditions complement and improve earlier publications on conventional neural networks with continuous or discontinuous right-hand side. Numerical simulations are also presented to illustrate the effectiveness of the obtained results.
On exponential stability for systems with state delays
无
2007-01-01
This paper considers the issue of delay-dependent exponential stability for time-delay systems. Both nominal and uncertain systems are investigated. New sufficient conditions in terms of linear matrix inequalities (LMIs) are obtained. These criteria are simple owing to the use of an integral inequality. The model transformation approaches, bounding techniques for cross terms and slack matrices are all avoided in the derivation. Rigorous proof and numerical examples showed that the proposed criteria and those based on introducing slack matrices are equivalent.
Chen, Huabin; Shi, Peng; Lim, Cheng-Chew; Hu, Peng
2016-06-01
In this paper, the exponential stability in p th( p > 1 )-moment for neutral stochastic Markov systems with time-varying delay is studied. The derived stability conditions comprise two forms: 1) the delay-independent stability criteria which are obtained by establishing an integral inequality and 2) the delay-dependent stability criteria which are captured by using the theory of the functional differential equations. As its applications, the obtained stability results are used to investigate the exponential stability in p th( p > 1 )-moment for the neutral stochastic neural networks with time-varying delay and Markov switching, and the globally exponential adaptive synchronization for the neutral stochastic complex dynamical systems with time-varying delay and Markov switching, respectively. On the delay-independent criteria, sufficient conditions are given in terms of M -matrix and thus are easy to check. The delay-dependent criteria are presented in the forms of the algebraic inequalities, and the least upper bound of the time-varying delay is also provided. The primary advantages of these obtained results over some recent and similar works are that the differentiability or continuity of the delay function is not required, and that the difficulty stemming from the presence of the neutral item and the Markov switching is overcome. Three numerical examples are provided to examine the effectiveness and potential of the theoretic results obtained.
Global exponential stabilisation of a class of nonlinear time-delay systems
Benabdallah, Amel; Echi, Nadhem
2016-12-01
This paper deals with the state and output feedback stabilisation problems for a family of nonlinear time-delay systems satisfying some relaxed triangular-type condition. The delay is supposed to be constant. Parameter-dependent control laws are used to compensate for the nonlinearities. Based on the Lyapunov-Krasovskii functionals, global exponential stability of the closed-loop systems is achieved. Finally, an extension to nonlinear time-varying delay systems is given.
Xu, Changjin; Li, Peiluan; Pang, Yicheng
2016-12-01
In this letter, we deal with a class of memristor-based neural networks with distributed leakage delays. By applying a new Lyapunov function method, we obtain some sufficient conditions that ensure the existence, uniqueness, and global exponential stability of almost periodic solutions of neural networks. We apply the results of this solution to prove the existence and stability of periodic solutions for this delayed neural network with periodic coefficients. We then provide an example to illustrate the effectiveness of the theoretical results. Our results are completely new and complement the previous studies Chen, Zeng, and Jiang ( 2014 ) and Jiang, Zeng, and Chen ( 2015 ).
Kwon, O.M., E-mail: madwind@chungbuk.ac.k [School of Electrical Engineering, Chungbuk National University, Cheongju (Korea, Republic of); Lee, S.M., E-mail: moony@daegu.ac.k [School of Electronics Engineering, Daegu University, Kyongsan (Korea, Republic of); Park, Ju H., E-mail: jessie@ynu.ac.k [Department of Electrical Engineering, Yeungnam University, Kyongsan (Korea, Republic of)
2010-02-22
This Letter investigates the problem of delay-dependent exponential stability analysis for uncertain stochastic neural networks with time-varying delay. Based on the Lyapunov stability theory, improved delay-dependent exponential stability criteria for the networks are established in terms of linear matrix inequalities (LMIs).
Exponential stability of Takagi-Sugeno fuzzy systems with impulsive effects and small delays
Yu Yong-Bin; Zhong Qi-Shui; Liao Xiao-Feng; Yu Jue-Bang
2008-01-01
This paper deals with the exponential stability of impulsive Takagi-Sugeno fuzzy systems with delay. Impulsive control and delayed fuzzy control are applied to the system, and the criterion on exponential stability expressed in terms of linear matrix inequalities (LMIs) is presented.
Xiao, Shuiming; Chen, Huabin
2017-03-01
In this paper, the existence and uniqueness, the exponential stability, and the almost sure exponential stability of mild solution for impulsive stochastic partial functional differential equations with finite delay are considered. Some sufficient conditions are established for our concerned problems, and some existing results are generalized and improved. Finally, an illustrative example is provided to show the feasibility and effectiveness of the obtained results.
Loss of exponential stability for a thermoelastic system with memory
Bruno Ferreira Alves
2010-09-01
Full Text Available In this article we study a thermoelastic system considering the linearized model proposed by Gurtin and Pipkin [8] instead of the Fourier's law for the heat flux. We use theory of semigroups [9, 11] combining Pruss' Theorem [10] and the idea developed in [5] to show that the system is not exponentially stable.
Exponential Stabilization for C0 -Semigroups Under Compact Perturbation
LILT Li-xin
2008-01-01
It is proved that a system under compact perturbation cannot be uniformly exponentially stable for an isometric C0-semigroup or a C0-group with polynomial growth for negative time in a Banach space. The results extend and improve the corresponding results of previous literature.
Uniform exponential stability of linear periodic systems in a Banach space
David N. Cheban
2001-01-01
Full Text Available This article is devoted to the study of linear periodic dynamical systems, possessing the property of uniform exponential stability. It is proved that if the Cauchy operator of these systems possesses a certain compactness property, then the asymptotic stability implies the uniform exponential stability. We also show applications to different classes of linear evolution equations, such as ordinary linear differential equations in the space of Banach, retarded and neutral functional differential equations, some classes of evolution partial differential equations.
Almost Surely Exponential Stability of Numerical Solutions for Stochastic Pantograph Equations
Shaobo Zhou
2014-01-01
Full Text Available Our effort is to develop a criterion on almost surely exponential stability of numerical solution to stochastic pantograph differential equations, with the help of the discrete semimartingale convergence theorem and the technique used in stable analysis of the exact solution. We will prove that the Euler-Maruyama (EM method can preserve almost surely exponential stability of stochastic pantograph differential equations under the linear growth conditions. And the backward EM method can reproduce almost surely exponential stability for highly nonlinear stochastic pantograph differential equations. A highly nonlinear example is provided to illustrate the main theory.
Mean Square Exponential Stability of Stochastic Switched System with Interval Time-Varying Delays
Manlika Rajchakit
2012-01-01
Full Text Available This paper is concerned with mean square exponential stability of switched stochastic system with interval time-varying delays. The time delay is any continuous function belonging to a given interval, but not necessary to be differentiable. By constructing a suitable augmented Lyapunov-Krasovskii functional combined with Leibniz-Newton’s formula, a switching rule for the mean square exponential stability of switched stochastic system with interval time-varying delays and new delay-dependent sufficient conditions for the mean square exponential stability of the switched stochastic system are first established in terms of LMIs. Numerical example is given to show the effectiveness of the obtained result.
The motion planning problem and exponential stabilization of a heavy chain. Part II
Piotr Grabowski
2008-01-01
Full Text Available This is the second part of paper [P. Grabowski, The motion planning problem and exponential stabilization of a heavy chain. Part I, to appear in International Journal of Control], where a model of a heavy chain system with a punctual load (tip mass in the form of a system of partial differential equations was interpreted as an abstract semigroup system and then analysed on a Hilbert state space. In particular, in [P. Grabowski, The motion planning problem and exponential stabilization of a heavy chain. Part I, to appear in International Journal of Control] we have formulated the problem of exponential stabilizability of a heavy chain in a given position. It was also shown that the exponential stability can be achieved by applying a stabilizer of the colocated-type. The proof used the method of Lyapunov functionals. In the present paper, we give other two proofs of the exponential stability, which provides an additional intrinsic insight into the exponential stabilizability mechanism. The first proof makes use of some spectral properties of the system. In the second proof, we employ some relationships between exponential stability and exact observability.
Qiankun Song
2007-06-01
Full Text Available Impulsive bidirectional associative memory neural network model with time-varying delays and reaction-diffusion terms is considered. Several sufficient conditions ensuring the existence, uniqueness, and global exponential stability of equilibrium point for the addressed neural network are derived by M-matrix theory, analytic methods, and inequality techniques. Moreover, the exponential convergence rate index is estimated, which depends on the system parameters. The obtained results in this paper are less restrictive than previously known criteria. Two examples are given to show the effectiveness of the obtained results.
Cao Jinde
2007-01-01
Full Text Available Impulsive bidirectional associative memory neural network model with time-varying delays and reaction-diffusion terms is considered. Several sufficient conditions ensuring the existence, uniqueness, and global exponential stability of equilibrium point for the addressed neural network are derived by M-matrix theory, analytic methods, and inequality techniques. Moreover, the exponential convergence rate index is estimated, which depends on the system parameters. The obtained results in this paper are less restrictive than previously known criteria. Two examples are given to show the effectiveness of the obtained results.
A kernel representation for exponential splines with global tension
Barendt, Sven; Fischer, Bernd; Modersitzki, Jan
2009-02-01
Interpolation is a key ingredient in many imaging routines. In this note, we present a thorough evaluation of an interpolation method based on exponential splines in tension. They are based on so-called tension parameters, which allow for a tuning of their properties. As it turns out, these interpolants have very many nice features, which are, however, not born out in the literature. We intend to close this gap. We present for the first time an analytic representation of their kernel which enables one to come up with a space and frequency domain analysis. It is shown that the exponential splines in tension, as a function of the tension parameter, bridging the gap between linear and cubic B-Spline interpolation. For example, with a certain tension parameter, one is able to suppress ringing artefacts in the interpolant. On the other hand, the analysis in the frequency domain shows that one derives a superior signal reconstruction quality as known from the cubic B-Spline interpolation, which, however, suffers from ringing artifacts. With the ability to offer a trade-off between opposing features of interpolation methods we advocate the use of the exponential spline in tension from a practical point of view and use the new kernel representation to qualify the trade-off.
Tianxiang Yao
2014-01-01
Full Text Available This work addresses the stability study for stochastic cellular neural networks with time-varying delays. By utilizing the new research technique of the fixed point theory, we find some new and concise sufficient conditions ensuring the existence and uniqueness as well as mean-square global exponential stability of the solution. The presented algebraic stability criteria are easily checked and do not require the differentiability of delays. The paper is finally ended with an example to show the effectiveness of the obtained results.
Delay-Dependent Exponential Stability Criterion for BAM Neural Networks with Time-Varying Delays
Wei-Wei Su; Yi-Ming Chen
2008-01-01
By employing the Lyapunov stability theory and linear matrix inequality (LMI) technique, delay dependent stability criterion is derived to ensure the exponential stability of bi-directional associative memory (BAM) neural networks with time-varying delays. The proposed condition can be checked easily by LMI control toolbox in Matlab. A numerical example is given to demonstrate the effectiveness of our results.
无
2011-01-01
The visual servoing stabilization of nonholonomic mobile robot with unknown camera parameters is investigated.A new kind of uncertain chained model of nonholonomic kinemetic system is obtained based on the visual feedback and the standard chained form of type (1,2) mobile robot.Then,a novel time-varying feedback controller is proposed for exponentially stabilizing the position and orientation of the robot using visual feedback and switching strategy when the camera parameters are not known.The exponential s...
ON EXPONENTIAL STABILITY OF NON-AUTONOMOUS STOCHASTIC SEMILINEAR EVOLUTION EQUATIONS
夏学文; 刘凯
2002-01-01
Sufficient conditions for the exponential stability of a class of nonlinear, nonautonomous stochastic differential equations in infinite dimensions are studied. The analysis consists of introducing a suitable approximating solution systems and usig a limiting argument to pass on stability of strong solutions to mild ones. Consequently, under these conditions the random attractors of given stochastic systems are reduced to zero with exponential decay. Lastly, two examples are investigated to illustrate the theory.
无
2012-01-01
In this paper,a class of bidirectional associative memory(BAM) recurrent neural networks with delays are studied.By a fixed point theorem and a Lyapunov functional,some new sufficient conditions for the existence,uniqueness and global exponential stability of the almost periodic solutions are established.These conditions are easy to be verified and our results complement the previous known results.
Ruofeng Rao
2013-01-01
Full Text Available The robust exponential stability of delayed fuzzy Markovian-jumping Cohen-Grossberg neural networks (CGNNs with nonlinear p-Laplace diffusion is studied. Fuzzy mathematical model brings a great difficulty in setting up LMI criteria for the stability, and stochastic functional differential equations model with nonlinear diffusion makes it harder. To study the stability of fuzzy CGNNs with diffusion, we have to construct a Lyapunov-Krasovskii functional in non-matrix form. But stochastic mathematical formulae are always described in matrix forms. By way of some variational methods in W1,p(Ω, Itô formula, Dynkin formula, the semi-martingale convergence theorem, Schur Complement Theorem, and LMI technique, the LMI-based criteria on the robust exponential stability and almost sure exponential robust stability are finally obtained, the feasibility of which can efficiently be computed and confirmed by computer MatLab LMI toolbox. It is worth mentioning that even corollaries of the main results of this paper improve some recent related existing results. Moreover, some numerical examples are presented to illustrate the effectiveness and less conservatism of the proposed method due to the significant improvement in the allowable upper bounds of time delays.
THE MEAN-SQUARE EXPONENTIAL STABILITY AND INSTABILITY OF STOCHASTIC NONHOLONOMIC SYSTEMS
SHANG MEI; GUO YONG-XIN
2001-01-01
We present a new methodology for studying the mean-square exponential stability and instability of nonlinear nonholonomic systems under disturbance of Gaussian white-noise by the first approximation. Firstly, we give the linearized equations of nonlinear nonholonomic stochastic systems; then we construct a proper stochastic Lyapunov function to investigate the mean-square exponential stability and instability of the linearized systems, and thus determine the stability and instability in probability of corresponding competing systems. An example is given to illustrate the application procedures.
Kanit Mukdasai
2012-01-01
Full Text Available This paper investigates the problem of robust exponential stability for linear parameter-dependent (LPD systems with discrete and distributed time-varying delays and nonlinear perturbations. Parameter dependent Lyapunov-Krasovskii functional, Leibniz-Newton formula, and linear matrix inequality are proposed to analyze the stability. On the basis of the estimation and by utilizing free-weighting matrices, new delay-dependent exponential stability criteria are established in terms of linear matrix inequalities (LMIs. Numerical examples are given to demonstrate the effectiveness and less conservativeness of the proposed methods.
Huang Tingwen
2009-01-01
Full Text Available This paper studies the exponential stability of a class of periodically time-switched nonlinear systems. Three cases of such systems which are composed, respectively, of a pair of unstable subsystems, of both stable and unstable subsystems, and of a pair of stable systems, are considered. For the first case, the proposed result shows that there exists periodically switching rule guaranteeing the exponential stability of the whole system with (sufficient small switching period if there is a Hurwitz linear convex combination of two uncertain linear systems derived from two subsystems by certain linearization. For the second case, we present two general switching criteria by means of multiple and single Lyapunov function, respectively. We also investigate the stability issue of the third case, and the switching criteria of exponential stability are proposed. The present results for the second case are further applied to the periodically intermittent control. Several numerical examples are also given to show the effectiveness of theoretical results.
Exponential Stability of Uncertain T-S Fuzzy Switched Systems with Time Delay
Fatima Ahmida; El Houssaine Tissir
2013-01-01
This paper discusses the delay-dependent exponential stability of a class of uncertain T-S fuzzy switched systems with time delay.The method is based on Lyapunov stability theorem and free weighting matrices approach.Two illustrative examples are given to demonstrate the effectiveness of the proposed method.
Exponential stability of cellular neural networks with multiple time delays and impulsive effects
Li Dong; Wang Hui; Yang Dan; Zhang Xiao-Hong; Wang Shi-Long
2008-01-01
In this work,the stability issues of the equilibrium points of the cellular neural networks with multiple time delays and impulsive effects are investigated.Based on the stability theory of Lyapunov-Krasovskii,the method of linear matrix inequality (LMI) and parametrized first-order model transformation,several novel conditions guaranteeing the delaydependent and the delay-independent exponential stabilities are obtained.A numerical example is given to illustrate the effectiveness of our results.
Robust exponential stability analysis of a larger class of discrete-time recurrent neural networks
无
2007-01-01
The robust exponential stability of a larger class of discrete-time recurrent neural networks (RNNs) is explored in this paper. A novel neural network model, named standard neural network model (SNNM), is introduced to provide a general framework for stability analysis of RNNs. Most of the existing RNNs can be transformed into SNNMs to be analyzed in a unified way.Applying Lyapunov stability theory method and S-Procedure technique, two useful criteria of robust exponential stability for the discrete-time SNNMs are derived. The conditions presented are formulated as linear matrix inequalities (LMIs) to be easily solved using existing efficient convex optimization techniques. An example is presented to demonstrate the transformation procedure and the effectiveness of the results.
Wan-sheng WANG; Shou-fu LI; Run-sheng YANG
2012-01-01
A series of contractivity and exponential stability results for the solutions to nonlinear neutral functional differential equations (NFDEs) in Banach spaces are obtained,which provide unified theoretical foundation for the contractivity analysis of solutions to nonlinear problems in functional differential equations (FDEs),neutral delay differential equations (NDDEs) and NFDEs of other types which appear in practice.
2011-01-01
International audience; In this paper, stabilizing control design for a class of nonlinear affine systems is presented by using a new generalized Gronwall-Bellman lemma approach. The nonlinear systems under consideration can be non Lipschitz. Two cases are treated for the exponential stabilization~: the static state feedback and the static output feedback. The robustness of the proposed control laws with regards to parameter uncertainties is also studied. A numerical example is given to show ...
Buffered Aloha with K-Exponential Backoff -- Part I: Stability and Throughput Analysis
Lee, Tony T
2009-01-01
This two-part paper series studies the performance of buffered Aloha networks with K-Exponential Backoff collision resolution algorithms. Part I focuses on stability and throughput analysis and Part II presents the delay analysis. In Part I, the buffered Aloha network is modeled as a multi-queue single-server system. We adopt a widely used approach in packet switching systems to decompose the multi-queue system into independent first-in-first-out (FIFO) queues, which are hinged together by the probability of success of head-of-line (HOL) packets. A unified method is devised to tackle the stability and throughput problems of K-Exponential Backoff with any cutoff phase K. We demonstrate that a network with K-Exponential Backoff can be stabilized if the retransmission factor q is properly selected. The stable region of q is characterized and illustrated via examples of Geometric Retransmission (K=1) and Exponential Backoff (K=infinity). With an increasing number of nodes n, we show that the stable region of Geom...
UNCONDITIONAL NONLINEAR EXPONENTIAL STABILITY OF THE MOTIONLESS CONDUCTION-DIFFUSION SOLUTION
许兰喜
2000-01-01
Nonlinear stability of the motionless state of a heterogeneous fluid with constant temperature-gradient and concentration-gradient is studied for both cases of stress-free and rigid boundary conditions. By introducing new energy functionals we have shown that for τ = PC/PT _＜ 1, α = C/R ＞ 1 the motionless state is always stable and for τ＜ 1, α ＜ 1 the sufficient and necessary conditions for stability coincide, where PC, PT, C and R are the Schmidt number, Prandtl number,Rayleigh number for solute and heat, respectively. Moreover, the criteria guarantees the exponential stability.
Exponential stability of a PI plus reset integrator controller by a sampled-data system approach
Davó, M. A.; Gouaisbaut, F.; Baños, A; Tarbouriech, S.; Seuret, A.
2016-01-01
The paper deals with the stability analysis of time-delay reset control systems, for which the resetting law is assumed to satisfy a time-dependent condition. A stability analysis of the closed-loop system is performed based on an appropriate sampled-data system. New linear matrix inequality (LMI) conditions are proposed to ensure the exponential stability of the closed-loop resulting of the connection of a plant with a proportional and integral controller together with a reset integrator (PI...
Exponential Stability of Cohen-Grossberg Neural Networks with Impulse Time Window
Mei Liu
2016-01-01
Full Text Available This paper concerns the problem of exponential stability for a class of Cohen-Grossberg neural networks with impulse time window and time-varying delays. In our letter, the impulsive effects we considered can stochastically occur at a definitive time window and the impulsive controllers we considered can be nonlinear and even rely on the states of all the neurons. Hence, the impulses here can be more applicable and more general. By utilizing Lyapunov functional theory, inequality technique, and the analysis method, we obtain some novel and effective exponential stability criteria for the Cohen-Grossberg neural networks. These results generalize a few previous known results and numerical simulations are given to show the effectiveness of the derived results.
ASYMPTOTIC BEHAVIOUR AND EXPONENTIAL STABILITY FOR THERMOELASTIC PROBLEM WITH LOCALIZED DAMPING
GAO Hong-jun; ZHAO Yu-juan
2006-01-01
A semi-linear thermoelastic problem with localized damping is considered,which is one of the most important mathematical models in material science. The existence and decays exponentially to zero of solution of this problem are obtained. Moreover,the existence of absorbing sets is achieved in the non-homogeneous case. The result indicates that the system which we studied here is asymptotic stability.
LIU Hai-feng; WANG Chun-hua; WEI Guo-liang
2008-01-01
The exponential stability problem is investigated fora class of stochastic recurrent neural networks with time delay and Markovian switching.By using It(o)'s differential formula and the Lyapunov stabifity theory,sufficient condition for the solvability of this problem is derived in telm of linear matrix inequalities,which can be easily checked by resorting to available software packages.A numerical example and the simulation are exploited to demonstrate the effectiveness of the proposed results.
Exponential stability of time-delay systems via new weighted integral inequalities
Hien, L. V.; Trinh, H.
2015-01-01
In this paper, new weighted integral inequalities (WIIs) are first derived by refining the Jensen single and double inequalities. It is shown that the newly derived inequalities in this paper encompass both the Jensen inequality and its most recent improvements based on Wirtinger integral inequality. The potential capability of the proposed WIIs is demonstrated through applications in exponential stability analysis for some classes of time-delay systems in the framework of linear matrix inequ...
Exponential Stabilization of Delay Neutral Systems under Sampled-Data Control
Seuret, Alexandre; Fridman, Emilia; Richard, Jean-Pierre
2005-01-01
International audience; This paper considers the exponential stabilization of delay systems of the neutral type via sampled-data control. The control input of the neutral system can present a delay, constant or variable. The sampling period is not necessarily constant. It is only assumed that the time between to successive sampling instants is bounded. Since the sampling effect (sampling and zero-holder) is equivalent to a variable delay, the resulting system is modelled as a continuous-time ...
Yang, Shiju; Li, Chuandong; Huang, Tingwen
2016-03-01
The problem of exponential stabilization and synchronization for fuzzy model of memristive neural networks (MNNs) is investigated by using periodically intermittent control in this paper. Based on the knowledge of memristor and recurrent neural network, the model of MNNs is formulated. Some novel and useful stabilization criteria and synchronization conditions are then derived by using the Lyapunov functional and differential inequality techniques. It is worth noting that the methods used in this paper are also applied to fuzzy model for complex networks and general neural networks. Numerical simulations are also provided to verify the effectiveness of theoretical results.
Stagnation-point flow and heat transfer over an exponentially shrinking sheet: A stability analysis
Ismail, Nurul Syuhada; Arifin, Norihan Md.; Bachok, Norfifah; Mahiddin, Norhasimah
2016-06-01
Numerical solutions for the stagnation-point flow and heat transfer over an exponentially shrinking sheet have been investigated. The governing boundary layer equations are transformed into an ordinary differential equation using a non-similar transformation. By using the bvp4c solver in MATLAB, the results of the equations can be solved numerically. Numerical results indicate that in certain parameter, the non-unique solutions for the velocity and the temperature do exist. A linear stability analysis shows that only one solution is linearly stable otherwise is unstable. Then, the stability analysis is performed to identify which solution is stable between the two non-unique solutions.
Xinghua Liu; Hongsheng Xi
2013-01-01
The exponential stability of neutral Markovian jump systems with interval mode-dependent time-varying delays, nonlinear perturbations, and partially known transition rates is investigated. A novel augmented stochastic Lyapunov functional is constructed, which employs the improved bounding technique and contains triple-integral terms to reduce conservativeness; then the delay-range-dependent and rate-dependent exponential stability criteria are developed by Lyapunov stability theory, reciproca...
On the absolute stability regions corresponding to partial sums of the exponential function
Ketcheson, David I.
2013-12-03
Certain numerical methods for initial value problems have as stability function the nth partial sum of the exponential function. We study the stability region, i.e., the set in the complex plane over which the nth partial sum has at most unit modulus. It is known that the asymptotic shape of the part of the stability region in the left half-plane is a semi-disk. We quantify this by providing disks that enclose or are enclosed by the stability region or its left half-plane part. The radius of the smallest disk centered at the origin that contains the stability region (or its portion in the left half-plane) is determined for 1 n 20. Bounds on such radii are proved for n 2; these bounds are shown to be optimal in the limit n ! +1. We prove that the stability region and its complement, restricted to the imaginary axis, consist of alternating intervals of length tending to , as n ! 1. Finally, we prove that a semi-disk in the left half-plane with vertical boundary being the imaginary axis and centered at the origin is included in the stability region if and only if n 0 mod 4 or n 3 mod 4. The maximal radii of such semi-disks are exactly determined for 1 n 20.
Generic super-exponential stability of elliptic equilibrium positions for symplectic vector fields
Niederman, Laurent
2013-11-01
In this article, we consider linearly stable elliptic fixed points (equilibrium) for a symplectic vector field and prove generic results of super-exponential stability for nearby solutions. We will focus on the neighborhood of elliptic fixed points but the case of linearly stable isotropic reducible invariant tori in a Hamiltonian system should be similar. More specifically, Morbidelli and Giorgilli have proved a result of stability over superexponentially long times if one considers an analytic Lagrangian torus, invariant for an analytic Hamiltonian system, with a diophantine translation vector which admits a sign-definite torsion. Then, the solutions of the system move very little over times which are super-exponentially long with respect to the inverse of the distance to the invariant torus. The proof proceeds in two steps: first one constructs a high-order Birkhoff normal form, then one applies the Nekhoroshev theory. Bounemoura has shown that the second step of this construction remains valid if the Birkhoff normal form linked to the invariant torus or the elliptic fixed point belongs to a generic set among the formal series. This is not sufficient to prove this kind of super-exponential stability results in a general setting. We should also establish that the most strongly non resonant elliptic fixed point or invariant torus in a Hamiltonian system admits Birkhoff normal forms fitted for the application of the Nekhoroshev theory. Actually, the set introduced by Bounemoura is already very large but not big enough to ensure that a typical Birkhoff normal form falls into this class. We show here that this property is satisfied generically in the sense of the measure (prevalence) through infinite-dimensional probe spaces (that is, an infinite number of parameters chosen at random) with methods similar to those developed in a paper of Gorodetski, Kaloshin and Hunt in another setting.
Global Stability of a Discrete Mutualism Model
Kun Yang
2014-01-01
difference equations, sufficient conditions which ensure the global asymptotical stability of the interior equilibrium of the system are obtained. The conditions which ensure the local stability of the positive equilibrium is enough to ensure the global attractivity are proved.
Louihi, M.; Hbid, M. L.
2007-05-01
In this paper we are concerned with the exponential asymptotic stability of the solution of a class of differential equations with state dependent delays. Our approach is based on the Crandall-Liggett approximation and the properties of semigroups.
Delay-Dependent Exponential Stability for Discrete-Time BAM Neural Networks with Time-Varying Delays
Yonggang Chen
2008-01-01
Full Text Available This paper considers the delay-dependent exponential stability for discrete-time BAM neural networks with time-varying delays. By constructing the new Lyapunov functional, the improved delay-dependent exponential stability criterion is derived in terms of linear matrix inequality (LMI. Moreover, in order to reduce the conservativeness, some slack matrices are introduced in this paper. Two numerical examples are presented to show the effectiveness and less conservativeness of the proposed method.
Junhao Hu
2014-01-01
Full Text Available We develop exponential stability of neutral stochastic functional differential equations with two-time-scale Markovian switching modeled by a continuous-time Markov chain which has a large state space. To overcome the computational effort and the complexity, we split the large-scale system into several classes and lump the states in each class into one class by the different states of changes of the subsystems; then, we give a limit system to effectively “replace” the large-scale system. Under suitable conditions, using the stability of the limit system as a bridge, the desired asymptotic properties of the large-scale system with Brownian motion and Poisson jump are obtained by utilizing perturbed Lyapunov function methods and Razumikhin-type criteria. Two examples are provided to demonstrate our results.
Gerbi, Stéphane
2013-01-15
The goal of this work is to study a model of the wave equation with dynamic boundary conditions and a viscoelastic term. First, applying the Faedo-Galerkin method combined with the fixed point theorem, we show the existence and uniqueness of a local in time solution. Second, we show that under some restrictions on the initial data, the solution continues to exist globally in time. On the other hand, if the interior source dominates the boundary damping, then the solution is unbounded and grows as an exponential function. In addition, in the absence of the strong damping, then the solution ceases to exist and blows up in finite time.
Weihua Mao
2012-01-01
Full Text Available This paper discusses the mean-square exponential stability of uncertain neutral linear stochastic systems with interval time-varying delays. A new augmented Lyapunov-Krasovskii functional (LKF has been constructed to derive improved delay-dependent robust mean-square exponential stability criteria, which are forms of linear matrix inequalities (LMIs. By free-weight matrices method, the usual restriction that the stability conditions only bear slow-varying derivative of the delay is removed. Finally, numerical examples are provided to illustrate the effectiveness of the proposed method.
Yang Fang
2016-01-01
Full Text Available The robust exponential stability problem for a class of uncertain impulsive stochastic neural networks of neutral-type with Markovian parameters and mixed time-varying delays is investigated. By constructing a proper exponential-type Lyapunov-Krasovskii functional and employing Jensen integral inequality, free-weight matrix method, some novel delay-dependent stability criteria that ensure the robust exponential stability in mean square of the trivial solution of the considered networks are established in the form of linear matrix inequalities (LMIs. The proposed results do not require the derivatives of discrete and distributed time-varying delays to be 0 or smaller than 1. Moreover, the main contribution of the proposed approach compared with related methods lies in the use of three types of impulses. Finally, two numerical examples are worked out to verify the effectiveness and less conservativeness of our theoretical results over existing literature.
Global existence and exponential decay of the solution for a viscoelastic wave equation with a delay
Dai, Qiuyi; Yang, Zhifeng
2014-10-01
In this paper, we consider initial-boundary value problem of viscoelastic wave equation with a delay term in the interior feedback. Namely, we study the following equation together with initial-boundary conditions of Dirichlet type in Ω × (0, + ∞) and prove that for arbitrary real numbers μ 1 and μ 2, the above-mentioned problem has a unique global solution under suitable assumptions on the kernel g. This improve the results of the previous literature such as Nicaise and Pignotti (SIAM J. Control Optim 45:1561-1585, 2006) and Kirane and Said-Houari (Z. Angew. Math. Phys. 62:1065-1082, 2011) by removing the restriction imposed on μ 1 and μ 2. Furthermore, we also get an exponential decay results for the energy of the concerned problem in the case μ 1 = 0 which solves an open problem proposed by Kirane and Said-Houari (Z. Angew. Math. Phys. 62:1065-1082, 2011).
On Global Stability for Lifschitz-Slyozov-Wagner like equations
Conlon, Joseph G
2011-01-01
This paper is concerned with the stability and asymptotic stability at large time of solutions to a system of equations, which includes the Lifschitz-Slyozov-Wagner (LSW) system in the case when the initial data has compact support. The main result of the paper is a proof of weak global asymptotic stability for LSW like systems. Previously strong local asymptotic stability results were obtained by Niethammer and Vel\\'{a}zquez for the LSW system with initial data of compact support. Comparison to a quadratic model plays an important part in the proof of the main theorem when the initial data is critical. The quadratic model extends the linear model of Carr and Penrose, and has a time invariant solution which decays exponentially at the edge of its support in the same way as the infinitely differentiable self-similar solution of the LSW model.
Yimin Zhang
2009-01-01
Full Text Available By the continuation theorem of coincidence degree and M-matrix theory, we obtain some sufficient conditions for the existence and exponential stability of periodic solutions for a class of generalized neural networks with arbitrary delays, which are milder and less restrictive than those of previous known criteria. Moreover our results generalize and improve many existing ones.
Stability of multiple access network control schemes with carrier sensing and exponential backoff
Barany, Ernest; Krupa, Maciej
2006-05-01
A new approach to determine the stability of multiple access network control schemes is presented. A “busy” network (the precise meaning of the term “busy” will be presented in the text) is modelled as a switched single-server hybrid dynamical system whose switching laws are stochastic and are based on typical multiple access network control protocols such as ALOHA and ethernet. The techniques are used to compute the critical ratio of traffic production per network node to total available bandwidth that ensures that data packets will not accumulate unboundedly in waiting queues at each node. This is a measure of stability of the network and is an emergent, global, property determined by decentralized, autonomous behavior of each node. The behavior of each individual node is regarded as “microscopic” and the collective behavior of the network as a whole are emergent consequences of such microscopic laws. The results follow from the stationary distribution property of ergodic Markov chains.
Ivashchuk, V D
2016-01-01
A (n+1)-dimensional gravitational model with Gauss-Bonnet term and cosmological constant term is considered. When ansatz with diagonal cosmological metrics is adopted, the solutions with exponential dependence of scale factors: a_i \\sim \\exp{ ( v^i t) }, i =1, ..., n, are analysed for n > 3. We study the stability of the solutions with non-static volume factor, i.e. if K(v) = \\sum_{k = 1}^{n} v^k \
Yingwei Li
2014-01-01
properties, the existence and uniqueness of the equilibrium point for SNNs without noise perturbations are proved. Secondly, by applying the Lyapunov-Krasovskii functional approach, stochastic analysis theory, and linear matrix inequality (LMI technique, new delay-dependent sufficient criteria are achieved in terms of LMIs to ensure the SNNs with noise perturbations to be globally exponentially stable in the mean square. Finally, two simulation examples are provided to demonstrate the validity of the theoretical results.
Oberlack, Martin; Nold, Andreas; Sanjon, Cedric Wilfried; Wang, Yongqi; Hau, Jan
2016-11-01
Classical hydrodynamic stability theory for laminar shear flows, no matter if considering long-term stability or transient growth, is based on the normal-mode ansatz, or, in other words, on an exponential function in space (stream-wise direction) and time. Recently, it became clear that the normal mode ansatz and the resulting Orr-Sommerfeld equation is based on essentially three fundamental symmetries of the linearized Euler and Navier-Stokes equations: translation in space and time and scaling of the dependent variable. Further, Kelvin-mode of linear shear flows seemed to be an exception in this context as it admits a fourth symmetry resulting in the classical Kelvin mode which is rather different from normal-mode. However, very recently it was discovered that most of the classical canonical shear flows such as linear shear, Couette, plane and round Poiseuille, Taylor-Couette, Lamb-Ossen vortex or asymptotic suction boundary layer admit more symmetries. This, in turn, led to new problem specific non-modal ansatz functions. In contrast to the exponential growth rate in time of the modal-ansatz, the new non-modal ansatz functions usually lead to an algebraic growth or decay rate, while for the asymptotic suction boundary layer a double-exponential growth or decay is observed.
Global stabilization of a Lorenz system
李世华; 田玉平
2003-01-01
In this paper,using feedback linearizing technique,we show that a Lorenz system can be considered as a cascade system.Moreover,this system satisfies the assumptions of global stabilization of cascade systems.Thus continuous state feedback control laws are proposed to globally stabilize the Lorenz system at the equilibrium point.Simulation results are presented to verify our method.This method can be further generalized to other chaotic systems such as Chen system,coupled dynamos system,etc.
Exponential Growth and the Shifting Global Center of Gravity of Science Production, 1900-2011
Zhang, Liang; Powell, Justin J. W.; Baker, David P.
2015-01-01
Long historical trends in scientific discovery led mid-20th century scientometricians to mark the advent of "big science"--extensive science production--and predicted that over the next few decades, the exponential growth would slow, resulting in lower rates of increase in production at the upper limit of a logistic curve. They were…
Exponential Growth and the Shifting Global Center of Gravity of Science Production, 1900-2011
Zhang, Liang; Powell, Justin J. W.; Baker, David P.
2015-01-01
Long historical trends in scientific discovery led mid-20th century scientometricians to mark the advent of "big science"--extensive science production--and predicted that over the next few decades, the exponential growth would slow, resulting in lower rates of increase in production at the upper limit of a logistic curve. They were…
Lack of exponential stability to Timoshenko system with viscoelastic Kelvin-Voigt type
Malacarne, Andréia; Muñoz Rivera, Jaime Edilberto
2016-06-01
We study the Timoshenko systems with a viscoelastic dissipative mechanism of Kelvin-Voigt type. We prove that the model is analytical if and only if the viscoelastic damping is present in both the shear stress and the bending moment. Otherwise, the corresponding semigroup is not exponentially stable no matter the choice of the coefficients. This result is different to all others related to Timoshenko model with partial dissipation, which establish that the system is exponentially stable if and only if the wave speeds are equal. Finally, we show that the solution decays polynomially to zero as {t^{-1/2}} , no matter where the viscoelastic mechanism is effective and that the rate is optimal whenever the initial data are taken on the domain of the infinitesimal operator.
Linghai Zhang
2004-01-01
We establish the exponential stability of fast traveling pulse solutions to nonlinear singularly perturbedsystems of integral di.erential equations arising from neuronal networks. It has been proved that exponentialstability of these orbits is equivalent to linear stability. Let L be the linear di.erential operator obtainedby linearizing the nonlinear system about its fast pulse, and let σ(L) be the spectrum of L. The linearizedstability criterion says that if max{Reλ: λ∈σ(L), λ ≠ 0} ≤ .D, for some positive constant D, and λ = 0 is asimple eigenvalue of L(ε), then the stability follows immediately (see [13] and [37]). Therefore, to establish theexponential stability of the fast pulse, it su.ces to investigate the spectrum of the operator L. It is relativelyeasy to .nd the continuous spectrum, but it is very di.cult to .nd the isolated spectrum. The real part ofthe continuous spectrum has a uniformly negative upper bound, hence it causes no threat to the stability. Itremains to see if the isolated spectrum is safe.Eigenvalue functions (see [14] and [35,36]) have been a powerful tool to study the isolated spectrum of the associatedlinear di.erential operators because the zeros of the eigenvalue functions coincide with the eigenvaluesof the operators. There have been some known methods to de.ne eigenvalue functions for nonlinear systems ofreaction di.usion equations and for nonlinear dispersive wave equations. But for integral di.erential equations,we have to use di.erent ideas to construct eigenvalue functions. We will use the method of variation of parametersto construct the eigenvalue functions in the complex plane C. By analyzing the eigenvalue functions, we.nd that there are no nonzero eigenvalues of L in {λ∈ C: Reλ≥ .D} for the fast traveling pulse. Moreoverλ = 0 is simple. This implies that the exponential stability of the fast orbits is true.
Exponential stability of solutions to nonlinear time-delay systems of neutral type
Gennadii V. Demidenko
2016-01-01
Full Text Available We consider a nonlinear time-delay system of neutral equations with constant coefficients in the linear terms $$ \\frac{d}{dt}\\big(y(t + D y(t-\\tau\\big = A y(t + B y(t-\\tau + F(t, y(t, y(t-\\tau, $$ where $$ \\|F(t,u,v\\| \\le q_1\\|u\\|^{1+\\omega_1} + q_2\\|v\\|^{1+\\omega_2}, \\quad q_1, q_2, \\omega_1, \\omega_2 > 0. $$ We obtain estimates characterizing the exponential decay of solutions at infinity and estimates for attraction sets of the zero solution.
Some equivalent conditions for exponential stabilization of linear systems with unbounded contro1
吴汉忠
1999-01-01
It is proved that the equivalences among the exponential stabilizability of the control system, the existences of admissible controls for every initial state condition and the solvability of some Riccati equation or some LQ problem also hold for the case in Hilbert space with unbounded control. The results do not need the compactness assumption for the resolvents of the infinitesimal generator, and improve the results available. They can be applied to the parabolic systems with boundary control through Dirichlet, Neumann condition or pointwise control on not only bounded domain but also unbounded domain.
Hua CHEN; Gongwei LIU
2013-01-01
In this paper,we consider the nonlinearly damped semi-linear wave equation associated with initial and Dirichlet boundary conditions.We prove the existence of a local weak solution and introduce a family of potential wells and discuss the invariants and vacuum isolating behavior of solutions.Furthermore,we prove the global existence of solutions in both cases which are polynomial and exponential decay in the energy space respectively,and the asymptotic behavior of solutions for the cases of potential well family with 0 ＜ E(0) ＜ d.At last we show that the energy will grow up as an exponential function as time goes to infinity,provided the initial data is large enough or E(0) ＜ 0.
郭汴京; 滕志东; 蒋海军
2008-01-01
研究了带有变时滞的高阶模糊细胞神经网络(HFCNNs)的全局指数稳定性.通过引入非奇异M-矩阵和使用Lyapunov泛函方法,得到了带有常时滞和变时滞的高阶模糊细胞神经网络全局指数稳定性的充分条件.%In this paper,the global exponential stability of high-order fuzzy cellular neural networks (HFCNNs) with time-varying delays is proposed.Employing nonsingular M-matrix and Lyapunov functional method,some new sufficient conditions are derived for checking global exponential stability of the HFCNNs with constant and time-varying delays.
Stability and Space Phase Analysis in f(R) theory with Generalized Exponential model
Boko, R D; Tossa, J
2016-01-01
We have studied in this paper, the stability of dynamical system in $f(R)$ gravity. We have considered the $f(R)$ $\\gamma$-gravity and explored its dynamical analysis. We found six critical points among which only one describes an universe fulled of both matter and dominated dark energy. It's shown that these critical points presents specific phase spaces described by the corresponding fluids. Furthermore, we've investigated the stability conditions of these critical points and find that theses conditions are dependent of the model parameters. We also study the stability of a new power-law $f_\\ast(R)$ model with de Sitter and power law solutions.
Zhu, Ke; 10.1214/11-AOS895
2012-01-01
This paper investigates the asymptotic theory of the quasi-maximum exponential likelihood estimators (QMELE) for ARMA--GARCH models. Under only a fractional moment condition, the strong consistency and the asymptotic normality of the global self-weighted QMELE are obtained. Based on this self-weighted QMELE, the local QMELE is showed to be asymptotically normal for the ARMA model with GARCH (finite variance) and IGARCH errors. A formal comparison of two estimators is given for some cases. A simulation study is carried out to assess the performance of these estimators, and a real example on the world crude oil price is given.
Global stability of prey-taxis systems
Jin, Hai-Yang; Wang, Zhi-An
2017-02-01
In this paper, we prove the global boundedness and stability of the predator-prey system with prey-taxis in a two-dimensional bounded domain with Neumann boundary conditions. By deriving an entropy-like equality and a boundedness criterion, we show that the intrinsic interaction between predators and preys is sufficient to prevent the population overcrowding even the prey-taxis is included and strong. Furthermore, by constructing appropriate Lyapunov functionals, we show that prey-only steady state is globally asymptotically stable if the predation is weak, and the co-existence steady state is globally asymptotically stable under some conditions (like the prey-taxis is weak or the prey diffuses fast) if the predation is strong. The convergence rates of solutions to the steady states are derived in the paper.
Ivashchuk, V.D. [VNIIMS, Center for Gravitation and Fundamental Metrology, Moscow (Russian Federation); Peoples' Friendship University of Russia (RUDN University), Institute of Gravitation and Cosmology, Moscow (Russian Federation)
2016-08-15
A (n + 1)-dimensional gravitational model with Gauss-Bonnet term and a cosmological constant term is considered. When ansatz with diagonal cosmological metrics is adopted, the solutions with an exponential dependence of the scale factors, a{sub i} ∝ exp(v{sup i}t), i = 1,.., n, are analyzed for n > 3. We study the stability of the solutions with non-static volume factor, i.e. K(v) = sum {sub k=1}{sup n} v{sup k} ≠ 0. We prove that under a certain restriction R imposed solutions with K(v) > 0 are stable, while solutions with K(v) < 0 are unstable. Certain examples of stable solutions are presented. We show that the solutions with v{sup 1} = v{sup 2} = v{sup 3} = H > 0 and zero variation of the effective gravitational constant are stable if the restriction R is obeyed. (orig.)
Apalara, Tijani A., E-mail: tijani@kfupm.edu.sa [King Fahd University of Petroleum and Minerals, Affiliated Colleges at Hafr Al-Batin, General Science and Studies Unit-Mathematics (Saudi Arabia); Messaoudi, Salim A., E-mail: messaoud@kfupm.edu.sa [King Fahd University of Petroleum and Minerals, Department of Mathematics and Statistics (Saudi Arabia)
2015-06-15
In this paper, we consider a one-dimensional linear thermoelastic system of Timoshenko type with a delay, where the heat flux is given by Cattaneo’s law. We prove an exponential decay result under a smallness condition on the delay and a stability number introduced first in Santos et al. (J Diff Eqs 253:2715–2733, 2012), using a method different from that of Santos et al. (J Diff Eqs 253:2715–2733, 2012). We also reproduce the polynomial decay of Santos et al. (J Diff Eqs 253:2715–2733, 2012) using the multiplier method in the case of absence of delay. The polynomial decay issue in the presence of a small delay is an open question.
Global stability analysis of axisymmetric boundary layers
Vinod, N
2016-01-01
This paper presents the linear global stability analysis of the incompressible axisymmetric boundary layer on a circular cylinder. The base flow is parallel to the axis of the cylinder at inlet. The pressure gradient is zero in the streamwise direction. The base flow velocity profile is fully non-parallel and non-similar in nature. The boundary layer grows continuously in the spatial directions. Linearized Navier-Stokes(LNS) equations are derived for the disturbance flow quantities in the cylindrical polar coordinates. The LNS equations along with homogeneous boundary conditions forms a generalized eigenvalues problem. Since the base flow is axisymmetric, the disturbances are periodic in azimuthal direction. Chebyshev spectral collocation method and Arnoldi's iterative algorithm is used for the solution of the general eigenvalues problem. The global temporal modes are computed for the range of Reynolds numbers and different azimuthal wave numbers. The largest imaginary part of the computed eigenmodes are nega...
Global stability of self-gravitating discs in modified gravity
Ghafourian, Neda; Roshan, Mahmood
2017-07-01
Using N-body simulations, we study the global stability of a self-gravitating disc in the context of modified gravity (MOG). This theory is a relativistic scalar-tensor-vector theory of gravity and it is presented to address the dark matter problem. In the weak field limit, MOG possesses two free parameters α and μ0, which have already been determined using the rotation curve data of spiral galaxies. The evolution of a stellar self-gravitating disc and, more specifically, the bar instability in MOG are investigated and compared to a Newtonian case. Our models have exponential and Mestel-like surface densities as Σ ∝ exp (-r/h) and Σ ∝ 1/r. It is found that, surprisingly, the discs are more stable against the bar mode in MOG than in Newtonian gravity. In other words, the bar growth rate is effectively slower than the Newtonian discs. Also, we show that both free parameters (i.e. α and μ0) have stabilizing effects. In other words, an increase in these parameters will decrease the bar growth rate.
Global stabilization of nonlinear systems with uncertain structure
无
2005-01-01
The global stabilization problem of nonlinear systems with uncertain structure is dealt with. Based on control Lyapunov function (CLF), a sufficient and necessary condition for Lyapunov stabilization is given. From the condition,several simply sufficient conditions for the globally asymptotical stability are deduced. A state feedback control law is designed to globally asymptotically stabilize the equilibrium of the closed system. Last, a simulation shows the effectiveness of the method.
Li, Zhihong; Liu, Lei; Zhu, Quanxin
2016-12-01
This paper studies the mean-square exponential input-to-state stability of delayed Cohen-Grossberg neural networks with Markovian switching. By using the vector Lyapunov function and property of M-matrix, two generalized Halanay inequalities are established. By means of the generalized Halanay inequalities, sufficient conditions are also obtained, which can ensure the exponential input-to-state stability of delayed Cohen-Grossberg neural networks with Markovian switching. Two numerical examples are given to illustrate the efficiency of the derived results. Copyright © 2016 Elsevier Ltd. All rights reserved.
Sirada Pinjai
2013-01-01
Full Text Available This paper is concerned with the problem of robust exponential stability for linear parameter-dependent (LPD neutral systems with mixed time-varying delays and nonlinear perturbations. Based on a new parameter-dependent Lyapunov-Krasovskii functional, Leibniz-Newton formula, decomposition technique of coefficient matrix, free-weighting matrices, Cauchy’s inequality, modified version of Jensen’s inequality, model transformation, and linear matrix inequality technique, new delay-dependent robust exponential stability criteria are established in terms of linear matrix inequalities (LMIs. Numerical examples are given to show the effectiveness and less conservativeness of the proposed methods.
Global stability of predator-prey system with alternative prey.
Sahoo, Banshidhar
2013-01-01
A predator-prey model in presence of alternative prey is proposed. Existence and local stability conditions for interior equilibrium points are derived. Global stability conditions for interior equilibrium points are also found. Bifurcation analysis is done with respect to predator's searching rate and handling time. Bifurcation analysis confirms the existence of global stability in presence of alternative prey.
王力; 周宗福
2011-01-01
本文考虑具有S型分布时滞和脉冲的Cohen-Grossberg神经网络模型,应用Lyapunov函数,M矩阵和Razumikhin技巧,得到了该模型稳定的充分条件.%In this paper, we consider the Cohen-Grossberg nerual networks with S-typed distributed delays and impulses. Applying the method of Lyapunov functions, M-matrix theory and the Razumikhin technique,a sufficient criterion of stability of equilibrium of the networks is obtained.
王继禹; 李耀堂
2007-01-01
In this paper, by employing the homeomorphism theory and M-matrix theory, Young ine-quality technique and some analysis techniques, some sufficient conditions is obtained for the globalexponential stability and existence of equilibrium point for a general class of bidirectional associativememory(BAM) neural networks. The results remove the assumptions that the boundedness, monoto-nieity or differentiability of the activation functions. It is shown that in some cases, the stability criteriacan be easily checked. Finally, one illustrative example is also provided to demonstrate the effective-ness of the obtained results.%应用同胚理论,M-矩阵理论和Young不等式技巧,给出了一族双向关联记忆神经网络的平衡点存在性和全局指数稳定性的几个充分条件,这些条件去掉了对激活函数的有界性,单调性和可微性的要求且在某些情况下更易验证.
Sisto, Alessandro
2011-01-01
Using ultrafilter techniques we show that in any partition of $\\mathbb{N}$ into 2 cells there is one cell containing infinitely many exponential triples, i.e. triples of the kind $a,b,a^b$ (with $a,b>1$). Also, we will show that any multiplicative $IP^*$ set is an "exponential $IP$ set", the analogue of an $IP$ set with respect to exponentiation.
Exponential estimation of generalized state-space time-delay systems
Lien, C-H; Yu, K-W [Department of Marine Engineering, National Kaohsiung Marine University, Taiwan 811 (China); Lin, J-S; Hung, M-L [Department of Electrical Engineering, Far East University, Tainan, Taiwan 744 (China)], E-mail: chlien@mail.nkmu.edu.tw
2008-02-15
In this paper, global exponential stability for a class of generalized state-space time-delay systems is considered. Delay-dependent criteria are proposed to guarantee the exponential stability and estimate the convergence rate for the generalized state-space systems with two cases of uncertainties. Finally, some numerical examples are illustrated to show the usefulness of the theory.
Global stability analysis on a class of cellular neural networks
ZHANG; Yi
2001-01-01
［1］Chua， L. O., Yang, L., Cellular neural networks: Theory, IEEE Trans. CAS, 1988, (10): 1257.［2］Chua, L. O., Yang, L., Cellular neural networks: Applications, IEEE Trans. CAS, 1988, (10): 1273.［3］Chua, L. O., Roska, T., The CNN paradigm, IEEE Trans. CAS-I, 1993, (3): 147.［4］Matsumoto, T. Chua, L. O., Suzuki, H., CNN cloning template: Connected component detector, IEEE Trans. CAS, 1990, (8): 633.［5］Cao, L, Sun, Y, Yu, J., A CNN-based signature verification system，Proc. ICONIP′95, Beijing, 1995, 913—916.［6］Roska, T., Chua, L. O., The CNN universal machine: An analogic array computer, IEEE Trans. CAS Ⅱ, 1993, (3): 163.［7］Chua, L. O., Roska, T., Stability of a class of nonreciprocal cellular neural networks, IEEE Trans. CAS, 1990, (3): 1520.［8］Roska, T., Wu, C. W., Balsi, M. Et al., Stability and dynamics of delay type general and cellular neural networks, IEEE Trans. CAS, 1992, (6): 487.［9］Roska, T., Wu, C. W., Chua, L. O., Stability of cellular neural networks with dominant nonlinear and delaytype templates, IEEE Trans. CAS, 1993, (4): 270.［10］Civalleri, P. P., On stability of cellular neural networks with delay, IEEE Trans. CAS-I, 1993, (3): 157.［11］Gilli, G., Stability of cellular neural network and delayed cellular neural networks with nonpositive templates and nonmonotonic output functions, IEEE Trans CAS-I， 1994， (8)： 518.［12］Baldi, P., Atiya, A. F., How delays affect neural dynamics and learning, IEEE Trans. On Neural Networks, 1994, (4): 612.［13］Liao, X. X., Mathematic foundation of cellular neural networks (Ⅰ), Science in China, Ser. A, 1994, 37(9): 902.［14］Liao, X. X., Mathematic foundation of cellular neural networks (Ⅱ), Science in China, Ser. A, 1994, 37(9): 1037.［15］Zhang, Y., Global exponential stability and periodic solutions of delay Hopfild neural networks, International J. Sys. Sci., 1996, (2): 227.［16］Zhang Yi, Zhong, S. M., Li, Z. L., Periodic solutions and global
Global Stability for a HIV/AIDS Model
Silva, Cristiana J.; Torres, Delfim F. M.
2017-01-01
We investigate global stability properties of a HIV/AIDS population model with constant recruitment rate, mass action incidence, and variable population size. Existence and uniqueness results for disease-free and endemic equilibrium points are proved. Global stability of the equilibria is obtained through Lyapunov's direct method and LaSalle's invariance principle.
GLOBAL STABILITY IN HOPFIELD NEURAL NETWORKS WITH DISTRIBUTED TIME DELAYS
Zhang Jiye; Wu Pingbo; Dai Huanyun
2001-01-01
In this paper, without assuming the boundedness, monotonicity and differentiability of the activation functions, the conditions ensuring existence, uniqueness, and global asymptotical stability of the equilibrium point of Hopfield neural network models with distributed time delays are studied. Using M-matrix theory and constructing proper Liapunov functionals, the sufficient conditions for global asymptotic stability are obtained.
Global asymptotic stability of cellular neural networks with multiple delays
无
2006-01-01
Global asymptotic stability (GAS) is discussed for cellular neural networks (CNN) with multiple time delays. Several criteria are proposed to ascertain the uniqueness and global asymptotic stability of the equilibrium point for the CNN with delays. These criteria can eliminate the difference between the neuronal excitatory and inhibitory effects. Two examples are presented to demonstrate the effectiveness of the criteria.
Feng, Baowei
2017-02-01
This paper is concerned with a class of plate equation with past history and time-varying delay in the internal feedback u_{tt}+α Δ ^2 u-int limits ^t_{-∞}g(t-s)Δ ^2 u(s)ds+μ _1u_t+μ _2u_t(t-τ (t))+f(u)=h(x), defined in a bounded domain of {R}^n (n≥1) with some suitable initial data and boundary conditions. For arbitrary real numbers μ _1 and μ _2, we proved the global well-posedness of the problem. Results on stability of energy are also proved under some restrictions on μ _1, μ _2 and h(x)=0.
Li, Xiaodi; Song, Shiji
2013-06-01
In this paper, a class of recurrent neural networks with discrete and continuously distributed delays is considered. Sufficient conditions for the existence, uniqueness, and global exponential stability of a periodic solution are obtained by using contraction mapping theorem and stability theory on impulsive functional differential equations. The proposed method, which differs from the existing results in the literature, shows that network models may admit a periodic solution which is globally exponentially stable via proper impulsive control strategies even if it is originally unstable or divergent. Two numerical examples and their computer simulations are offered to show the effectiveness of our new results.
Ma Bao-Li
2013-09-01
Full Text Available In this work, we investigate the trajectory tracking and point stabilization problems of asymmetric underactuated surface ships with non-diagonal inertia and damping matrices. By combining the novel state and input transformations, the direct Lyapunov approach, and the nonlinear time-varying tools, the trajectory tracking controller is derived, guaranteeing global κ-exponential convergence of state trajectory to the reference one satisfying mild persistent exciting conditions. By properly designing the reference trajectory, the proposed tracking scheme is also generalized to achieve global uniform asymptotic point stabilization. Simulation examples are given to illustrate the effectiveness of the proposed control schemes.
Winkler, Michael
2017-02-01
The Neumann initial-boundary value problem for the chemotaxis system {ut=∇ṡ(D(u)∇u)-∇ṡ(S(u)∇v),vt=Δv-v+u,(⋆) is considered in a bounded domain Ω \\subset {{{R}}n} , n≥slant 1 , with smooth boundary. In compliance with refined modeling approaches, the diffusivity function D therein is allowed to decay considerably fast at large densities, where a particular focus will be on the mathematically delicate case when D(s) decays exponentially as s\\to ∞ . In such situations, namely, straightforward Moser-type recursive arguments for the derivation of {{L}∞} estimates for u from corresponding L p bounds seem to fail. Accordingly, results on global existence, and especially on quantitative upper bounds for solutions, so far mainly concentrate on cases when D decays at most algebraically, and hence are unavailable in the present context. This work develops an alternative approach, at its core based on a Moser-type iteration for the quantity {{\\text{e}}u} , to establish global existence of classical solutions for all reasonably regular initial data, as well as a logarithmic upper estimate for the possible growth of \\parallel u(\\centerdot,t){{\\parallel}{{L∞}(Ω )}} as t\\to ∞ , under the assumptions that with some K 1 > 0, K 2 > 0, {β-}>0 and {β+}\\in ≤ft(-∞,{β-}\\right] we have {{K}1}{{\\text{e}}-{β-}s}}≤slant D(s)≤slant {{K}2}{{\\text{e}}-{{β+}s}} for all s≥slant 0 , and that the size of S relative to D can be estimated according to \\frac{S(s)}{D(s)}≤slant {{K}3}{{\\text{e}}γ s} for all s≥slant 0 with some K 3 > 0 and γ \\in ≤ft[\\frac{{{β+}-{β-}}{2},\\frac{{β+}}{2}\\right) . Making use of the fact that this allows for certain superalgebraic growth of \\frac{S}{D} , as a particular consequence of this and known results on nonexistence of global bounded solutions we shall see that in the prototypical case when D(s)={{\\text{e}}-β s} and S(s)=s{{\\text{e}}-α s} for all s≥slant 0 and some
Tijani A. Apalara
2014-12-01
Full Text Available In this article we consider one-dimensional linear thermoelastic system of Timoshenko type with linear frictional damping and a distributed delay acting on the displacement equation. The heat flux of the system is governed by Cattaneo's law. Under suitable assumption on the weight of the delay and that of frictional damping, we establish the well-posedness result and prove that the system is exponentially stable regardless of the speeds of wave propagation.
Global Stability of SEIRS Model in Epidemiology
柏灵; 王克
2002-01-01
In this article,an infectious model with saturation effect is considered,By using compound matrix theory and a series of theorems associated to qualitative theory of differential equations which are introduced by Muldowney and Micheal Li,we study globally stable problem of the model.
Global stability in ecological models with continuous time delays
Post, W M; Travis, C C
1979-01-01
This model examines the stability properties of a general system of first-order integro-differential equations which describe the dynamics of interacting species populations. A sufficient condition for the global stability of an equilibrium state is derived. This condition is an improvement over the condition derived by Woerz-Busekros (1978) for similar equations in that this condition has intuitive biological interpretations and is verifiable in a finite number of arithmetical steps. This condition is shown to be both necessary and sufficient for global asymptotic stability of the equilibrium for communities of mutualistically interacting species. Application of the results to an ecological system is also provided. (PCS)
GLOBAL ASYMPTOTIC STABILITY CONDITIONS OF DELAYED NEURAL NETWORKS
ZHOU Dong-ming; CAO Jin-de; ZHANG Li-ming
2005-01-01
Utilizing the Liapunov functional method and combining the inequality of matrices technique to analyze the existence of a unique equilibrium point and the global asymptotic stability for delayed cellular neural networks (DCNNs), a new sufficient criterion ensuring the global stability of DCNNs is obtained. Our criteria provide some parameters to appropriately compensate for the tradeoff between the matrix definite condition on feedback matrix and delayed feedback matrix. The criteria can easily be used to design and verify globally stable networks. Furthermore, the condition presented here is independent of the delay parameter and is less restrictive than that given in the references.
Electronic image stabilization system based on global feature tracking
Zhu Juanjuan; Guo Baolong
2008-01-01
A new robust electronic image stabilization system is presented, which involves feature-point, tracking based global motion estimation and Kalman filtering based motion compensation. First, global motion is estimated from the local motions of selected feature points. Considering the local moving objects or the inevitable mismatch,the matching validation, based on the stable relative distance between the points set is proposed, thus maintaining high accuracy and robustness. Next, the global motion parameters are accumulated for correction by Kalman filter-ation. The experimental result illustrates that the proposed system is effective to stabilize translational, rotational,and zooming jitter and robust to local motions.
On Global Stability of Financial Networks
Bhaskar DasGupta; Lakshmi Kaligounder
2012-01-01
The recent financial crisis have generated renewed interests in fragilities of global financial networks among economists and regulatory authorities. In particular, a potential vulnerability of the financial networks is the "financial contagion" process in which insolvencies of individual entities propagate through the "web of dependencies" to affect the entire system. In this paper, we formalize an extension of a financial network model originally proposed by Nier et al. for scenarios such a...
Global warming and thermohaline circulation stability.
Wood, Richard A; Vellinga, Michael; Thorpe, Robert
2003-09-15
The Atlantic thermohaline circulation (THC) plays an important role in global climate. Theoretical and palaeoclimatic evidence points to the possibility of rapid changes in the strength of the THC, including a possible quasi-permanent shutdown. The climatic impacts of such a shutdown would be severe, including a cooling throughout the Northern Hemisphere, which in some regions is greater in magnitude than the changes expected from global warming in the next 50 years. Other climatic impacts would likely include a severe alteration of rainfall patterns in the tropics, the Indian subcontinent and Europe. Modelling the future behaviour of the THC focuses on two key questions. (i) Is a gradual weakening of the THC likely in response to global warming, and if so by how much? (ii) Are there thresholds beyond which rapid or irreversible changes in the THC are likely? Most projections of the response of the THC to increasing concentrations of greenhouse gases suggest a gradual weakening over the twenty-first century. However, there is a wide variation between different models over the size of the weakening. Rapid or irreversible THC shutdown is considered a low-probability (but high-impact) outcome; however, some climate models of intermediate complexity do show the possibility of such events. The question of the future of the THC is beset with conceptual, modelling and observational uncertainties, but some current and planned projects show promise to make substantial progress in tackling these uncertainties in future.
司守奎
2000-01-01
The stabilization of the Timoshenko equation of a nonuniform beam with locally dis-tributed feedbacks is considered. It is proved that the system is exponentially stabilizable. The frequency domain method and the multiplier technique are applied.
王雪萍; 蒋海军
2012-01-01
对具有分布时滞的非自治Cohen-Grossberg神经网络进行了研究.通过构造适当的Lyapunov函数,利用不等式分析方法,引入多参数,得到了一系列解的一致有界性且最终有界性和全局指数稳定性的判别准则.%In this paper,nonautonomous Cohen-Grossberg neural networks with distributed delays are investigated. By applying the inequality analysis technique,introducing inge-niously many real parameters and constructing new Lyapunov functions,we establish a series of new and useful criteria on the ultimate boundedness and global exponential stability of solutions.
杨喜陶
2006-01-01
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 in corporate variable delays in the processing part of the network architectures.
Global Transient Stability and Voltage Regulation for Multimachine Power Systems
Gordon, Mark; Hill, David J.
2008-01-01
This paper addresses simultaneously the major fundamental and difficult issues of nonlinearity, uncertainty, dimensionality and globality to derive performance enhancing power system stability control. The main focus is on simultaneous enhancement of transient stability and voltage regulation...... law is implemented to coordinate transient stabilizer and voltage regulator for each machine. Digital simulation studies show that global control scheme achieves unified transient stability and voltage regulation in the presence of parametric uncertainties and significant sudden changes in the network...... of power systems. This problem arises from the practical concern that both frequency and voltage control are important indices of power system control and operation but they are ascribed to different stages of system operation, i.e. the transient and post transient period respectively. The Direct Feedback...
New global stability conditions for a class of difference equations
Yoshiaki MUROYA; Emiko ISHIWATA; Nicola GUGLIELMIa
2009-01-01
In this paper we consider some classes of difference equations,including the well-known Clark model,and study the stability of their solutions. In order to do that we introduce a property,namely semicontractivity,and study relations between 'semi-contractive' functions and sufficient conditions for the solution of the difference equation to be globally asymptotically stable.Moreover,we establish new sufficient conditions for the solution to be globally asymptotically stable,and we improve the '3/2criteria' type stability conditions.
Global point tracking based panoramic image stabilization system
朱娟娟; 郭宝龙; 吴宪祥
2009-01-01
A novel image stabilization system is presented,which consists of a global feature point tracking based motion estimation,a Kalman filtering based motion smoothing and an image mosaic based panoramic compensation.The global motion is estimated using feature point matching and iteration with the least-square method.Then,the Kalman filter is applied to smooth the original motion vectors to effectively alleviate unwanted camera vibrations and follow the intentional camera scan.Lastly,the loss information of im...
The exponential rank of nonarchimedean exponential fields
Kuhlmann, Franz-Viktor; Kuhlmann, Salma
2000-01-01
For an exponential on a nonarchimedean ordered field, we introduce the notion of the exponential rank, in analogy to the rank of the field. This gives information about the growth rate of the exponential, and about the convex valuations on the field which are compatible with the exponential. We give several characterizations of these valuations, using maps induced by the exponential on the value group of the natural valuation and on the rank of the field. Finally, we construct exponential fie...
Local Stability and Global Instability in Iron-opaque Disks
Grzȩdzielski, Mikołaj; Janiuk, Agnieszka; Czerny, Bożena
2017-08-01
The thermal stability of accretion disks and the possibility of seeing a limit-cycle behavior strongly depends on the ability of the disk plasma to cool down. Various processes connected with radiation-matter interaction appearing in hot accretion disk plasma contribute to opacity. For the case of geometrically thin and optically thick accretion disks, we can estimate the influence of several different components of function κ, given by the Roseland mean. In the case of high temperatures of ˜107 K, the electron Thomson scattering is dominant. At lower temperatures, atomic processes become important. The slope d{log}κ /d{log}T can have a locally stabilizing or destabilizing effect on the disk. Although the local MHD simulation postulates the stabilizing influence of the atomic processes, only the global time-dependent model can reveal the global disk stability range estimation. This is due to the global diffusive nature of those processes. In this paper, using the previously tested GLADIS code with a modified prescription of the viscous dissipation, we examine the stabilizing effect of the iron opacity bump.
Global μ-Stability of Impulsive Complex-Valued Neural Networks with Leakage Delay and Mixed Delays
Xiaofeng Chen
2014-01-01
Full Text Available The impulsive complex-valued neural networks with three kinds of time delays including leakage delay, discrete delay, and distributed delay are considered. Based on the homeomorphism mapping principle of complex domain, a sufficient condition for the existence and uniqueness of the equilibrium point of the addressed complex-valued neural networks is proposed in terms of linear matrix inequality (LMI. By constructing appropriate Lyapunov-Krasovskii functionals, and employing the free weighting matrix method, several delay-dependent criteria for checking the global μ-stability of the complex-valued neural networks are established in LMIs. As direct applications of these results, several criteria on the exponential stability, power-stability, and log-stability are obtained. Two examples with simulations are provided to demonstrate the effectiveness of the proposed criteria.
Global Asymplotic Stability of Neural Networks with Time Delay
肖晓丹; 张洁
2008-01-01
The global asymptotic stability problem of Cellular neural networks with delay is investigated.A new stability condition is presented based on Lyapunov-Krasovskii method,which is dependent On the size of delay.The result is given in the form of LMI.and the admitted upper bound of the delay can be obtained easily.The time delay dependent and independent results can be obtained,which include some results in the former literature.Finally,a numerical example is siven to illustrate the effectiveness of the main results.
A climatic stability approach to prioritizing global conservation investments.
Takuya Iwamura
Full Text Available Climate change is impacting species and ecosystems globally. Many existing templates to identify the most important areas to conserve terrestrial biodiversity at the global scale neglect the future impacts of climate change. Unstable climatic conditions are predicted to undermine conservation investments in the future. This paper presents an approach to developing a resource allocation algorithm for conservation investment that incorporates the ecological stability of ecoregions under climate change. We discover that allocating funds in this way changes the optimal schedule of global investments both spatially and temporally. This allocation reduces the biodiversity loss of terrestrial endemic species from protected areas due to climate change by 22% for the period of 2002-2052, when compared to allocations that do not consider climate change. To maximize the resilience of global biodiversity to climate change we recommend that funding be increased in ecoregions located in the tropics and/or mid-elevation habitats, where climatic conditions are predicted to remain relatively stable. Accounting for the ecological stability of ecoregions provides a realistic approach to incorporating climate change into global conservation planning, with potential to save more species from extinction in the long term.
Global ocean wind power sensitivity to surface layer stability
Capps, Scott B.; Zender, Charles S.
2009-05-01
Global ocean wind power has recently been assessed (W. T. Liu et al., 2008) using scatterometry-based 10 m winds. We characterize, for the first time, wind power at 80 m (typical wind turbine hub height) above the global ocean surface, and account for the effects of surface layer stability. Accounting for realistic turbine height and atmospheric stability increases mean global ocean wind power by +58% and -4%, respectively. Our best estimate of mean global ocean wind power is 731 W m-2, about 50% greater than the 487 W m-2 based on previous methods. 80 m wind power is 1.2-1.5 times 10 m power equatorward of 30° latitude, between 1.4 and 1.7 times 10 m power in wintertime storm track regions and >6 times 10 m power in stable regimes east of continents. These results are relatively insensitive to methodology as wind power calculated using a fitted Weibull probability density function is within 10% of power calculated from discrete wind speed measurements over most of the global oceans.
马保离
2005-01-01
For regulating the dynamic nonholonomic mobile cart with parameter uncertainties, a time-varying robust control law is derived to yield globally exponential convergence of cart's position and orientation to the desired set point. The controller design relies on converting the cart's dynamics to an advantageous form, and the robust linear feedback control laws steer the cart's position and orientation errors to zero exponentially. Simulation results show the effectiveness of the proposed control law.
New results in global stabilization for stochastic nonlinear systems
Tao BIAN; Zhong-Ping JIANG
2016-01-01
This paper presents new results on the robust global stabilization and the gain assignment problems for stochastic nonlinear systems. Three stochastic nonlinear control design schemes are developed. Furthermore, a new stochastic gain assignment method is developed for a class of uncertain interconnected stochastic nonlinear systems. This method can be combined with the nonlinear small-gain theorem to design partial-state feedback controllers for stochastic nonlinear systems. Two numerical examples are given to illustrate the effectiveness of the proposed methodology.
刘艳; 蒋卫生; 黄发伦
2004-01-01
It has been observed that for many stable feedback control systems, the introduction of arbitrarily small delays into the loop causes instability. Therefore, robustness of stablility with respect to small delays is of great importance. The authors study the robustness with respect to small delays for exponential stability of Pritchard-Salamon systems with admissible state feedback,i.e. the exponential stability of the following systems are equivalent:(x(t)=S(t)x0+∫t0S(t-s)ds)(u(t)=Fx(t),x0∈V,t≥0)(x(t)=S(t)x0+∫t0S(t-s)BFx(s-r)ds)(u(t)=Fx(t-r),x0∈V,t≥0)and obtain a mumber of necessary and sufficient conditions,particularly,frepuency domain characterization for robustness with respect to small delays for exponential stability.
Global stability of two models with incomplete treatment for tuberculosis
Yang Yali, E-mail: yylhgr@126.co [Department of Applied Mathematics, Xi' an Jiaotong University, Xi' an 710049 (China) and Department of Applied Mathematics and Physics, Air Force Engineering University, Xi' an 710051 (China); Li Jianquan, E-mail: jianq_li@263.ne [Department of Applied Mathematics and Physics, Air Force Engineering University, Xi' an 710051 (China); Ma Zhien, E-mail: zhma@mail.xjtu.edu.c [Department of Applied Mathematics, Xi' an Jiaotong University, Xi' an 710049 (China); Liu Luju, E-mail: dahai20401095@yahoo.com.c [Department of Mathematics, Henan University of Science and Technology, Luoyang 471003 (China)
2010-12-15
Research highlights: Two tuberculosis models with incomplete treatment. Intuitive epidemiological interpretations for the basic reproduction numbers. Global dynamics of the two models. Strategies to control the spread of tuberculosis. - Abstract: Two tuberculosis (TB) models with incomplete treatment are investigated. It is assumed that the treated individuals may enter either the latent compartment due to the remainder of Mycobacterium tuberculosis or the infectious compartment due to the treatment failure. The first model is a simple one with treatment failure reflecting the current TB treatment fact in most countries with high tuberculosis incidence. The second model refines the simple one by dividing the latent compartment into slow and fast two kinds of progresses. This improvement can be used to describe the case that the latent TB individuals have been infected with some other chronic diseases (such as HIV and diabetes) which may weaken the immunity of infected individuals and shorten the latent period of TB. Both of the two models assume mass action incidence and exponential distributions of transfers between different compartments. The basic reproduction numbers of the two models are derived and their intuitive epidemiological interpretations are given. The global dynamics of two models are all proved by using Liapunov functions. At last, some strategies to control the spread of tuberculosis are discussed.
Lotito, Luca; Russo, Alessandra; Chillemi, Giovanni; Bueno, Susana; Cavalieri, Duccio; Capranico, Giovanni
2008-03-21
To establish the cellular functions of DNA topoisomerase I-B (Top1p) at a global level, we have determined the expression profiles and histone modification patterns affected by TOP1 gene deletion (DeltaTOP1) in Saccharomyces cerevisiae. In exponentially growing cells, DeltaTOP1 specifically increases transcription of telomere-proximal genes and decreases glucose utilization and energy production pathways. Immunoprecipitation data demonstrate that Top1p can bind to and is catalytically active at telomeric DNA repeats, and that both DeltaTOP1 and an inactive Y727F Top1p mutant increase H4 histone acetylation at telomere-proximal regions. Interestingly, while the Y727F mutation has no influence on enzyme recruitment to chromatin sites, it has a marked effect on H4 K16 acetylation at subtelomeric regions. The Top1p mutation also increases H3 histone K4 dimethylation, which has been associated with gene transcription, at 3' termini of subtelomeric genes. No major effect of DeltaTOP1 or mutation was detected on Sir3p recruitment; however, DeltaTOP1 has an effect on transcript levels of genes known to regulate telomeric silencing. Thus, the findings indicate that Top1p activity can favor both a repressed chromatin organization and a reduced gene expression level at telomere-proximal regions in yeast. As telomere-proximal regions are known to be enriched for stress-activated genes, our findings show that Top1p can optimize transcript levels for cell growth in exponentially growing cells under a synthetic medium with glucose.
Global stability analysis of turbulent 3D wakes
Rigas, Georgios; Sipp, Denis; Juniper, Matthew
2015-11-01
At low Reynolds numbers, corresponding to laminar and transitional regimes, hydrodynamic stability theory has aided the understanding of the dynamics of bluff body wake-flows and the application of effective control strategies. However, flows of fundamental importance to many industries, in particular the transport industry, involve high Reynolds numbers and turbulent wakes. Despite their turbulence, such wake flows exhibit organisation which is manifested as coherent structures. Recent work has shown that the turbulent coherent structures retain the shape of the symmetry-breaking laminar instabilities and only those manifest as large-scale structures in the near wake (Rigas et al., JFM vol. 750:R5 2014, JFM vol. 778:R2 2015). Based on the findings of the persistence of the laminar instabilities at high Reynolds numbers, we investigate the global stability characteristics of a turbulent wake generated behind a bluff three-dimensional axisymmetric body. We perform a linear global stability analysis on the experimentally obtained mean flow and we recover the dynamic characteristics and spatial structure of the coherent structures, which are linked to the transitional instabilities. A detailed comparison of the predictions with the experimental measurements will be provided.
张迎迎; 周立群
2012-01-01
The exponential stability of a class of cellular neural networks with multi-pantograph delays is studied. In view of nonlinear measure,a sufficient condition is derived for the existence,uniqueness and exponential stability of the equilibrium point. And the method gains the exponential convergent velocity of the solutions. Finally,an example is provided to illustrate effectiveness of the method.%讨论了一类具多比例延时的细胞神经网络的指数稳定性.利用非线性测度得到了一个保证平衡点存在唯一且指数稳定的充分条件,并给出了解的指数收敛速度.最后验证了结论的正确性并进行了模拟仿真.
梁金玲; 黄霞
2005-01-01
Stability analysis of cellular neural networks (CNNs)has been an important topic in the neuralnetwork field since it has great significance for many applications. The qualitative analysis of the neurodynamics has attracted considerable attention thus far[1～7]. In electronic implementation of neural networks,many problems such as switching delays, integration, and communication delays have arisen. In such a case, a delay parameter must be introduced into the system model. Study of neural dynamics with consideration of delays becomes particularly important in manufacturing high quality microelectronic neural networks. Global stability of delayed cellular neural networks (DCNNs) has been extensively studied[1～11]. Sufficient conditions[5,9,12,13] for global stability of DCNNs have been proposed, but the output of the cell is a piecewise linear function and the time-delay is constant. A wider adaptive range without assuming the output of the cell to be piecewise linear function[10,13] is introduced and the time-delay terms of DCNNs are also constant.Based on the Lyapunov stability theorem as well as some facts about the negative definiteness and inequality of matrices, a new sufficient condition is presented for the existence of a unique equilibrium point and its global exponential stability of the delayed CNNs. This condition imposes constraints on the size of the delay parameter. An illustrative example and its numerical simulation is also given to show the effectiveness of our results.%细胞神经网络(CNNs)由于有许多重要的应用价值,所以它的稳定性分析一直是神经网络领域里的一个重要课题.近年来,神经动力系统的定性分析吸引了众多学者的关注[1-7].在神经网络的电子器件实现中,出现了许多问题,诸如:转换延时,积分器,连接延时等.在这种情况下,在系统模型中一定要引进一个延时参数.要制造高质量的微电子神经网络,研究带有延时的神经动
Irigül-Sönmez, Öykü; Köroğlu, Türkan E; Öztürk, Büşra; Kovács, Ákos T; Kuipers, Oscar P; Yazgan-Karataş, Ayten
2014-02-01
The lutR gene, encoding a product resembling a GntR-family transcriptional regulator, has previously been identified as a gene required for the production of the dipeptide antibiotic bacilysin in Bacillus subtilis. To understand the broader regulatory roles of LutR in B. subtilis, we studied the genome-wide effects of a lutR null mutation by combining transcriptional profiling studies using DNA microarrays, reverse transcription quantitative PCR, lacZ fusion analyses and gel mobility shift assays. We report that 65 transcriptional units corresponding to 23 mono-cistronic units and 42 operons show altered expression levels in lutR mutant cells, as compared with lutR(+) wild-type cells in early stationary phase. Among these, 11 single genes and 25 operons are likely to be under direct control of LutR. The products of these genes are involved in a variety of physiological processes associated with the onset of stationary phase in B. subtilis, including degradative enzyme production, antibiotic production and resistance, carbohydrate utilization and transport, nitrogen metabolism, phosphate uptake, fatty acid and phospholipid biosynthesis, protein synthesis and translocation, cell-wall metabolism, energy production, transfer of mobile genetic elements, induction of phage-related genes, sporulation, delay of sporulation and cannibalism, and biofilm formation. Furthermore, an electrophoretic mobility shift assay performed in the presence of both SinR and LutR revealed a close overlap between the LutR and SinR targets. Our data also revealed a significant overlap with the AbrB regulon. Together, these findings reveal that LutR is part of the global complex, interconnected regulatory systems governing adaptation of bacteria to the transition from exponential growth to stationary phase.
The global non-linear stability of the Kerr-de Sitter family of black holes
Hintz, Peter
2016-01-01
We establish the full global non-linear stability of the Kerr-de Sitter family of black holes, as solutions of the initial value problem for the Einstein vacuum equations with positive cosmological constant, for small angular momenta, and without any symmetry assumptions on the initial data. We achieve this by extending the linear and non-linear analysis on black hole spacetimes described in a sequence of earlier papers by the authors: We develop a general framework which enables us to deal systematically with the diffeomorphism invariance of Einstein's equations. In particular, the iteration scheme used to solve Einstein's equations automatically finds the parameters of the Kerr-de Sitter black hole that the solution is asymptotic to, the exponentially decaying tail of the solution, and the gauge in which we are able to find the solution; the gauge here is a wave map/DeTurck type gauge, modified by source terms which are treated as unknowns, lying in a suitable finite-dimensional space.
Globally exponentially attractive set of disk dynamo system and its application%发电机系统的全局指数吸引集及其应用
袁红; 张付臣
2011-01-01
The globally exponentially attractive sets of a disk dynamo system are investigated via constructing a Lyapunov function and by definition and optimization theorem.For this system,a four-dimensional ellipsoidal globally exponentially attractive set is derived.The result is applied to the chaos synchronization.Numerical simulations are presented to show the effectiveness of the proposed scheme.%通过定义和一个构造性引理并且借助一个适当的Lyapunov函数和最优化理论,研究了一个发电机混沌系统的全局指数吸引集得到了四维椭球估计.将所得到的结果应用到混沌同步之中去,数值模拟验证了同步理论的可行性.
Global stability of the ballooning mode in a cylindrical model
Mazur, N. G.; Fedorov, E. N.; Pilipenko, V. A.
2013-07-01
Ballooning disturbances in a finite-pressure plasma in a curvilinear magnetic field are described by the system of coupled equations for the Alfvén and slow magnetosonic modes. In contrast to most previous works that locally analyzed the stability of small-scale disturbances using the dispersion relationship, a global analysis outside a WKB approximation but within a simple cylindrical geometry, when magnetic field lines are circles with constant curvature, is performed in the present work. This model is relatively simple; nevertheless, it has the singularities necessary for the formation of the ballooning mode: field curvature and non-uniform thermal plasma pressure. If the disturbance finite radial extent is taken into account, the instability threshold increases as compared to a WKB approximation. The simplified model used in this work made it possible to consider the pattern of unstable disturbances at arbitrary values of the azimuthal wavenumber ( k y ). Azimuthally large-scale disturbances can also be unstable, although the increment increases with decreasing azimuthal scale and reaches saturation when the scales are of the order of the pressure nonuniformity dimension.
Stability analysis of stochastic delayed cellular neural networks by LMI approach
Zhu Wenli [Department of Economic Mathematics, South Western University of Finance and Economics, Chengdu 610074 (China)]. E-mail: zhuwenli67@hotmail.com; Hu Jin [School of Applied Mathematics, University of Electronic Science and Technology of China, Chengdu 610054 (China)
2006-07-15
Some sufficient mean square exponential stability conditions for a class of stochastic DCNN model are obtained via the LMI approach. These conditions improve and generalize some existing global asymptotic stability conditions for DCNN model.
Global stabilization of nonlinear systems based on vector control lyapunov functions
Karafyllis, Iasson
2012-01-01
This paper studies the use of vector Lyapunov functions for the design of globally stabilizing feedback laws for nonlinear systems. Recent results on vector Lyapunov functions are utilized. The main result of the paper shows that the existence of a vector control Lyapunov function is a necessary and sufficient condition for the existence of a smooth globally stabilizing feedback. Applications to nonlinear systems are provided: simple and easily checkable sufficient conditions are proposed to guarantee the existence of a smooth globally stabilizing feedback law. The obtained results are applied to the problem of the stabilization of an equilibrium point of a reaction network taking place in a continuous stirred tank reactor.
LI Hong; L(U) Shu; ZHONG Shou-ming
2005-01-01
The global uniform asymptotic stability of competitive neural networks with different time scales and delay is investigated. By the method of variation of parameters and the method of inequality analysis, the condition for global uniformly asymptotically stable are given. A strict Lyapunov function for the flow of a competitive neural system with different time scales and delay is presented. Based on the function, the global uniform asymptotic stability of the equilibrium point can be proved.
Extended Poisson Exponential Distribution
Anum Fatima
2015-09-01
Full Text Available A new mixture of Modified Exponential (ME and Poisson distribution has been introduced in this paper. Taking the Maximum of Modified Exponential random variable when the sample size follows a zero truncated Poisson distribution we have derived the new distribution, named as Extended Poisson Exponential distribution. This distribution possesses increasing and decreasing failure rates. The Poisson-Exponential, Modified Exponential and Exponential distributions are special cases of this distribution. We have also investigated some mathematical properties of the distribution along with Information entropies and Order statistics of the distribution. The estimation of parameters has been obtained using the Maximum Likelihood Estimation procedure. Finally we have illustrated a real data application of our distribution.
Marius Apostoaie
2010-01-01
...: price stability and financial stability. These two key concepts are part of an old and ongoing debate that the current turmoil has revived, and that is whether monetary policy should aim, or not, at ensuring financial stability in parallel...
管巍; 孙虹霞
2011-01-01
利用Lyapunov稳定性理论和线性矩阵不等式技术,得到了保证时变时滞BAM神经网络系统指数稳定性的时滞依赖稳定性准则.所给的准则可用Matlab中的LMI控制工具箱进行验证.仿真实例进一步说明了结果的有效性.%By employing the Lyapunov stability theory and linear matrix inequality (LMI) technique, delay-dependent stability criterion is derived to ensure the exponential stability of bi-directional associative memory (BAM) neural networks with time-varying delays. The proposed condition can be checked easily by LMI Control Toolbox in Matlab. A numerical example is given to demonstrate the effectiveness of our results.
Avetisyan S.A.
2015-06-01
Full Text Available In the framework of plane theory of fluid established filtration the boundary problem on fluid filtration in porous ground strip, the coefficient of which along the depth of the strip changes by exponential law, is considered. In this case by the system of the segments of the upper bound of the strip under the given pressure the fluid inject into the ground strip, and the lower bound of the strip is water-impermeable. Filtration characteristics of the problem are determined.
Theory and methods of global stability analysis for high arch dam
无
2011-01-01
The global stability of high arch dam is one of the key problems in the safety study of arch dams,but no feasible method with theoretical basis is available.In this paper,based on the stability theory of mechanical system,it is demonstrated that the global failure of high arch dams belongs to a physical instability starting from local strength failure,which is the extreme point instability according to the characteristics of load-displacement curve obtained from the failure process of dam-foundation system. So the global failure of dam-foundation system should be studied with the stability theory of mechanical system.It is also pointed out that the current stability analysis methods used in engineering are consistent with the stability theory,but not established according to the mechanical system stability theory directly.A perfect method can be obtained through the study of physical disturbance equations.
Weighted exponential polynomial approximation
邓冠铁
2003-01-01
A necessary and sufficient condition for completeness of systems of exponentials with a weightin Lp is established and a quantitative relation between the weight and the system of exponential in Lp isobtained by using a generalization of Malliavin's uniqueness theorem about Watson's problem.
Global asymptotic stability of positive equilibrium in a 3-species cooperating model with time delay
WANG Chang-you
2007-01-01
The asymptotic behavior of the time-dependent solution for a 3-species cooperating model was investigated with the effects of both diffusion and time delay taken into consideration. We proved the global asymptotic stability of a positive steady-state solution to the model problem by using coupled upper and lower solutions for a more general reaction-diffusion system that gives a common framework for 3-species cooperating model problems. The result of global asymptotic stability implies that the model system coexistence is permanent. Some global asymptotic stability results for 2-species cooperating reaction-diffusion systems are included in the discussion, and some known results are extended.
Exponential Dowling structures
Ehrenborg, Richard
2010-01-01
The notion of exponential Dowling structures is introduced, generalizing Stanley's original theory of exponential structures. Enumerative theory is developed to determine the M\\"obius function of exponential Dowling structures, including a restriction of these structures to elements whose types satisfy a semigroup condition. Stanley's study of permutations associated with exponential structures leads to a similar vein of study for exponential Dowling structures. In particular, for the extended r-divisible partition lattice we show the M\\"obius function is, up to a sign, the number of permutations in the symmetric group on rn+k elements having descent set {r, 2r, ..., nr}. Using Wachs' original EL-labeling of the r-divisible partition lattice, the extended r-divisible partition lattice is shown to be EL-shellable.
GLOBAL STABILITY OF AN SIRS EPIDEMIC MODEL WITH DELAYS
Zhen Jin; Ma Zhien; Han Maoan
2006-01-01
In this article, an SIRS epidemic model spread by vectors (mosquitoes) which have an incubation time to become infectious is formulated. It is shown that a disease-free equilibrium point is globally stable if no endemic equilibrium point exists. Further, the endemic equilibrium point (if it exists) is globally stable with a respect "weak delay". Some known results are generalized.
ON GLOBAL STABILITY OF A NONRESIDENT COMPUTER VIRUS MODEL
Yoshiaki MUROYA; Huaixing LI; Toshikazu KUNIYA
2014-01-01
In this paper, we establish new sufficient conditions for the infected equilibrium of a nonresident computer virus model to be globally asymptotically stable. Our results extend two kind of known results in recent literature.
GLOBAL STABILITY OF AN SVIR EPIDEMIC MODEL WITH VACCINATION
无
2011-01-01
In this paper, an SIR epidemic model with vaccination for both the newborns and susceptibles is investigated, where it is assumed that the vaccinated individuals have the temporary immunity. The basic reproduction number determining the extinction or persistence of the infection is found. By constructing a Lyapunov function, it is proved that the disease free equilibrium is globally stable when the basic reproduction number is less than or equal to one, and that the endemic equilibrium is globally stable wh...
Global Stability of an HIV-1 Infection Model with General Incidence Rate and Distributed Delays
Ndongo, Abdoul Samba; Talibi Alaoui, Hamad
2014-01-01
.... Lyapunov functionals are constructed and LaSalle invariant principle for delay differential equation is used to establish the global asymptotic stability of the infection-free equilibrium, infected...
Globally Asymptotic Stability of Stochastic Nonlinear Systems by the Output Feedback
Wenwen Cheng
2015-01-01
the traditional mathematical induction method. Indeed, we develop a new method to study the globally asymptotic stability by introducing a series of specific inequalities. Moreover, an example and its simulations are given to illustrate the theoretical result.
无
2006-01-01
In this paper, using the theory of topological degree and Liapunov functional methods, the authors study the competitive neural networks with time delays and different time scales and present some criteria of global robust stability for this neural network model.
曹科才
2009-01-01
The output tracking control problem of nonholonomic chained form systems is studied in this paper and global a time-varying coordinate transformation is introduced to avoid manipulating exponentially converging signals. Then, with the help feature of the proposed controller is that the output tracking control problem of nonholonomic chained form systems is also resolvble without the popular condition of persistent excitation or not converging to zero on reference signals in the previous works. The proposed method is demonstrated and discussed by means of nonholonomic mobile robots and cars with one trailer.
徐晓惠; 张继业; 张克跃
2012-01-01
On the assumption that all the isolated subsystems of the interconnected system are exponentially stable,the exponential stability analysis and control for a class of look-ahead vehicle longitudinal following system with impulsive effects and time-varying delays are studied. Firstly,some sufficient conditions for exponential stability of the system are obtained by applying vector Lyapunov function method and mathematical induction method. Then,the controller for the look-ahead vehicle following system with impulsive effects and time-varying delays is designed by sliding mode control method based on the obtained results. Finally,a simulation example illustrates how to apply the obtained results in practice.%针对具有脉冲扰动和变时滞的顾前车辆纵向跟随系统,在假设各孤立子系统指数稳定的前提下,分析了该系统的群指数稳定性与控制.首先利用向量Lyapunov函数法和数学归纳法给出确保该系统群指数稳定的充分条件；然后基于得到的稳定性条件,采用滑模变结构控制策略对脉冲变时滞车辆纵向跟随系统进行控制器设计；最后通过一个数值仿真算例验证了所得结论的正确性以及在实际中如何应用.
LMI Conditions for Global Stability of Fractional-Order Neural Networks.
Zhang, Shuo; Yu, Yongguang; Yu, Junzhi
2016-08-02
Fractional-order neural networks play a vital role in modeling the information processing of neuronal interactions. It is still an open and necessary topic for fractional-order neural networks to investigate their global stability. This paper proposes some simplified linear matrix inequality (LMI) stability conditions for fractional-order linear and nonlinear systems. Then, the global stability analysis of fractional-order neural networks employs the results from the obtained LMI conditions. In the LMI form, the obtained results include the existence and uniqueness of equilibrium point and its global stability, which simplify and extend some previous work on the stability analysis of the fractional-order neural networks. Moreover, a generalized projective synchronization method between such neural systems is given, along with its corresponding LMI condition. Finally, two numerical examples are provided to illustrate the effectiveness of the established LMI conditions.
阎庆旭; 陈振国; 冯德兴
2003-01-01
The stabilization problem of a nonuniform Timoshenko beam system with coupled locally distributed feedback is studied. First, based on the criterion of the asymptotical stability of bounded C0 semigroups, it is shown that the energy corresponding to the closed loop system is asymptotically stable. Then, by virtue of frequency domain multiplier method, it is proved that the closed loop system is exponentially stable.%研究了非均质Timoshenko梁在局部耦合反馈下的指数稳定性. 首先利用有界C0-半群渐近稳定性判据,证明了闭环系统是渐近稳定的,然后用频域乘子方法证明了闭环系统也是指数稳定的.
周凤燕
2012-01-01
研究了一类反应扩散广义时滞细胞神经网络在噪声干扰下的指数稳定性.利用Ito公式,Holder不等式,M矩阵性质和微分不等式技巧,给出了系统均值指数稳定的充分条件,并且判断方法简单易操作.最后给出了主要定理的两个应用实例,表明结论的有效性.%The exponential stability of a class of reaction-diffusion general cellular neural network with time delay and noise perturbation is studied. Using the Ito formula, Holder inequality, M-matric properties and a skill of differential inequality, some sufficient conditions are given to guarantee the mean value exponential stability of the equilibrium for the stochastic reaction-diffusion general cellular neural network with time delay and the sufficient conditions are easier to operate. In the end, two examples are given to illustrate the main theoretical results.
张强; 马润年; 许进
2003-01-01
Global asymptotic stability of the equilibrium point of bidirectional associative memory (BAM) neural networks with continuously distributed delays is studied. Under two mild assumptions on the acti-vation functions, two sufficient conditions ensuring global stability of such networks are derived by utiliz-ing Lyapunov functional and some inequality analysis technique. The results here extend some previous results. A numerical example is given showing the validity of our method.
A Simple Proof for the Stability of Global FIFO Queueing Networks
Jian-kui Yang
2009-01-01
We study the stability of multiclass queueing networks under the global FIFO (first in first out) service discipline,which was established by Bramson in 2001.For these networks,the service priority of a customer is determined by his entrance time.Using fluid models,we describe the entrance time of the most senior customer in the networks at time t,which is the key to simplify the proof for the stability of the global FIFO queueing networks.
Stability of Charged Global AdS$_4$ Spacetimes
Arias, Raúl; Serantes, Alexandre
2016-01-01
We study linear and nonlinear stability of asymptotically AdS$_4$ solutions in Einstein-Maxwell-scalar theory. After summarizing the set of static solutions we first examine thermodynamical stability in the grand canonical ensemble and the phase transitions that occur among them. In the second part of the paper we focus on nonlinear stability in the microcanonical ensemble by evolving radial perturbations numerically. We find hints of an instability corner for vanishingly small perturbations of the same kind as the ones present in the uncharged case. Collapses are avoided, instead, if the charge and mass of the perturbations come to close the line of solitons. Finally we examine the soliton solutions. The linear spectrum of normal modes is not resonant and instability turns on at extrema of the mass curve. Linear stability extends to nonlinear stability up to some threshold for the amplitude of the perturbation. Beyond that, the soliton is destroyed and collapses to a hairy black hole. The relative width of t...
Local Exponential Methods: a domain decomposition approach to exponential time integration of PDEs
Bonaventura, Luca
2015-01-01
A local approach to the time integration of PDEs by exponential methods is proposed, motivated by theoretical estimates by A.Iserles on the decay of off-diagonal terms in the exponentials of sparse matrices. An overlapping domain decomposition technique is outlined, that allows to replace the computation of a global exponential matrix by a number of independent and easily parallelizable local problems. Advantages and potential problems of the proposed technique are discussed. Numerical experiments on simple, yet relevant model problems show that the resulting method allows to increase computational efficiency with respect to standard implementations of exponential methods.
Syed, M. Qasim; Lovatt, Ian
2014-01-01
This paper is an addition to the series of papers on the exponential function begun by Albert Bartlett. In particular, we ask how the graph of the exponential function y = e[superscript -t/t] would appear if y were plotted versus ln t rather than the normal practice of plotting ln y versus t. In answering this question, we find a new way to…
Global stabilization of linear periodically time-varying switched systems via matrix inequalities
无
2006-01-01
In this paper, we address the stabilization problem for linear periodically time-varying switched systems.Using discretization technique, we derive new conditions for the global stabilizability in terms of the solution of matrix inequalities. An algorithm for finding stabilizing controller and switching strategy is presented.
Global stability analysis of a ratio-dependent predator-prey system
Lu Tie-jun; WANG Mei-juan; LIU Yan
2008-01-01
A ratio dependent predator-prey system with Holling type III functional response is considered.A sufficient condition of the global asymptotic stability for the positive equilibrium and existence of the limit cycle are given by studying locally asymptotic stability of the positive equilibrium.The condition under which positive equilibrium is not a hyperbolic equilibrium is investigated using Hopf bifurcation.
Global Stability of a Predator-Prey System with Stage Structure for the Predator
Yan Ni XIAO; Lan Sun CHEN
2004-01-01
In this paper, some feasibly sufficient conditions are obtained for the global asymptotic stability of a positive steady state of a predator-prey system with stage structure for the predator by using the theory of competitive systems, compound matrices and stability of periodic orbits, and then the work of Wang [4] is improved.
Lyapunov functions and global stability for SIR and SEIR models with age-dependent susceptibility
Korobeinikov, Andrei
2013-01-01
We consider global asymptotic properties for the SIR and SEIR age structured models for infectious diseases where the susceptibility depends on the age. Using the direct Lyapunov method with Volterra type Lyapunov functions, we establish conditions for the global stability of a unique endemic steady state and the infection-free steady state.
Lyapunov functions and global stability for SIR and SEIR models with age-dependent susceptibility.
Melnik, Andrey V; Korobeinikov, Andrei
2013-04-01
We consider global asymptotic properties for the SIR and SEIR age structured models for infectious diseases where the susceptibility depends on the age. Using the direct Lyapunov method with Volterra type Lyapunov functions, we establish conditions for the global stability of a unique endemic steady state and the infection-free steady state.
Pandey, Vikas; Singh, Suneet, E-mail: suneet.singh@iitb.ac.in
2017-04-15
Highlights: • Non-linear stability analysis of nuclear reactor is carried out. • Global and local stability boundaries are drawn in the parameter space. • Globally stable, bi-stable, and unstable regions have been demarcated. • The identification of the regions is verified by numerical simulations. - Abstract: Nonlinear stability study of the neutron coupled thermal hydraulics instability has been carried out by several researchers for boiling water reactors (BWRs). The focus of these studies has been to identify subcritical and supercritical Hopf bifurcations. Supercritical Hopf bifurcation are soft or safe due to the fact that stable limit cycles arise in linearly unstable region; linear and global stability boundaries are same for this bifurcation. It is well known that the subcritical bifurcations can be considered as hard or dangerous due to the fact that unstable limit cycles (nonlinear phenomena) exist in the (linearly) stable region. The linear stability leads to a stable equilibrium in such regions, only for infinitesimally small perturbations. However, finite perturbations lead to instability due to the presence of unstable limit cycles. Therefore, it is evident that the linear stability analysis is not sufficient to understand the exact stability characteristics of BWRs. However, the effect of these bifurcations on the stability boundaries has been rarely discussed. In the present work, the identification of global stability boundary is demonstrated using simplified models. Here, five different models with different thermal hydraulics feedback have been investigated. In comparison to the earlier works, current models also include the impact of adding the rate of change in temperature on void reactivity as well as effect of void reactivity on rate of change of temperature. Using the bifurcation analysis of these models the globally stable region in the parameter space has been identified. The globally stable region has only stable solutions and
GLOBAL STABILITY ANALYSIS IN CELLULAR NEURAL NETWORKS WITH UNBOUNDED TIME DELAYS
张继业
2004-01-01
Without assuming the boundedness and differentiability of the activation functions,the conditions ensuring existence,uniqueness,and global asymptotical stability of the equilibrium point of cellular neural networks with unbounded time delays and variable delays were studied.Using the idea of vector Liapunov method,the intero-differential inequalities with unbounded delay and variable delays were constructed.By the stability analysis of the intero-differential inequalities,the sufficient conditions for global asymptotic stability of cellular neural networks were obtained.
Global asymptotic stability for Hopfield-type neural networks with diffusion effects
YAN Xiang-ping; LI Wan-tong
2007-01-01
The existence, uniqueness and global asymptotic stability for the equilibrium of Hopfield-type neural networks with diffusion effects are studied. When the activation functions are monotonously nondecreasing, differentiable, and the interconnected matrix is related to the Lyapunov diagonal stable matrix, the sufficient conditions guaranteeing the existence of the equilibrium of the system are obtained by applying the topological degree theory. By means of constructing the suitable average Lyapunov functions, the global asymptotic stability of the equilibrium of the system is also investigated. It is shown that the equilibrium (if it exists) is globally asymptotically stable and this implies that the equilibrium of the system is unique.
Global analysis on slope stability and its engineering application
无
2009-01-01
In hydraulic engineering, sometimes it is necessary to consider the stability of sliding bodies with lateral frictional boundaries. Neither the existing three dimensional limit equilibrium methods nor the commercial software products are able to treat such situations. The three dimensional factor of safety is accordingly underestimated; while the shearing strength based on the three dimensional back analysis is overestimated. In this study, the lateral boundaries are regarded as the part of the slip surface. Based on the expression of the normal pressure on the slip surface and the patch interpolation, a rigorous solution for the three dimensional limit equilibrium analysis is realized. Meanwhile, the proposed procedure is applied to the stability analysis of the slope with a cable platform on the right bank in Da Gang Shan hydraulic project under construction.
Cosmological evolution in exponential gravity
Bamba, Kazuharu; Geng, Chao-Qiang; Lee, Chung-Chi, E-mail: bamba@phys.nthu.edu.tw, E-mail: geng@phys.nthu.edu.tw, E-mail: g9522545@oz.nthu.edu.tw [Department of Physics, National Tsing Hua University, Hsinchu, Taiwan (China)
2010-08-01
We explore the cosmological evolution in the exponential gravity f(R) = R+c{sub 1}(1−e{sup −c{sub 2}R}) (c{sub 1,2} = constant). We summarize various viability conditions and explicitly demonstrate that the late-time cosmic acceleration following the matter-dominated stage can be realized. We also study the equation of state for dark energy and confirm that the crossing of the phantom divide from the phantom phase to the non-phantom (quintessence) one can occur. Furthermore, we illustrate that the cosmological horizon entropy globally increases with time.
Cosmological evolution in exponential gravity
Bamba, Kazuharu; Lee, Chung-Chi
2010-01-01
We explore the cosmological evolution in the exponential gravity $f(R)=R +c_1 \\left(1-e^{- c_2 R} \\right)$ ($c_{1, 2} = \\mathrm{constant}$). We summarize various viability conditions and explicitly demonstrate that the late-time cosmic acceleration following the matter-dominated stage can be realized. We also study the equation of state for dark energy and confirm that the crossing of the phantom divide from the phantom phase to the non-phantom (quintessence) one can occur. Furthermore, we illustrate that the cosmological horizon entropy globally increases with time.
Antonio Yarza
2011-09-01
Full Text Available An unsolved ancient problem in position control of robot manipulators is to find a stability analysis that proves global asymptotic stability of the classical PID control in closed loop with robot manipulators. The practical evidence suggests that in fact the classical PID in industrial robots is a global regulator. The main goal of the present paper is theoretically to show why in the practice such a fact is achieved. We show that considering the natural saturations of every control stage in practical robots, the classical PID becomes a type of saturated nonlinear PID controller. In this work such a nonlinear PID controller with bounded torques for robot manipulators is proposed. This controller, unlike other saturated nonlinear PID controllers previously proposed, uses a single saturation for the three terms of the controller. Global asymptotical stability is proved via Lyapunov stability theory. Experimental results are presented in order to observe the performance of the proposed controller.
Rukes, Lothar; Paschereit, Oliver; Oberleithner, Kilian
2016-01-01
Modal linear stability analysis has proven very successful in the analysis of coherent structures of turbulent flows. Formally, it describes the evolution of a disturbance in the limit of infinite time. In this work we apply modal linear stability analysis to a turbulent swirling jet undergoing a control parameter transient. The flow undergoes a transition from a non-vortex breakdown state to a state with a strong recirculation bubble and the associated global mode. High-speed Particle Image Velocimetry (PIV) measurements are the basis for a local linear stability analysis of the temporarily evolving base flow. This analysis reveals that the onset of the global mode is strongly linked to the formation of the internal stagnation point. Several transition scenarios are discussed and the ability of a frequency selection criterion to predict the wavemaker location, frequency and growth rate of the global mode are evaluated. We find excellent agreement between the linear global mode frequency and the experimental ...
Marius Apostoaie
2010-12-01
Full Text Available This study is focused upon the involvement of the central banks regarding the fulfillment of the two main objectives: price stability and financial stability. These two key concepts are part of an old and ongoing debate that the current turmoil has revived, and that is whether monetary policy should aim, or not, at ensuring financial stability in parallel to its main objective of price stability. On both sides there are solid and well known arguments. In the beginning of the study I have considered a literature review with regard to price and financial stability issues. After that I have tried to shed some light (from a theoretical point of view on the nature and dynamics of the fundamental interlinkages between the two aspects and there implications on the central banks and the economy. Finally I outline some general conclusions that have emerged in the present study.
LMI-based approach for global asymptotic stability analysis of continuous BAM neural networks
ZHANG Sen-lin; LIU Mei-qin
2005-01-01
Studies on the stability of the equilibrium points of continuous bidirectional associative memory (BAM) neural network have yielded many useful results. A novel neural network model called standard neural network model (SNNM) is advanced. By using state affine transformation, the BAM neural networks were converted to SNNMs. Some sufficient conditions for the global asymptotic stability of continuous BAM neural networks were derived from studies on the SNNMs' stability. These conditions were formulated as easily verifiable linear matrix inequalities (LMIs), whose conservativeness is relatively low. The approach proposed extends the known stability results, and can also be applied to other forms of recurrent neural networks (RNNs).
Global Stability of an Epidemic Model of Computer Virus
Xiaofan Yang
2014-01-01
Full Text Available With the rapid popularization of the Internet, computers can enter or leave the Internet increasingly frequently. In fact, no antivirus software can detect and remove all sorts of computer viruses. This implies that viruses would persist on the Internet. To better understand the spread of computer viruses in these situations, a new propagation model is established and analyzed. The unique equilibrium of the model is globally asymptotically stable, in accordance with the reality. A parameter analysis of the equilibrium is also conducted.
彭培让
2012-01-01
The exponential stability analysis of a two unit deteriorating standby modified system is studied by the method of functional analysis and the theory of a linear-operator semi-group that is on the Banach space.Firstly,the existence of rigorous dominant eigenvalue is proved,then that the time-dependent solution of the system converging exponentially to the static solution of the system is proved by analyzing the restriction of the growth of the system operator essential spectrum and the change of the system operator essential spectral radius after disturbance.%运用泛函分析的方法和Banach空间上的线性算子半群理论,研究了两部件退化备用可修复系统的指数稳定性.首先证明了该系统存在严格占优本征值,而后通过对系统本质谱的增长性约束以及经扰动本质谱半径变化的分析,证明了该系统的时间依赖解指数收敛于系统的稳态解.
Study of global stability of tall buildings with prestressed slabs
L. A. Feitosa
Full Text Available The use of prestressed concrete flat slabs in buildings has been increasing in recent years in the Brazilian market. Since the implementation of tall and slender buildings a trend in civil engineering and architecture fields, arises from the use of prestressed slabs a difficulty in ensuring the overall stability of a building without beams. In order to evaluate the efficiency of the main bracing systems used in this type of building, namely pillars in formed "U" in elevator shafts and stairs, and pillars in which the lengths are significantly larger than their widths, was elaborated a computational models of fictional buildings, which were processed and analyzed using the software CAD/TQS. From the variation of parameters such as: geometry of the pillars, thick slabs, characteristic strength of the concrete, reduceofthe coefficient of inertia for consideration of non-linearities of the physical elements, stiffness of the connections between slabs and pillars, among others, to analyze the influence of these variables on the overall stability of the building from the facing of instability parameter Gama Z, under Brazilian standard NBR 6118, in addition to performing the processing of building using the P-Delta iterative calculation method for the same purpose.
Methods of Fast Exponentiation
Mohammed A. Maitah
2010-01-01
Full Text Available Problem statement: Modular exponentiation constitutes the basis of many well-known and widely used public key cryptosystems. Approach: A fast portable modular exponentiation algorithm considerably enhanced the speed and applicability of these systems, also an efficient implementation of this algorithm was the key to high performance of such system. Results: In this study, two main approaches for solving this problem were proposed. The proposed approaches involved calculations without usage of extra operational memory for saving constants and calculations with usage of preliminary calculated constants. Conclusion/Recommendations: The estimation of complexity of the speedup and effectiveness of proposed approaches for the data were presented.
Global Stability in Dynamical Systems with Multiple Feedback Mechanisms
Andersen, Morten; Vinther, Frank; Ottesen, Johnny T.
2016-01-01
. This is a bounded set with non-negative elements where solutions cannot escape. All solutions are shown to converge to a “minimal” trapping region. 2) At least one fixed point exists. 3) Sufficient criteria for a unique fixed point are formulated. One case where this is fulfilled is when the feedbacks are negative.......A class of n-dimensional ODEs with up to n feedbacks from the n’th variable is analysed. The feedbacks are represented by non-specific, bounded, non-negative C1 functions. The main result is the formulation and proof of an easily applicable criterion for existence of a globally stable fixed point...... of the system. The proof relies on the contraction mapping theorem. Applications of this type of systems are numerous in biology, e.g., models of the hypothalamic-pituitary-adrenal axis and testosterone secretion. Some results important for modelling are: 1) Existence of an attractive trapping region...
Global stability of a vaccination model with immigration
Sarah Henshaw
2015-04-01
Full Text Available We study an SVIR model of disease transmission with immigration into all four classes. Vaccinated individuals may only receive partial immunity to the disease, giving a leaky vaccine. The incidence function permits a nonlinear response to the number of infectives, so that mass action and saturating incidence are included as special cases. Because of the immigration of infected individuals, there is no disease-free equilibrium and hence no basic reproduction number. We use the Brouwer Fixed Point Theorem to show that an endemic equilibrium exists and the Poincare-Hopf Theorem to show that it is unique. We show the equilibrium is globally asymptotically stable by using a Lyapunov function.
Improved Offshore Wind Resource Assessment in Global Climate Stabilization Scenarios
Arent, D.; Sullivan, P.; Heimiller, D.; Lopez, A.; Eurek, K.; Badger, J.; Jorgensen, H. E.; Kelly, M.; Clarke, L.; Luckow, P.
2012-10-01
This paper introduces a technique for digesting geospatial wind-speed data into areally defined -- country-level, in this case -- wind resource supply curves. We combined gridded wind-vector data for ocean areas with bathymetry maps, country exclusive economic zones, wind turbine power curves, and other datasets and relevant parameters to build supply curves that estimate a country's offshore wind resource defined by resource quality, depth, and distance-from-shore. We include a single set of supply curves -- for a particular assumption set -- and study some implications of including it in a global energy model. We also discuss the importance of downscaling gridded wind vector data to capturing the full resource potential, especially over land areas with complex terrain. This paper includes motivation and background for a statistical downscaling methodology to account for terrain effects with a low computational burden. Finally, we use this forum to sketch a framework for building synthetic electric networks to estimate transmission accessibility of renewable resource sites in remote areas.
Global asymptotic stability of a class of nonlinear systems with parametric uncertainty
Cai Xiushan; Lǜ Ganyun; Zhang Changfiang; He Xiuhui
2009-01-01
Stability of a class of nonlinear systems with parametric uncertainty is dealt with. This kind of systems can be viewed as feedback interconnection systems. By constructing the Lyapunov function for one of the feedback interconnection systems, the Lyapunov function for this kind of systems is obtained. Sufficient conditions of global asymptotic stability for this class of systems axe deduced. The simulation shows the effectiveness of the method.
Global Stability for a Delayed Predator-Prey System with Stage Structure for the Predator
Xiao Zhang
2009-01-01
Full Text Available A delayed predator-prey system with stage structure for the predator is investigated. By analyzing the corresponding characteristic equations, the local stability of equilibria of the system is discussed. The existence of Hopf bifurcation at the positive equilibrium is established. By using an iteration technique and comparison argument, respectively, sufficient conditions are derived for the global stability of the positive equilibrium and two boundary equilibria of the system. Numerical simulations are carried out to illustrate the theoretical results.
Global Stability Analysis for an Internet Congestion Control Model with a Time-Varying Link Capacity
Rezaie, B; Analoui, M; Khorsandi, S
2009-01-01
In this paper, a global stability analysis is given for a rate-based congestion control system modeled by a nonlinear delayed differential equation. The model determines the dynamics of a single-source single-link network, with a time-varying capacity of link and a fixed communication delay. We obtain a sufficient delay-independent conditions on system parameters under which global asymptotic stability of the system is guarantied. The proof is based on an extension of Lyapunov-Krasovskii theorem for a class of nonlinear time-delay systems. The numerical simulations for a typical scenario justify the theoretical results.
Global stability and optimal control of an SIRS epidemic model on heterogeneous networks
Chen, Lijuan; Sun, Jitao
2014-09-01
In this paper, we consider an SIRS epidemic model with vaccination on heterogeneous networks. By constructing suitable Lyapunov functions, global stability of the disease-free equilibrium and the endemic equilibrium of the model is investigated. Also we firstly study an optimally controlled SIRS epidemic model on complex networks. We show that an optimal control exists for the control problem. Finally some examples are presented to show the global stability and the efficiency of this optimal control. These results can help in adopting pragmatic treatment upon diseases in structured populations.
Global Stabilization of High-Order Time-Delay Nonlinear Systems under a Weaker Condition
Nengwei Zhang
2014-01-01
Full Text Available Under the weaker condition on the system growth, this paper further investigates the problem of global stabilization by state feedback for a class of high-order nonlinear systems with time-varying delays. By skillfully using the homogeneous domination approach, a continuous state feedback controller is successfully designed, which preserves the equilibrium at the origin and guarantees the global asymptotic stability of the resulting closed-loop system. A simulation example is given to demonstrate the effectiveness of the proposed design procedure.
Xu Rui(徐瑞); Chen Lansun(陈兰荪); M.A.J. Chaplain
2003-01-01
A delayed n-species nonautonomous Lotka-Volterra type competitive systemwithout dominating instantaneous negative feedback is investigated. By means of a suitableLyapunov functional, sufficient conditions are derived for the global asymptotic stability ofthe positive solutions of the system. As a corollary, it is shown that the global asymptoticstability of the positive solution is maintained provided that the delayed negative feedbacksdominate other interspecific interaction effects with delays and the delays are sufficientlysmall.
Global Stability and Dynamics of Strongly Nonlinear Systems Using Koopman Operator Theory
2017-03-01
calculus, applied mathematics, Director’s Research Initiative 16. SECURITY CLASSIFICATION OF: 17. LIMITATION OF ABSTRACT UU 18...ARL-TR-7959 MAR 2017 US Army Research Laboratory Global Stability and Dynamics of Strongly Nonlinear Systems Using Koopman...report when it is no longer needed. Do not return it to the originator. ARL-TR-7959 ● MAR 2017 US Army Research Laboratory Global
Uniform Exponential Growth in Algebras /
Briggs, Christopher Alan
2013-01-01
We consider uniform exponential growth in algebras. We give conditions for the uniform exponential growth of descending-filtered algebras and prove that an N-graded algebra has uniform exponential growth if it has exponential growth. We use this to prove that Golod- Shafarevich algebras and group algebras of Golod- Shafarevich groups have uniform exponential growth. We prove that the twisted Laurent extension of a free commutative polynomial algebra with respect to an endomorphism with some e...
Estimating exponential scheduling preferences
Hjorth, Katrine; Börjesson, Maria; Engelson, Leonid
time by maximising expected total utility over the day, their departure times are conditional on rates of utility derived at these locations. For forecasting and economic evaluation of planning alternatives, it is desirable to have simple forms of utility rates with few parameters. Several forms...... the travel time is random, Noland and Small (1995) suggested using expected utility theory to derive the reduced form of expected travel time cost that includes the cost of TTV. For the α-β-γ formulation of scheduling preferences and exponential or uniform distribution of travel time, Noland and Small (1995....... The purpose of this paper is to explore how well these scheduling preferences explain behaviour, compared to other possible scheduling models, and whether empirical estimation of the more complex exponential scheduling preferences is feasible. We use data from a stated preference survey conducted among car...
Estimating exponential scheduling preferences
Hjorth, Katrine; Börjesson, Maria; Engelson, Leonid
time by maximising expected total utility over the day, their departure times are conditional on rates of utility derived at these locations. For forecasting and economic evaluation of planning alternatives, it is desirable to have simple forms of utility rates with few parameters. Several forms...... the travel time is random, Noland and Small (1995) suggested using expected utility theory to derive the reduced form of expected travel time cost that includes the cost of TTV. For the α-β-γ formulation of scheduling preferences and exponential or uniform distribution of travel time, Noland and Small (1995....... The purpose of this paper is to explore how well these scheduling preferences explain behaviour, compared to other possible scheduling models, and whether empirical estimation of the more complex exponential scheduling preferences is feasible. We use data from a stated preference survey conducted among car...
Exponential random graph models
Fronczak, Agata
2012-01-01
Nowadays, exponential random graphs (ERGs) are among the most widely-studied network models. Different analytical and numerical techniques for ERG have been developed that resulted in the well-established theory with true predictive power. An excellent basic discussion of exponential random graphs addressed to social science students and researchers is given in [Anderson et al., 1999][Robins et al., 2007]. This essay is intentionally designed to be more theoretical in comparison with the well-known primers just mentioned. Given the interdisciplinary character of the new emerging science of complex networks, the essay aims to give a contribution upon which network scientists and practitioners, who represent different research areas, could build a common area of understanding.
邓飞其; 赵碧蓉; 罗琦
2005-01-01
Based on stochastic Fubini theorem,the Hopfield neural network system depicted by a stochastic partial differential equation is translated into a stochastic ordinary differential equation. By constructing a mean Lyapunov function with respect to the space variables and using Ito formula under the integral operators, the exponential stability of stochastic neutral systems with distributed parameters is investigated by deviating of the function along the trajectories of the systems. Also, the Lyapunov exponent estimate is obtained. Thus, the stability of stochastic systems with distributed parameters is studied by Lyapunov direct method.%基于随机Fubini定理,将随机偏微分方程描述的Hopfield神经网络系统转化为用相应的随机常微分方程来描述.利用关于空间变量平均的Lyapunov函数与Ito公式,通过对所构造的Lyapunov函数在Ito微分规则下对相应系统求导的方法,获得了系统指数稳定的代数判据及其Lyapunov指数估计.实现了运用Lyapunov直接法对分布参数系统稳定性的研究.
Possibilistic Exponential Fuzzy Clustering
Kiatichai Treerattanapitak; Chuleerat Jaruskulchai
2013-01-01
Generally,abnormal points (noise and outliers) cause cluster analysis to produce low accuracy especially in fuzzy clustering.These data not only stay in clusters but also deviate the centroids from their true positions.Traditional fuzzy clustering like Fuzzy C-Means (FCM) always assigns data to all clusters which is not reasonable in some circumstances.By reformulating objective function in exponential equation,the algorithm aggressively selects data into the clusters.However noisy data and outliers cannot be properly handled by clustering process therefore they are forced to be included in a cluster because of a general probabilistic constraint that the sum of the membership degrees across all clusters is one.In order to improve this weakness,possibilistic approach relaxes this condition to improve membership assignment.Nevertheless,possibilistic clustering algorithms generally suffer from coincident clusters because their membership equations ignore the distance to other clusters.Although there are some possibilistic clustering approaches that do not generate coincident clusters,most of them require the right combination of multiple parameters for the algorithms to work.In this paper,we theoretically study Possibilistic Exponential Fuzzy Clustering (PXFCM) that integrates possibilistic approach with exponential fuzzy clustering.PXFCM has only one parameter and not only partitions the data but also filters noisy data or detects them as outliers.The comprehensive experiments show that PXFCM produces high accuracy in both clustering results and outlier detection without generating coincident problems.
Wei, Xiaodan; Liu, Lijun; Zhou, Wenshu
2017-03-01
In this paper, we study the global stability and attractivity of the endemic equilibrium for a network-based SIS epidemic model with nonmonotone incidence rate. The model was introduced in Li (2015). We prove that the endemic equilibrium is globally asymptotically stable if α (a parameter of this model) is sufficiently large, and is globally attractive if the transmission rate λ satisfies λ/λc ∈(1 , 2 ] , where λc is the epidemic threshold. Some numerical experiments are also presented to illustrate the theoretical results.
Global Output-Feedback Control for Simultaneous Tracking and Stabilization of Wheeled Mobile Robots
Chang, J.; Zhang, L. J.; Xue, D.
A time-varying global output-feedback controller is presented that solves both tracking and stabilization for wheeled mobile robots simultaneously at the torque level. The controller synthesis is based on a coordinate transformation, Lyapunov direct method and backstepping technique. The performance of the proposed controller is demonstrated by simulation.
PERMANENCE AND GLOBAL STABILITY OF A FEEDBACK CONTROL SYSTEM WITH DELAYS
无
2006-01-01
This paper considers a feedback control systems of differential equations with delays. By applying the differential inequality theorem, sufficient conditions for the permanence of the system are obtained. Also, by constructing a suitable Lyapunov functional, a criterion for the global stability of the model is obtained.
Stability and change in political conservatism following the global financial crisis.
Milojev, Petar; Greaves, Lara; Osborne, Danny; Sibley, Chris G
2015-01-01
The current study analyzes data from a national probability panel sample of New Zealanders (N = 5,091) to examine stability and change in political orientation over four consecutive yearly assessments (2009-2012) following the 2007/2008 global financial crisis. Bayesian Latent Growth Modeling identified systematic variation in the growth trajectory of conservatism that was predicted by age and socio-economic status. Younger people (ages 25-45) did not change in their political orientation. Older people, however, became more conservative over time. Likewise, people with lower socio-economic status showed a marked increase in political conservatism. In addition, tests of rank-order stability showed that age had a cubic relationship with the stability of political orientation over our four annual assessments. Our findings provide strong support for System Justification Theory by showing that increases in conservatism in the wake of the recent global financial crisis occurred primarily among the poorest and most disadvantaged.
无
2008-01-01
A parametric method for the gain-scheduled controller design of a linear time-varying system is given. According to the proposed scheduling method, the performance between adjacent characteristic points is preserved by the invariant eigenvalues and the gradually varying eigenvectors. A sufficient stability criterion is given by constructing a series of Lyapunov functions based on the selected discrete characteristic points. An important contribution is that it provides a simple and feasible approach for the design of gain-scheduled controllers for linear time-varying systems, which can guarantee both the global stability and the desired closed-loop performance of the resulted system. The method is applied to the design of a BTT missile autopilot and the simulation results show that the method is superior to the traditional one in sense of either global stability or system performance.
Stability Analysis of Cohen-Grossberg Neural Networks with Time-Varying Delays
LIU Yanqing; TANG Wansheng
2007-01-01
The global exponential stability of Cohen-Grossberg neural networks with time-varying delays is studied. By constructing several suitable Lyapunov functionals and utilizing differential inequality techniques, some sufficient criteria for the global exponential stability and the exponential convergence rate of the equilibrium point of the system are obtained. The criteria do not require the activation functions to be differentiable or monotone nondecreasing. Some stability results from previous works are extended and improved. Comparisons are made to demonstrate the advantage of our results.
Tao Teng
2016-02-01
Full Text Available In this article, a global adaptive neural dynamic surface control with predefined tracking performance is developed for a class of hypersonic flight vehicles, whose accurate dynamics is hard to obtain. The control scheme developed in this paper overcomes the limitations of neural approximation region by employing a switching mechanism which incorporates an additional robust controller outside the neural approximation region to pull the transient state variables back when they overstep the neural approximation region, such that globally uniformly ultimately bounded stability can be guaranteed. Especially, the developed global adaptive neural control also improves the tracking performance by introducing an error transformation mechanism, such that both transient and steady-state performance can be shaped according to the predefined bounds. Simulation studies on the hypersonic flight vehicle validate that the designed controller has good velocity modulation and velocity stability performance.
Robust Global Control Strategies for Improvement of Angular Stability using FACTS and HVDC Devices
Agnihotri, P.; Kulkarni, A. M.; Gole, A. M.
2013-05-01
System-wide feedback signals made available by Wide-Area Measurement Systems technology can be used in FACTS/HVDC based controllers for the improvement of angular stability. These global signals can facilitate the efficient use of controller effort to stabilize critical swing modes. This paper introduces a restricted global strategy which involves the use of specific global feedback signals which are available at the HVDC/FACTS locations. The strategy is expected to be robust to changes in the power grid as well as communication uncertainties. This paper presents a heuristic introduction to this strategy using a circuit analogy of a simplified model of a power system. Preliminary results on a small system are also presented.
Kuhlmann, Salma
1999-01-01
Model theoretic algebra has witnessed remarkable progress in the last few years. It has found profound applications in other areas of mathematics, notably in algebraic geometry and in singularity theory. Since Wilkie's results on the o-minimality of the expansion of the reals by the exponential function, and most recently even by all Pfaffian functions, the study of o-minimal expansions of the reals has become a fascinating topic. The quest for analogies between the semi-algebraic case and the o-minimal case has set a direction to this research. Through the Artin-Schreier Theory of real closed
The Global Stability of Predator-Prey System of Gause-Type with Holling Ⅲ Functional Response
无
2000-01-01
This paper deals with the question of global stability of the positive locally asymptotically stable equilibrium in a class of predator-prey system of Gause-type with Holling Ⅲ functional response. The Dulac's criterion is applied and liapunov functions are constructed to establish the global stability.
Liu, Qun
2015-02-01
In this paper, a stochastic Lotka-Volterra competitive model with time-dependent delays is investigated. Sufficient conditions for global asymptotic stability of the positive equilibrium are established. The obtained result demonstrates that time-dependent delays have important impacts on the global asymptotic stability of the positive equilibrium of the considered system.
Advanced technology paths to global climate stability: energy for a greenhouse planet.
Hoffert, Martin I; Caldeira, Ken; Benford, Gregory; Criswell, David R; Green, Christopher; Herzog, Howard; Jain, Atul K; Kheshgi, Haroon S; Lackner, Klaus S; Lewis, John S; Lightfoot, H Douglas; Manheimer, Wallace; Mankins, John C; Mauel, Michael E; Perkins, L John; Schlesinger, Michael E; Volk, Tyler; Wigley, Tom M L
2002-11-01
Stabilizing the carbon dioxide-induced component of climate change is an energy problem. Establishment of a course toward such stabilization will require the development within the coming decades of primary energy sources that do not emit carbon dioxide to the atmosphere, in addition to efforts to reduce end-use energy demand. Mid-century primary power requirements that are free of carbon dioxide emissions could be several times what we now derive from fossil fuels (approximately 10(13) watts), even with improvements in energy efficiency. Here we survey possible future energy sources, evaluated for their capability to supply massive amounts of carbon emission-free energy and for their potential for large-scale commercialization. Possible candidates for primary energy sources include terrestrial solar and wind energy, solar power satellites, biomass, nuclear fission, nuclear fusion, fission-fusion hybrids, and fossil fuels from which carbon has been sequestered. Non-primary power technologies that could contribute to climate stabilization include efficiency improvements, hydrogen production, storage and transport, superconducting global electric grids, and geoengineering. All of these approaches currently have severe deficiencies that limit their ability to stabilize global climate. We conclude that a broad range of intensive research and development is urgently needed to produce technological options that can allow both climate stabilization and economic development.
Semi-Global Practical Stabilization and Disturbance Adaptation for an Underactuated Ship
Kristin Y. Pettersen
2001-04-01
Full Text Available We consider the problem of stabilizing the position and orientation of a ship to constant desired values, when the ship has only two independent controls and also the ship is subject to an environmental force of unknown magnitude. We propose a time-varying feedback control law and a disturbance adaptation law, and show that this provides semi-global practical asymptotic stability. The control and adaptation laws are derived using a combined integrator backstepping and averaging approach. Simulation results are presented.
Global Stability of an Eco-Epidemiological Model with Time Delay and Saturation Incidence
Shuxue Mao
2011-01-01
Full Text Available We investigate a delayed eco-epidemiological model with disease in predator and saturation incidence. First, by comparison arguments, the permanence of the model is discussed. Then, we study the local stability of each equilibrium of the model by analyzing the corresponding characteristic equations and find that Hopf bifurcation occurs when the delay τ passes through a sequence of critical values. Next, by means of an iteration technique, sufficient conditions are derived for the global stability of the disease-free planar equilibrium and the positive equilibrium. Numerical examples are carried out to illustrate the analytical results.
Global stability of a delayed mosquito-transmitted disease model with stage structure
B. G. Sampath Aruna Pradeep
2015-01-01
Full Text Available This article presents a new eco-epidemiological deterministic delay differential equation model considering a biological controlling approach on mosquitoes, for endemic dengue disease with variable host (human and variable vector (Aedes aegypti populations, and stage structure for mosquitoes. In this model, predator-prey interaction is considered by using larvae as prey and mosquito-fish as predator. We give a complete classification of equilibria of the model, and sufficient conditions for global stability/global attractivity of some equilibria are given by constructing suitable Lyapunov functionals and using Lyapunov-LaSalle invariance principle. Also, numerical simulations are presented to show the validity of our results.
Mingzhu Song
2016-01-01
Full Text Available We address the problem of globally asymptotic stability for a class of stochastic nonlinear systems with time-varying delays. By the backstepping method and Lyapunov theory, we design a linear output feedback controller recursively based on the observable linearization for a class of stochastic nonlinear systems with time-varying delays to guarantee that the closed-loop system is globally asymptotically stable in probability. In particular, we extend the deterministic nonlinear system to stochastic nonlinear systems with time-varying delays. Finally, an example and its simulations are given to illustrate the theoretical results.
Exponentially asymptotical synchronization in uncertain complex dynamical networks with time delay
Luo Qun; Yang Han; Li Lixiang; Yang Yixian [Information Security Center, State Key Laboratory of Networking and Switching Technology, Beijing University of Posts and Telecommunications, Beijing 100876 (China); Han Jiangxue, E-mail: luoqun@bupt.edu.c [National Engineering Laboratory for Disaster Backup and Recovery, Beijing University of Posts and Telecommunications, Beijing 100876 (China)
2010-12-10
Over the past decade, complex dynamical network synchronization has attracted more and more attention and important developments have been made. In this paper, we explore the scheme of globally exponentially asymptotical synchronization in complex dynamical networks with time delay. Based on Lyapunov stability theory and through defining the error function between adjacent nodes, four novel adaptive controllers are designed under four situations where the Lipschitz constants of the state function in nodes are known or unknown and the network structure is certain or uncertain, respectively. These controllers could not only globally asymptotically synchronize all nodes in networks, but also ensure that the error functions do not exceed the pre-scheduled exponential function. Finally, simulations of the synchronization among the chaotic system in the small-world and scale-free network structures are presented, which prove the effectiveness and feasibility of our controllers.
Exponential synchronization of memristive Cohen-Grossberg neural networks with mixed delays.
Yang, Xinsong; Cao, Jinde; Yu, Wenwu
2014-06-01
This paper concerns the problem of global exponential synchronization for a class of memristor-based Cohen-Grossberg neural networks with time-varying discrete delays and unbounded distributed delays. The drive-response set is discussed. A novel controller is designed such that the response (slave) system can be controlled to synchronize with the drive (master) system. Through a nonlinear transformation, we get an alternative system from the considered memristor-based Cohen-Grossberg neural networks. By investigating the global exponential synchronization of the alternative system, we obtain the corresponding synchronization criteria of the considered memristor-based Cohen-Grossberg neural networks. Moreover, the conditions established in this paper are easy to be verified and improve the conditions derived in most of existing papers concerning stability and synchronization for memristor-based neural networks. Numerical simulations are given to show the effectiveness of the theoretical results.
El-Bachir Yallaoui
2012-06-01
Full Text Available In this article, we introduce a new class of analytic functions of the unit disc $mathbf{D}$ namely the Exponential Cauchy Transforms $mathbf{{K}_{e}}$ defined by f(z= {displaystyleint_{mathbf{T}}} expleft[ Kleft( xzight ight] dmu(x where $Kleft( zight =left( 1-zight ^{-1}$ is classical Cauchy kernel and $mu(x$ is a complex Borel measures and $x$ belongs to the unit circle $mathbf{T}$ . We use Laguerre polynomials to explore the coefficients of the Taylor expansions of the kernel and Peron's formula to study the asymptotic behavior of the Taylor coefficients. Finally we investigate relationships between our new class $mathbf{{K}_{e}}$, the classical Cauchy space $mathbf{K}$ and the Hardy spaces $H^{p}$.
Iyer-Biswas, Srividya; Wright, Charles; Henry, Jon; Burov, Stas; Lin, Yihan; Crosson, Sean; Dinner, Aaron; Scherer, Norbert
2013-03-01
The interplay between growth and division of cells is has been studied in the context of exponential growth of bacterial cells (in suitable conditions) for decades. However, bulk culture studies obscure phenomena that manifest in single cells over many generations. We introduce a unique technology combining microfluidics, single-cell imaging, and quantitative analysis. This enables us to track the growth of single Caulobacter crescentus stalked cells over hundreds of generations. The statistics that we extract indicate a size thresholding mechanism for cell division and a non-trivial scaling collapse of division time distributions at different temperatures. In this talk I shall discuss these observations and a stochastic model of growth and division that captures all our observations with no free parameters.
Global stability analysis of birhythmicity in a self-sustained oscillator
Yamapi, R; Aziz-Aloui, M A
2010-01-01
We analyze global stability properties of birhythmicity in a self-sustained system with random excitations. The model is a multi-limit cycles variation of the van der Pol oscillatorintroduced to analyze enzymatic substrate reactions in brain waves. We show that the two frequencies are strongly influenced by the nonlinear coefficients $\\alpha$ and $\\beta$. With a random excitation, such as a Gaussian white noise, the attractor's global stability is measured by the mean escape time $\\tau$ from one limit-cycle. An effective activation energy barrier is obtained by the slope of the linear part of the variation of the escape time $\\tau$ versus the inverse noise-intensity 1/D. We find that the trapping barriers of the two frequencies can be very different, thus leaving the system on the same attractor for an overwhelming time. However, we also find that the system is nearly symmetric in a narrow range of the parameters.
Global stability analysis of birhythmicity in a self-sustained oscillator.
Yamapi, R; Filatrella, G; Aziz-Alaoui, M A
2010-03-01
We analyze the global stability properties of birhythmicity in a self-sustained system with random excitations. The model is a multi-limit-cycle variation in the van der Pol oscillator introduced to analyze enzymatic substrate reactions in brain waves. We show that the two frequencies are strongly influenced by the nonlinear coefficients alpha and beta. With a random excitation, such as a Gaussian white noise, the attractor's global stability is measured by the mean escape time tau from one limit cycle. An effective activation energy barrier is obtained by the slope of the linear part of the variation in the escape time tau versus the inverse noise intensity 1/D. We find that the trapping barriers of the two frequencies can be very different, thus leaving the system on the same attractor for an overwhelming time. However, we also find that the system is nearly symmetric in a narrow range of the parameters.
Global stability for delay SIR and SEIR epidemic models with nonlinear incidence rate.
Huang, Gang; Takeuchi, Yasuhiro; Ma, Wanbiao; Wei, Daijun
2010-07-01
In this paper, based on SIR and SEIR epidemic models with a general nonlinear incidence rate, we incorporate time delays into the ordinary differential equation models. In particular, we consider two delay differential equation models in which delays are caused (i) by the latency of the infection in a vector, and (ii) by the latent period in an infected host. By constructing suitable Lyapunov functionals and using the Lyapunov-LaSalle invariance principle, we prove the global stability of the endemic equilibrium and the disease-free equilibrium for time delays of any length in each model. Our results show that the global properties of equilibria also only depend on the basic reproductive number and that the latent period in a vector does not affect the stability, but the latent period in an infected host plays a positive role to control disease development.
Plietzsch, A.; Schultz, P.; Heitzig, J.; Kurths, J.
2016-05-01
When designing or extending electricity grids, both frequency stability and resilience against cascading failures have to be considered amongst other aspects of energy security and economics such as construction costs due to total line length. Here, we compare an improved simulation model for cascading failures with state-of-the-art simulation models for short-term grid dynamics. Random ensembles of realistic power grid topologies are generated using a recent model that allows for a tuning of global vs local redundancy. The former can be measured by the algebraic connectivity of the network, whereas the latter can be measured by the networks transitivity. We show that, while frequency stability of an electricity grid benefits from a global form of redundancy, resilience against cascading failures rather requires a more local form of redundancy and further analyse the corresponding trade-off.
Li, Chunhe; Wang, Erkang; Wang, Jin
2012-05-21
We developed a potential flux landscape theory to investigate the dynamics and the global stability of a chemical Lorenz chaotic strange attractor under intrinsic fluctuations. Landscape was uncovered to have a butterfly shape. For chaotic systems, both landscape and probabilistic flux are crucial to the dynamics of chaotic oscillations. Landscape attracts the system down to the chaotic attractor, while flux drives the coherent motions along the chaotic attractors. Barrier heights from the landscape topography provide a quantitative measure for the robustness of chaotic attractor. We also found that the entropy production rate and phase coherence increase as the molecular numbers increase. Power spectrum analysis of autocorrelation function provides another way to quantify the global stability of chaotic attractor. We further found that limit cycle requires more flux and energy to sustain than the chaotic strange attractor. Finally, by detailed analysis we found that the curl probabilistic flux may provide the origin of the chaotic attractor.
Global Stability of a Predator-prey Model with Stage Structure
WANG Li-li; XU Rui
2015-01-01
A Holling type III predator-prey model with stage structure for prey is investi-gated. By analyzing the corresponding characteristic equations, the local stability of each of feasible equilibria of the system is discussed. By using the uniformly persistence theory, the system is proven to be permanent if the coexistence equilibrium exists. By using Lyapunov functionals and LaSalle’s invariance principle, it is shown that the two boundary equilibria is globally asymptotically stable when the coexistence equilibrium is not feasible. By using compound matrix theory, the sucient conditions are obtained for the global stability of the coexistence equilibrium. At last, numerical simulations are carried out to illustrate the main results.
Global robust asymptotic stability of variable-time impulsive BAM neural networks.
Saylı, Mustafa; Yılmaz, Enes
2014-12-01
In this paper, the global robust asymptotic stability of the equilibrium point for a more general class of bidirectional associative memory (BAM) neural networks with variable time of impulses is addressed. Unlike most existing studies, the case of non-fix time impulses is focused on in the present study. By means of B-equivalence method, which was introduced in Akhmet (2003, 2005, 2009, 2010), Akhmet and Perestyuk (1990) and Akhmet and Turan (2009), we reduce these networks to a fix time impulsive neural networks system. Sufficient conditions ensuring the existence, uniqueness and global robust asymptotic stability of the equilibrium point are obtained by employing an appropriate Lyapunov function and linear matrix inequality (LMI). Finally, we give one illustrative example to show the effectiveness of the theoretical results.
Global stability of enzymatic chains of full reversible Michaelis-Menten reactions.
Belgacem, Ismail; Gouzé, Jean-Luc
2013-09-01
We consider a chain of metabolic reactions catalyzed by enzymes, of reversible Michaelis-Menten type with full dynamics, i.e. not reduced with any quasi-steady state approximations. We study the corresponding dynamical system and show its global stability if the equilibrium exists. If the system is open, the equilibrium may not exist. The main tool is monotone systems theory. Finally we study the implications of these results for the study of coupled genetic-metabolic systems.
A parallel and matrix free framework for global stability analysis of compressible flows
Henze, O; Sesterhenn, J
2015-01-01
An numerical iterative framework for global modal stability analysis of compressible flows using a parallel environment is presented. The framework uses a matrix-free implementation to allow computations of large scale problems. Various methods are tested with regard to convergence acceleration of the framework. The methods consist of a spectral Cayley transformation used to select desired Eigenvalues from a large spectrum, an improved linear solver and a parallel block-Jacobi preconditioning scheme.
Global stability and persistence in LG-Holling type II diseased predator ecosystems.
Sarwardi, Sahabuddin; Haque, Mainul; Venturino, Ezio
2011-01-01
A Leslie-Gower-Holling type II model is modified to introduce a contagious disease in the predator population, assuming that disease cannot propagate to the prey. All the system's equilibria are determined and the behaviour of the system near them is investigated. The main mathematical issues are global stability and bifurcations for some of the equilibria, together with sufficient conditions for persistence of the ecosystem. Counterintuitive results on the role played by intraspecific competition are highlighted.
Global stability and quadratic Hamiltonian structure in Lotka-Volterra and quasi-polynomial systems
Szederkenyi, Gabor; Hangos, Katalin M
2004-04-26
We show that the global stability of quasi-polynomial (QP) and Lotka-Volterra (LV) systems with the well-known logarithmic Lyapunov function is equivalent to the existence of a local generalized dissipative Hamiltonian description of the LV system with a diagonal quadratic form as a Hamiltonian function. The Hamiltonian function can be calculated and the quadratic dissipativity neighborhood of the origin can be estimated by solving linear matrix inequalities.
Masuda, Arata; Sato, Takeru
2016-04-01
This paper presents an experimental verification of a wideband nonlinear vibration energy harvester which has a globally stabilized high-energy resonating response. For the conventional linear vibration energy harvester, the maximum performance of the power generation and its bandwidth are in a relation of trade-off. The resonance frequency band can be expanded by introducing a Duffing-type nonlinear resonator in order to enable the harvester to generate larger electric power in a wider frequency range. However, since such nonlinear resonators often have multiple stable steady-state solutions in the resonance band, it is diﬃcult for the nonlinear harvester to maintain the high performance of the power generation constantly. The principle of self-excitation and entrainment has been utilized to provide the global stability to the highest-energy solution by destabilizing other unexpected lower-energy solutions by introducing a switching circuit of the load resistance between positive and the negative values depending on the response amplitude of the oscillator. In this study, an experimental verification of this concept are carried out. An experimental prototype harvester is designed and fabricated and the performance of the proposed harvester is experimentally verified. It has been shown that the numerical and experimental results agreed very well, and the highest-energy solutions above the threshold value were successfully stabilized globally.
Local and global stability analysis of compressible channel flow over wall impedance
Rahbari, Iman; Scalo, Carlo
2016-11-01
The stability properties of compressible channel flow over porous walls is investigated via Local (LSA) and Global Stability Analysis (GSA) for laminar and turbulent base flows at Reb = 6900 and Mb = 0 . 85 , 1 . 5 , 3 . 5 . Linearized Navier-Stokes equations are discretized via a sixth-order fully collocated Padé scheme leading to a Generalized Eigenvalue Problem (GEVP) solved using a parallel sparse eigenvalue solver based on the shift-invert Arnoldi method. The adopted discretization guarantees spectral-like spatial resolution. Fully sparsity of the system is retained via implicit calculation of the numerical derivatives ensuring computational efficiency on multi-processor platforms. The global eigen-spectrum exhibits various sets of modes grouped by streamwise wave-numbers, which are captured via LSA, as well as global acoustic modes. Consistently with the findings of C. Scalo et al., two unstable local modes are found for sufficiently high wall permeability: one standing-wave-like and one representing a bulk pressure mode, both generating additional Reynolds shear stresses concentrated in the viscous sublayer region. Stability properties of the flow over non-modal streamwise impedance distributions are also discussed.
A new delay-independent condition for global robust stability of neural networks with time delays.
Samli, Ruya
2015-06-01
This paper studies the problem of robust stability of dynamical neural networks with discrete time delays under the assumptions that the network parameters of the neural system are uncertain and norm-bounded, and the activation functions are slope-bounded. By employing the results of Lyapunov stability theory and matrix theory, new sufficient conditions for the existence, uniqueness and global asymptotic stability of the equilibrium point for delayed neural networks are presented. The results reported in this paper can be easily tested by checking some special properties of symmetric matrices associated with the parameter uncertainties of neural networks. We also present a numerical example to show the effectiveness of the proposed theoretical results.
Edgeworth, Matthew J; Phillips, Jonathan J; Lowe, David C; Kippen, Alistair D; Higazi, Daniel R; Scrivens, James H
2015-12-07
Immunoglobulin G (IgG) monoclonal antibodies (mAbs) are a major class of medicines, with high specificity and affinity towards targets spanning many disease areas. The antibody Fc (fragment crystallizable) region is a vital component of existing antibody therapeutics, as well as many next generation biologic medicines. Thermodynamic stability is a critical property for the development of stable and effective therapeutic proteins. Herein, a combination of ion-mobility mass spectrometry (IM-MS) and hydrogen/deuterium exchange mass spectrometry (HDX-MS) approaches have been used to inform on the global and local conformation and dynamics of engineered IgG Fc variants with reduced thermodynamic stability. The changes in conformation and dynamics have been correlated with their thermodynamic stability to better understand the destabilising effect of functional IgG Fc mutations and to inform engineering of future therapeutic proteins.
Robust Stability Clearance of Flight Control Law Based on Global Sensitivity Analysis
Liuli Ou
2014-01-01
Full Text Available To validate the robust stability of the flight control system of hypersonic flight vehicle, which suffers from a large number of parametrical uncertainties, a new clearance framework based on structural singular value (μ theory and global uncertainty sensitivity analysis (SA is proposed. In this framework, SA serves as the preprocess of uncertain model to be analysed to help engineers to determine which uncertainties affect the stability of the closed loop system more slightly. By ignoring these unimportant uncertainties, the calculation of μ can be simplified. Instead of analysing the effect of uncertainties on μ which involves solving optimal problems repeatedly, a simpler stability analysis function which represents the effect of uncertainties on closed loop poles is proposed. Based on this stability analysis function, Sobol’s method, the most widely used global SA method, is extended and applied to the new clearance framework due to its suitability for system with strong nonlinearity and input factors varying in large interval, as well as input factors subjecting to random distributions. In this method, the sensitive indices can be estimated via Monte Carlo simulation conveniently. An example is given to illustrate the efficiency of the proposed method.
Long-term stability of the Tevatron by verified global optimization
Berz, Martin; Makino, Kyoko; Kim, Youn-Kyung
2006-03-01
The tools used to compute high-order transfer maps based on differential algebraic (DA) methods have recently been augmented by methods that also allow a rigorous computation of an interval bound for the remainder. In this paper we will show how such methods can also be used to determine rigorous bounds for the global extrema of functions in an efficient way. The method is used for the bounding of normal form defect functions, which allows rigorous stability estimates for repetitive particle accelerator. However, the method is also applicable to general lattice design problems and can enhance the commonly used local optimization with heuristic successive starting point modification. The global optimization approach studied rests on the ability of the method to suppress the so-called dependency problem common to validated computations, as well as effective polynomial bounding techniques. We review the linear dominated bounder (LDB) and the quadratic fast bounder (QFB) and study their performance for various example problems in global optimization. We observe that the method is superior to other global optimization approaches and can prove stability times similar to what is desired, without any need for expensive long-term tracking and in a fully rigorous way.
Fermi, Enrico
The Patent contains an extremely detailed description of an atomic pile employing natural uranium as fissile material and graphite as moderator. It starts with the discussion of the theory of the intervening phenomena, in particular the evaluation of the reproduction or multiplication factor, K, that is the ratio of the number of fast neutrons produced in one generation by the fissions to the original number of fast neutrons, in a system of infinite size. The possibility of having a self-maintaining chain reaction in a system of finite size depends both on the facts that K is greater than unity and the overall size of the system is sufficiently large to minimize the percentage of neutrons escaping from the system. After the description of a possible realization of such a pile (with many detailed drawings), the various kinds of neutron losses in a pile are depicted. Particularly relevant is the reported "invention" of the exponential experiment: since theoretical calculations can determine whether or not a chain reaction will occur in a give system, but can be invalidated by uncertainties in the parameters of the problem, an experimental test of the pile is proposed, aimed at ascertaining if the pile under construction would be divergent (i.e. with a neutron multiplication factor K greater than 1) by making measurements on a smaller pile. The idea is to measure, by a detector containing an indium foil, the exponential decrease of the neutron density along the length of a column of uranium-graphite lattice, where a neutron source is placed near its base. Such an exponential decrease is greater or less than that expected due to leakage, according to whether the K factor is less or greater than 1, so that this experiment is able to test the criticality of the pile, its accuracy increasing with the size of the column. In order to perform this measure a mathematical description of the effect of neutron production, diffusion, and absorption on the neutron density in the
The global nonlinear stability of self-gravitating irrotational Chaplygin fluids in a FRW geometry
LeFloch, Philippe G
2015-01-01
We analyze the global nonlinear stability of FRW (Friedmann-Robertson-Walker) spacetimes in presence of an irrotational perfect fluid. We assume that the fluid is governed by the so-called (generalized) Chaplygin equation of state relating the pressure to the mass-energy density. We express the Einstein equations in wave gauge as a systems of coupled nonlinear wave equations and by performing a suitable conformal transformation, we are able to analyze the global behavior of solutions in future timelike directions. We establish that the (3+1)-spacetime metric and the mass density and velocity vector describing the evolution of the fluid remain globally close to a reference FRW solution, under small initial data perturbations. Our analysis provides also the precise asymptotic behavior of the perturbed solutions in the future directions.
Global Sea Level Stabilization-Sand Dune Fixation: A Solar-powered Sahara Seawater Textile Pipeline
Badescu, Viorel; Bolonkin, Alexander A
2007-01-01
Could anthropogenic saturation with pumped seawater of the porous ground of active sand dune fields in major deserts (e.g., the westernmost Sahara) cause a beneficial reduction of global sea level? Seawater extraction from the ocean, and its deposition on deserted sand dune fields in Mauritania and elsewhere via a Solar-powered Seawater Textile Pipeline (SSTP) can thwart the postulated future global sea level. Thus, Macro-engineering offers an additional cure for anticipated coastal change, driven by global sea level rise, that could supplement, or substitute for (1) stabilizing the shoreline with costly defensive public works (armoring macroprojects) and (2) permanent retreat from the existing shoreline (real and capital property abandonment). We propose Macro-engineering use tactical technologies that sculpt and vegetate barren near-coast sand dune fields with seawater, seawater that would otherwise, as commonly postulated, enlarge Earth seascape area! Our Macro-engineering speculation blends eremology with...
Choudhury, Prakriti Pal
2015-01-01
We perform global linear stability analysis and idealized numerical simulations in global thermal balance to understand the condensation of cold gas from hot/virial atmospheres (coronae), in particular the intracluster medium (ICM). We pay particular attention to geometry (e.g., spherical versus plane-parallel) and the nature of the gravitational potential. Global linear analysis gives a similar value for the fastest growing thermal instability modes in spherical and Cartesian geometries. Simulations and observations suggest that cooling in halos critically depends on the ratio of the cooling time to the free-fall time ($t_{cool}/t_{ff}$). Extended cold gas condenses out of the ICM only if this ratio is smaller than a threshold value close to 10. Previous works highlighted the difference between the nature of cold gas condensation in spherical and plane-parallel atmospheres; namely, cold gas condensation appeared easier in spherical atmospheres. This apparent difference due to geometry arises because the prev...
Long-term stability of global erosion rates and weathering during late-Cenozoic cooling.
Willenbring, Jane K; von Blanckenburg, Friedhelm
2010-05-13
Over geologic timescales, CO(2) is emitted from the Earth's interior and is removed from the atmosphere by silicate rock weathering and organic carbon burial. This balance is thought to have stabilized greenhouse conditions within a range that ensured habitable conditions. Changes in this balance have been attributed to changes in topographic relief, where varying rates of continental rock weathering and erosion are superimposed on fluctuations in organic carbon burial. Geological strata provide an indirect yet imperfectly preserved record of this change through changing rates of sedimentation. Widespread observations of a recent (0-5-Myr) fourfold increase in global sedimentation rates require a global mechanism to explain them. Accelerated uplift and global cooling have been given as possible causes, but because of the links between rates of erosion and the correlated rate of weathering, an increase in the drawdown of CO(2) that is predicted to follow may be the cause of global climate change instead. However, globally, rates of uplift cannot increase everywhere in the way that apparent sedimentation rates do. Moreover, proxy records of past atmospheric CO(2) provide no evidence for this large reduction in recent CO(2) concentrations. Here we question whether this increase in global weathering and erosion actually occurred and whether the apparent increase in the sedimentation rate is due to observational biases in the sedimentary record. As evidence, we recast the ocean dissolved (10)Be/(9)Be isotope system as a weathering proxy spanning the past approximately 12 Myr (ref. 14). This proxy indicates stable weathering fluxes during the late-Cenozoic era. The sum of these observations shows neither clear evidence for increased erosion nor clear evidence for a pulse in weathered material to the ocean. We conclude that processes different from an increase in denudation caused Cenozoic global cooling, and that global cooling had no profound effect on spatially and
On exponentiable soft topological spaces
Ghasem Mirhosseinkhani
2016-11-01
Full Text Available An object $X$ of a category $mathbf{C}$ with finite limits is called exponentiable if the functor $-times X:mathbf{C}rightarrow mathbf{C}$ has a right adjoint. There are many characterizations of the exponentiable spaces in the category $mathbf{Top}$ of topological spaces. Here, we study the exponentiable objects in the category $mathbf{STop}$ of soft topological spaces which is a generalization of the category $mathbf{Top}$. We investigate the exponentiability problem and give a characterization of exponentiable soft spaces. Also wegive the definition of exponential topology on the lattice of soft open sets of a soft space and present some characterizations of it.
Global Mittag-Leffler Stabilization of Fractional-Order Memristive Neural Networks.
Wu, Ailong; Zeng, Zhigang
2015-12-22
According to conventional memristive neural network theories, neurodynamic properties are powerful tools for solving many problems in the areas of brain-like associative learning, dynamic information storage or retrieval, etc. However, as have often been noted in most fractional-order systems, system analysis approaches for integral-order systems could not be directly extended and applied to deal with fractional-order systems, and consequently, it raises difficult issues in analyzing and controlling the fractional-order memristive neural networks. By using the set-valued maps and fractional-order differential inclusions, then aided by a newly proposed fractional derivative inequality, this paper investigates the global Mittag--Leffler stabilization for a class of fractional-order memristive neural networks. Two types of control rules (i.e., state feedback stabilizing control and output feedback stabilizing control) are designed for the stabilization of fractional-order memristive neural networks, while a list of stabilization criteria is established. Finally, two numerical examples are given to show the effectiveness and characteristics of the obtained theoretical results.
Global stabilization using LSS-Theorem: Applications to Robotics and Aerospace Vehicles
Selman, AbdulRazzak
Underactuated mechanical systems are gaining interest as they can sometimes provide the desired motion or functionality at reduced cost due to their using fewer expensive actuators. The term "underactuated" refers to the fact that such mechanical systems have fewer actuators than degrees of freedom, which makes them very difficult to control. Moreover, underactuated robots have nonlinear dynamics which must be tackled with nonlinear control techniques. Furthermore, control theory for underactuated mechanical systems has been an active area of research for the past 15-20 years. Most of the research has focused on local and global asymptotic stabilization by feedback. Underactuated systems can either possess nonminimum phase or minimum phase characteristics. For minimum phase underactuated systems, the stabilization problem is rather simple and many existing control design methodologies have been proved powerful in providing a solution to this problem. For nonminimum phase underactuated systems, asymptotic stabilization problem has been, and still is, an attractive subject to the researchers in the field of nonlinear control system and theory. In particular, global asymptotic stabilization (GAS) at a desired equilibrium point of such systems by means of a single smooth static or dynamic state feedback law is still largely an open problem in the literature. In this thesis, the problem of GAS via a smooth static state feedback law is addressed for a class of an underactuated nonlinear system that is affine (possibly non affine) in the control, partially feedback linearizable, nonminimum phase and (possibly) has a non-integrable acceleration constraint. The core result of the thesis is formulated through a theorem that the author refers to through this thesis as the Legend of Salah Salman (LSS) Theorem. LSS theorem states the existence of a smooth static state feedback law that globally asymptotically stabilizes the origin of the nonlinear underactuated system that is
De Keersmaecker, Wanda; Lhermitte, Stef; Honnay, Olivier; Farifteh, Jamshid; Somers, Ben; Coppin, Pol
2014-07-01
Increasing frequency of extreme climate events is likely to impose increased stress on ecosystems and to jeopardize the services that ecosystems provide. Therefore, it is of major importance to assess the effects of extreme climate events on the temporal stability (i.e., the resistance, the resilience, and the variance) of ecosystem properties. Most time series of ecosystem properties are, however, affected by varying data characteristics, uncertainties, and noise, which complicate the comparison of ecosystem stability metrics (ESMs) between locations. Therefore, there is a strong need for a more comprehensive understanding regarding the reliability of stability metrics and how they can be used to compare ecosystem stability globally. The objective of this study was to evaluate the performance of temporal ESMs based on time series of the Moderate Resolution Imaging Spectroradiometer derived Normalized Difference Vegetation Index of 15 global land-cover types. We provide a framework (i) to assess the reliability of ESMs in function of data characteristics, uncertainties and noise and (ii) to integrate reliability estimates in future global ecosystem stability studies against climate disturbances. The performance of our framework was tested through (i) a global ecosystem comparison and (ii) an comparison of ecosystem stability in response to the 2003 drought. The results show the influence of data quality on the accuracy of ecosystem stability. White noise, biased noise, and trends have a stronger effect on the accuracy of stability metrics than the length of the time series, temporal resolution, or amount of missing values. Moreover, we demonstrate the importance of integrating reliability estimates to interpret stability metrics within confidence limits. Based on these confidence limits, other studies dealing with specific ecosystem types or locations can be put into context, and a more reliable assessment of ecosystem stability against environmental disturbances
The range of time delay and the global stability of the equilibrium for an IVGTT model☆
Li, Jiaxu; Wang, Minghu; De Gaetano, Andrea; Palumbo, Pasquale; Panunzi, Simona
2011-01-01
Diabetes mellitus has become a prevalent disease in the world. Diagnostic protocol for the onset of diabetes mellitus is the initial step in the treatments. The intravenous glucose tolerance test (IVGTT) has been considered as the most accurate method to determine the insulin sensitivity and glucose effectiveness. It is well known that there exists a time delay in insulin secretion stimulated by the elevated glucose concentration level. However, the range of the length of the delay in the existing IVGTT models are not fully discussed and thus in many cases the time delay may be assigned to a value out of its reasonable range. In addition, several attempts had been made to determine when the unique equilibrium point is globally asymptotically stable. However, all these conditions are delay-independent. In this paper, we discuss the range of the time delay and provide easy-to-check delay-dependent conditions for the global asymptotic stability of the equilibrium point for a recent IVGTT model through Liapunov function approach. Estimates of the upper bound of the delay for global stability are given in corollaries. In addition, the numerical simulation in this paper is fully incorporated with functional initial conditions, which is natural and more appropriate in delay differential equation system. PMID:22123436
Generalized approach to non-exponential relaxation
R M Pickup; R Cywinski; C Pappas; P Fouquet; B Farago; P Falus
2008-11-01
Non-exponential relaxation is a universal feature of systems as diverse as glasses, spin glasses, earthquakes, financial markets and the universe. Complex relaxation results from hierarchically constrained dynamics with the strength of the constraints being directly related to the form of the relaxation, which changes from a simple exponential to a stretched exponential and a power law by increasing the constraints in the system. A global and unified approach to non-exponentiality was first achieved by Weron and was further generalized by Brouers and Sotolongo-Costa, who applied the concept of non-extensive entropy introduced by Tsallis to the relaxation of disordered systems. These concepts are now confronted with experimental results on the classical metallic spin glasses CuMn, AuFe and the insulating system EuSrS. The revisited data have also be complemented by new results on several compositions of the classical CuMn spin glass and on systems, like CoGa and CuCo, the magnetic behaviour of which is believed to arise from magnetic clusters and should be characteristic for superparamagnetism.
CHEN Jun; CUI Bao-Tong; GAO Ming
2008-01-01
The global asymptotic stability of delayed Cohen-Grossberg neural networks with impulses is investigated. Based on the new suitable Lyapunov functions and the Jacobsthal inequality, a set of novel sufficient criteria are derived for the global asymptotic stability of Cohen-Grossberg neural networks with time-varying delays and impulses.An illustrative example with its numerical simulations is given to demonstrate the effectiveness of the obtained results.
Stability analysis and design of fuzzy control system with bounded uncertain delays
Jianguo GUO; Juntao LI; Fengqi ZHOU; Jun ZHOU
2005-01-01
Fuzzy control problems for systems with bounded uncertain delays were studied.Based on Lyapunov stability theory and matrix theory,a nonlinear state feedback fuzzy controller was designed by linear matrix inequalities (LMI) approach,and the global exponential stability of the closed-loop system was strictly proved.For a fuzzy control system with bounded uncertain delays,under the global exponential stability condition which is reduced to p linear matrix inequalities,the controller guarantees stability performances of state variables.Finally,the simulation shows the validity of the method in this paper.
Expectation Propagation for Exponential Families
Seeger, Matthias
2005-01-01
This is a tutorial describing the Expectation Propagation (EP) algorithm for a general exponential family. Our focus is on simplicity of exposition. Although the overhead of translating a specific model into its exponential family representation can be considerable, many apparent complications of EP can simply be sidestepped by working in this canonical representation.
Multivariate Matrix-Exponential Distributions
Bladt, Mogens; Nielsen, Bo Friis
2010-01-01
-exponential distributions. We prove a characterization that states that a distribution is an MVME distribution if and only if all non-negative, non-null linear combinations of the coordinates have a univariate matrix-exponential distribution. This theorem is analog to a well-known characterization theorem...
Global stability analysis of structures and actions to control their effects
F. C. Freitas
Full Text Available ABSTRACT In this moment in which civil engineering is undergoing a phase where structural projects have been developed with structural systems composed of different and complex elements, some methods and criteria are used for the purpose of evaluating important aspects with regard to global and local stability. Among them, it is necessary to mention the parameters of instability a and ?z. In this sense, this work has the objective to present the basic concepts of the instability parameters a and ?z in accordance with what is clearly defined in the Brazilian standard ABNT NBR 6118; to present the results of simulations of models in the Brazilian structural software TQS varying the stress of compression in the columns in order to relate these values with the stability parameters.
Atkins, Stephen J; Bentley, Ian; Brooks, Darrell; Burrows, Mark P; Hurst, Howard T; Sinclair, Jonathan K
2015-06-01
Core stability training traditionally uses stable-base techniques. Less is known as to the use of unstable-base techniques, such as suspension training, to activate core musculature. This study sought to assess the neuromuscular activation of global core stabilizers when using suspension training techniques, compared with more traditional forms of isometric exercise. Eighteen elite level, male youth swimmers (age, 15.5 ± 2.3 years; stature, 163.3 ± 12.7 cm; body mass, 62.2 ± 11.9 kg) participated in this study. Surface electromyography (sEMG) was used to determine the rate of muscle contraction in postural musculature, associated with core stability and torso bracing (rectus abdominus [RA], external obliques [EO], erector spinae [ES]). A maximal voluntary contraction test was used to determine peak amplitude for all muscles. Static bracing of the core was achieved using a modified "plank" position, with and without a Swiss ball, and held for 30 seconds. A mechanically similar "plank" was then held using suspension straps. Analysis of sEMG revealed that suspension produced higher peak amplitude in the RA than using a prone or Swiss ball "plank" (p = 0.04). This difference was not replicated in either the EO or ES musculature. We conclude that suspension training noticeably improves engagement of anterior core musculature when compared with both lateral and posterior muscles. Further research is required to determine how best to activate both posterior and lateral musculature when using all forms of core stability training.
Global Stability of an HIV-1 Infection Model with General Incidence Rate and Distributed Delays.
Ndongo, Abdoul Samba; Talibi Alaoui, Hamad
2014-01-01
In this work an HIV-1 infection model with nonlinear incidence rate and distributed intracellular delays and with humoral immunity is investigated. The disease transmission function is assumed to be governed by general incidence rate f(T, V)V. The intracellular delays describe the time between viral entry into a target cell and the production of new virus particles and the time between infection of a cell and the emission of viral particle. Lyapunov functionals are constructed and LaSalle invariant principle for delay differential equation is used to establish the global asymptotic stability of the infection-free equilibrium, infected equilibrium without B cells response, and infected equilibrium with B cells response. The results obtained show that the global dynamics of the system depend on both the properties of the general incidence function and the value of certain threshold parameters R 0 and R 1 which depends on the delays.
Global stability and tumor clearance conditions for a cancer chemotherapy system
Valle, Paul A.; Starkov, Konstantin E.; Coria, Luis N.
2016-11-01
In this paper we study the global dynamics of a cancer chemotherapy system presented by de Pillis et al. (2007). This mathematical model describes the interaction between tumor cells, effector-immune cells, circulating lymphocytes and chemotherapy treatment. By applying the localization method of compact invariant sets, we find lower and upper bounds for these three cells populations. Further, we define a bounded domain in R+,04 where all compact invariant sets of the system are located and provide conditions under which this domain is positively invariant. We apply LaSalle's invariance principle and one result concerning two-dimensional competitive systems in order to derive sufficient conditions for tumor clearance and global asymptotic stability of the tumor-free equilibrium point. These conditions are computed by using bounds of the localization domain and they are given in terms of the chemotherapy treatment. Finally, we perform numerical simulations in order to illustrate our results.
Global Stability of an HIV-1 Infection Model with General Incidence Rate and Distributed Delays
2014-01-01
In this work an HIV-1 infection model with nonlinear incidence rate and distributed intracellular delays and with humoral immunity is investigated. The disease transmission function is assumed to be governed by general incidence rate f(T, V)V. The intracellular delays describe the time between viral entry into a target cell and the production of new virus particles and the time between infection of a cell and the emission of viral particle. Lyapunov functionals are constructed and LaSalle invariant principle for delay differential equation is used to establish the global asymptotic stability of the infection-free equilibrium, infected equilibrium without B cells response, and infected equilibrium with B cells response. The results obtained show that the global dynamics of the system depend on both the properties of the general incidence function and the value of certain threshold parameters R 0 and R 1 which depends on the delays. PMID:27355007
Persistence, Permanence and Global Stability for an $n$ n -Dimensional Nicholson System
Faria, Teresa; Röst, Gergely
2014-09-01
For a Nicholson's blowflies system with patch structure and multiple discrete delays, we analyze several features of the global asymptotic behavior of its solutions. It is shown that if the spectral bound of the community matrix is non-positive, then the population becomes extinct on each patch, whereas the total population uniformly persists if the spectral bound is positive. Explicit uniform lower and upper bounds for the asymptotic behavior of solutions are also given. When the population uniformly persists, the existence of a unique positive equilibrium is established, as well as a sharp criterion for its absolute global asymptotic stability, improving results in the recent literature. While our system is not cooperative, several sharp threshold-type results about its dynamics are proven, even when the community matrix is reducible, a case usually not treated in the literature.
L. F. Araghi
2014-01-01
Full Text Available Stability of switching systems with an infinite number of subsystems is important in some structure of systems, like fuzzy systems, neural networks, and so forth. Because of the relationship between stability of a set of matrices and switching systems, this paper first studies the stability of a set of matrices, then and the results are applied for stability of switching systems. Some new conditions for globally uniformly asymptotically stability (GUAS of discrete-time switched linear systems with an infinite number of subsystems are proposed. The paper considers some examples and simulation results.
The global stability of a delayed predator-prey system with two stage-structure
Wang Fengyan [College of Science, Jimei University, Xiamen Fujian 361021 (China)], E-mail: wangfy68@163.com; Pang Guoping [Department of Mathematics and Computer Science, Yulin Normal University, Yulin Guangxi 537000 (China)
2009-04-30
Based on the classical delayed stage-structured model and Lotka-Volterra predator-prey model, we introduce and study a delayed predator-prey system, where prey and predator have two stages, an immature stage and a mature stage. The time delays are the time lengths between the immature's birth and maturity of prey and predator species. Results on global asymptotic stability of nonnegative equilibria of the delay system are given, which generalize and suggest that good continuity exists between the predator-prey system and its corresponding stage-structured system.
Wu Huaiqin
2009-01-01
Full Text Available This paper considers a new class of additive neural networks where the neuron activations are modelled by discontinuous functions with nonlinear growth. By Leray-Schauder alternative theorem in differential inclusion theory, matrix theory, and generalized Lyapunov approach, a general result is derived which ensures the existence and global asymptotical stability of a unique periodic solution for such neural networks. The obtained results can be applied to neural networks with a broad range of activation functions assuming neither boundedness nor monotonicity, and also show that Forti's conjecture for discontinuous neural networks with nonlinear growth activations is true.
Global stability, periodic solutions, and optimal control in a nonlinear differential delay model
Anatoli F. Ivanov
2010-09-01
Full Text Available A nonlinear differential equation with delay serving as a mathematical model of several applied problems is considered. Sufficient conditions for the global asymptotic stability and for the existence of periodic solutions are given. Two particular applications are treated in detail. The first one is a blood cell production model by Mackey, for which new periodicity criteria are derived. The second application is a modified economic model with delay due to Ramsey. An optimization problem for a maximal consumption is stated and solved for the latter.
Xiaoming Fan
2014-01-01
Full Text Available We discuss multigroup SIRS (susceptible, infectious, and recovered epidemic models with random perturbations. We carry out a detailed analysis on the asymptotic behavior of the stochastic model; when reproduction number ℛ0>1, we deduce the globally asymptotic stability of the endemic equilibrium by measuring the difference between the solution and the endemic equilibrium of the deterministic model in time average. Numerical methods are employed to illustrate the dynamic behavior of the model and simulate the system of equations developed. The effect of the rate of immunity loss on susceptible and recovered individuals is also analyzed in the deterministic model.
Global Stability, Bifurcation, and Chaos Control in a Delayed Neural Network Model
Amitava Kundu
2014-01-01
Full Text Available Conditions for the global asymptotic stability of delayed artificial neural network model of n (≥3 neurons have been derived. For bifurcation analysis with respect to delay we have considered the model with three neurons and used suitable transformation on multiple time delays to reduce it to a system with single delay. Bifurcation analysis is discussed with respect to single delay. Numerical simulations are presented to verify the analytical results. Using numerical simulation, the role of delay and neuronal gain parameter in changing the dynamics of the neural network model has been discussed.
Rajchakit, G; Saravanakumar, R; Ahn, Choon Ki; Karimi, Hamid Reza
2017-02-01
This article examines the exponential stability analysis problem of generalized neural networks (GNNs) including interval time-varying delayed states. A new improved exponential stability criterion is presented by establishing a proper Lyapunov-Krasovskii functional (LKF) and employing new analysis theory. The improved reciprocally convex combination (RCC) and weighted integral inequality (WII) techniques are utilized to obtain new sufficient conditions to ascertain the exponential stability result of such delayed GNNs. The superiority of the obtained results is clearly demonstrated by numerical examples.
Rakkiyappan, R; Sivaranjani, R; Velmurugan, G; Cao, Jinde
2016-05-01
In this paper, the problem of the global O(t(-α)) stability and global asymptotic periodicity for a class of fractional-order complex-valued neural networks (FCVNNs) with time varying delays is investigated. By constructing suitable Lyapunov functionals and a Leibniz rule for fractional differentiation, some new sufficient conditions are established to ensure that the addressed FCVNNs are globally O(t(-α)) stable. Moreover, some sufficient conditions for the global asymptotic periodicity of the addressed FCVNNs with time varying delays are derived, showing that all solutions converge to the same periodic function. Finally, numerical examples are given to demonstrate the effectiveness and usefulness of our theoretical results.
Yang, Tao; Stoorvogel, Anton A.; Saberi, Ali; Johansson, Karl H.
2013-01-01
It is known that for single-input neutrally stable planar systems, there exists a class of saturated globally stabilizing linear state feedback control laws. The goal of this paper is to characterize the dynamic behavior for such a system under arbitrary locally stabilizing linear state feedback con
Yang, Tao; Stoorvogel, Antonie Arij; Saberi, Ali; Johansson, Karl H.
2013-01-01
It is known that for single-input neutrally stable planar systems, there exists a class of saturated globally stabilizing linear state feedback control laws. The goal of this paper is to characterize the dynamic behavior for such a system under arbitrary locally stabilizing linear state feedback
徐丽丽; 刘翙
2014-01-01
研究带跳随机延迟微分方程半隐式Euler方法的均方指数稳定性。将半隐式Euler方法应用到维纳过程和泊松过程驱动下的非线性随机延迟微分方程上进行讨论，给出了半隐式Euler方法的均方指数稳定性的条件。%In this paper ,the authors investigated the mean square exponential stability of the semi -implicit Euler method for stochastic delay differential equations with jumps .The semi implicit Euler method applied to the nonlinear stochastic delay dif -ferential equations which driven by Wiener process and Poisson process , and gave conditions about mean square exponential stability of the semi-implicit Euler method .
Stability analysis of a stochastic Gilpin-Ayala model driven by Lévy noise
Zhang, Xinhong; Wang, Ke
2014-05-01
A stochastic one-dimensional Gilpin-Ayala model driven by Lévy noise is presented in this paper. Firstly, we show that this model has a unique global positive solution under certain conditions. Then sufficient conditions for the almost sure exponential stability and moment exponential stability of the trivial solution are established. Results show that the jump noise can make the trivial solution stable under some conditions. Numerical example is introduced to illustrate the results.
Climate change impacts on US agriculture and forestry: benefits of global climate stabilization
Beach, Robert H.; Cai, Yongxia; Thomson, Allison; Zhang, Xuesong; Jones, Russell; McCarl, Bruce A.; Crimmins, Allison; Martinich, Jeremy; Cole, Jefferson; Ohrel, Sara; DeAngelo, Benjamin; McFarland, James; Strzepek, Kenneth; Boehlert, Brent
2015-09-01
Increasing atmospheric carbon dioxide levels, higher temperatures, altered precipitation patterns, and other climate change impacts have already begun to affect US agriculture and forestry, with impacts expected to become more substantial in the future. There have been numerous studies of climate change impacts on agriculture or forestry, but relatively little research examining the long-term net impacts of a stabilization scenario relative to a case with unabated climate change. We provide an analysis of the potential benefits of global climate change mitigation for US agriculture and forestry through 2100, accounting for landowner decisions regarding land use, crop mix, and management practices. The analytic approach involves a combination of climate models, a crop process model (EPIC), a dynamic vegetation model used for forests (MC1), and an economic model of the US forestry and agricultural sector (FASOM-GHG). We find substantial impacts on productivity, commodity markets, and consumer and producer welfare for the stabilization scenario relative to unabated climate change, though the magnitude and direction of impacts vary across regions and commodities. Although there is variability in welfare impacts across climate simulations, we find positive net benefits from stabilization in all cases, with cumulative impacts ranging from 32.7 billion to 54.5 billion over the period 2015-2100. Our estimates contribute to the literature on potential benefits of GHG mitigation and can help inform policy decisions weighing alternative mitigation and adaptation actions.
Climate change impacts on US agriculture and forestry: benefits of global climate stabilization
Beach, Robert H.; Cai, Yongxia; Thomson, Allison; Zhang, Xuesong; Jones, Russell; McCarl, Bruce A.; Crimmins, Allison; Martinich, Jeremy; Cole, Jefferson; Ohrel, Sara; DeAngelo, Benjamin; McFarland, James; Strzepek, Kenneth; Boehlert, Brent
2015-09-01
Increasing atmospheric carbon dioxide levels, higher temperatures, altered precipitation patterns, and other climate change impacts have already begun to affect US agriculture and forestry, with impacts expected to become more substantial in the future. There have been numerous studies of climate change impacts on agriculture or forestry, but relatively little research examining the long-term net impacts of a stabilization scenario relative to a case with unabated climate change. We provide an analysis of the potential benefits of global climate change mitigation for US agriculture and forestry through 2100, accounting for landowner decisions regarding land use, crop mix, and management practices. The analytic approach involves a combination of climate models, a crop process model (EPIC), a dynamic vegetation model used for forests (MC1), and an economic model of the US forestry and agricultural sector (FASOM-GHG). We find substantial impacts on productivity, commodity markets, and consumer and producer welfare for the stabilization scenario relative to unabated climate change, though the magnitude and direction of impacts vary across regions and commodities. Although there is variability in welfare impacts across climate simulations, we find positive net benefits from stabilization in all cases, with cumulative impacts ranging from $32.7 billion to $54.5 billion over the period 2015-2100. Our estimates contribute to the literature on potential benefits of GHG mitigation and can help inform policy decisions weighing alternative mitigation and adaptation actions.
Assessment of Global Voltage Stability Margin through Radial Basis Function Neural Network
Akash Saxena
2016-01-01
Full Text Available Dynamic operating conditions along with contingencies often present formidable challenges to the power engineers. Decisions pertaining to the control strategies taken by the system operators at energy management centre are based on the information about the system’s behavior. The application of ANN as a tool for voltage stability assessment is empirical because of its ability to do parallel data processing with high accuracy, fast response, and capability to model dynamic, nonlinear, and noisy data. This paper presents an effective methodology based on Radial Basis Function Neural Network (RBFN to predict Global Voltage Stability Margin (GVSM, for any unseen loading condition of the system. GVSM is used to assess the overall voltage stability status of the power system. A comparative analysis of different topologies of ANN, namely, Feedforward Backprop (FFBP, Cascade Forward Backprop (CFB, Generalized Regression (GR, Layer Recurrent (LR, Nonlinear Autoregressive Exogenous (NARX, ELMAN Backprop, and Feedforward Distributed Time Delay Network (FFDTDN, is carried out on the basis of capability of the prediction of GVSM. The efficacy of RBFN is better than other networks, which is validated by taking the predictions of GVSM at different levels of Additive White Gaussian Noise (AWGN in input features. The results obtained from ANNs are validated through the offline Newton Raphson (N-R method. The proposed methodology is tested over IEEE 14-bus, IEEE 30-bus, and IEEE 118-bus test systems.
Assessing the Benefits of Global Climate Stabilization Within an Integrated Modeling Framework
Beach, R. H.
2015-12-01
Increasing atmospheric carbon dioxide levels, higher temperatures, altered precipitation patterns, and other climate change impacts have already begun to affect US agriculture and forestry, with impacts expected to become more substantial in the future. There have been a number of studies of climate change impacts on agriculture or forestry. However, relatively few studies explore climate change impacts on both agriculture and forests simultaneously, including the interactions between alternative land uses and implications for market outcomes. Additionally, there is a lack of detailed analyses of the effects of stabilization scenarios relative to unabated emissions scenarios. Such analyses are important for developing estimates of the benefits of those stabilization scenarios, which can play a vital role in assessing tradeoffs associated with allocating resources across alternative mitigation and adaptation activities. We provide an analysis of the potential benefits of global climate change mitigation for US agriculture and forestry through 2100, accounting for landowner decisions regarding land use, crop mix, and management practices. The analytic approach involves a combination of climate models, a crop process model (EPIC), a dynamic vegetation model used for forests (MC1), and an economic model of the US forestry and agricultural sector (FASOM-GHG). We find substantial impacts on productivity, commodity markets, and consumer and producer welfare for the stabilization scenario relative to unabated climate change, though the magnitude and direction of impacts vary across regions and commodities. Although there is variability in welfare impacts across climate simulations, we find positive net benefits from stabilization in all cases, with cumulative impacts ranging from 32.7 billion to 54.5 billion over the period 2015-2100. Our estimates contribute to the literature on potential benefits of GHG mitigation and can help inform policy decisions weighing alternative
Is Radioactive Decay Really Exponential?
Aston, Philip J
2012-01-01
Radioactive decay of an unstable isotope is widely believed to be exponential. This view is supported by experiments on rapidly decaying isotopes but is more difficult to verify for slowly decaying isotopes. The decay of 14C can be calibrated over a period of 12,550 years by comparing radiocarbon dates with dates obtained from dendrochronology. It is well known that this approach shows that radiocarbon dates of over 3,000 years are in error, which is generally attributed to past variation in atmospheric levels of 14C. We note that predicted atmospheric variation (assuming exponential decay) does not agree with results from modelling, and that theoretical quantum mechanics does not predict exact exponential decay. We give mathematical arguments that non-exponential decay should be expected for slowly decaying isotopes and explore the consequences of non-exponential decay. We propose an experimental test of this prediction of non-exponential decay for 14C. If confirmed, a foundation stone of current dating meth...
Hsiao, Feng-Hsiag
2016-10-01
In this study, a novel approach via improved genetic algorithm (IGA)-based fuzzy observer is proposed to realise exponential optimal H∞ synchronisation and secure communication in multiple time-delay chaotic (MTDC) systems. First, an original message is inserted into the MTDC system. Then, a neural-network (NN) model is employed to approximate the MTDC system. Next, a linear differential inclusion (LDI) state-space representation is established for the dynamics of the NN model. Based on this LDI state-space representation, this study proposes a delay-dependent exponential stability criterion derived in terms of Lyapunov's direct method, thus ensuring that the trajectories of the slave system approach those of the master system. Subsequently, the stability condition of this criterion is reformulated into a linear matrix inequality (LMI). Due to GA's random global optimisation search capabilities, the lower and upper bounds of the search space can be set so that the GA will seek better fuzzy observer feedback gains, accelerating feedback gain-based synchronisation via the LMI-based approach. IGA, which exhibits better performance than traditional GA, is used to synthesise a fuzzy observer to not only realise the exponential synchronisation, but also achieve optimal H∞ performance by minimizing the disturbance attenuation level and recovering the transmitted message. Finally, a numerical example with simulations is given in order to demonstrate the effectiveness of our approach.
Sun, Yeong-Jeu; Wu, Yu-Biaw; Wang, Ching-Cheng
2013-06-01
In this study, the concept of global exponential ε-stabilization is introduced and the robust stabilization for a class of nonlinear systems with single input is investigated. Based on Lyapunov-like Theorem with differential and integral inequalities, a feedback control is proposed to realize the global stabilization of such nonlinear systems with any pre-specified exponential convergence rate. The guaranteed exponential convergence rate can be also correctly estimated. This result can be straightforwardly applicable to some famous chaotic systems. Besides, it will be proven that a single and linear control, with lower dimensions than that of the states, can realize the global exponential stability of some famous chaotic systems. Finally, comparisons of our main results with recently published results as well as numerical examples with circuit realization are provided to show the effectiveness and superiority of the obtained results.
Global Stabilization of Nonlinear Systems with Byrnes-Isidori Normal Form
WU Yu-qiang; YU Xing-huo
2002-01-01
The global stabilization of nonlinear cascade systems with partially linear composite dynamics is discussed in this paper using continuous terminal sliding modes (TSM). A two phase control strategy is proposed. The first phase is to use a linear control, called pre-TSM control, to bring the system state into a region where the TSM control is not singular. The second phase is to employ the TSM control in the region such that the equilibrium of the linear subsystem is reached in a finite time whose value is tunable by parameter setting of the TSMs. The finite time convergence of the proposed control strategy enables elimination of the effect of asymptotic convergence on the nonlinear systems. Although the proposed control strategy is sliding mode based, the control signal is continuous except at a single discontinuous point.Chattering phenomenon commonly associated with sliding mode control does not occur.
Global stability of synchronous and out-of-phase oscillations in central pattern generators
Landsman, A S
2010-01-01
Coupled arrays of Andronov-Hopf oscillators are investigated. These arrays can be diffusively or repulsively coupled, and can serve as central pattern generator models in animal locomotion and robotics. It is shown that repulsive coupling generates out-of-phase oscillations, while diffusive coupling generates synchronous oscillations. Specifically, symmetric solutions and their corresponding amplitudes are derived, and contraction analysis is used to prove global stability and convergence of oscillations to either symmetric out-of-phase or synchronous states, depending on the coupling constant. Next, the two mechanisms are used jointly by coupling multiple arrays. The resulting dynamics is analyzed, in a model inspired by the CPG-motorneuron network that controls the heartbeat of a medicinal leech.
Global existence and asymptotic stability of equilibria to reaction-diffusion systems
Wang, Rong-Nian; Tang, Zhong Wei
2009-06-01
In this paper, we study weakly coupled reaction-diffusion systems in unbounded domains of {\\bb R}^2 or {\\bb R}^3 , where the reaction terms are sums of quasimonotone nondecreasing and nonincreasing functions. Such systems are more complicated than those in many previous publications and little is known about them. A comparison principle and global existence, and boundedness theorems for solutions to these systems are established. Sufficient conditions on the nonlinearities, ensuring the positively Ljapunov stability of the zero solution with respect to H2-perturbations, are also obtained. As samples of applications, these results are applied to an autocatalytic chemical model and a concrete problem, whose nonlinearities are nonquasimonotone. Our results are novel. In particular, we present a solution to an open problem posed by Escher and Yin (2005 J. Nonlinear Anal. Theory Methods Appl. 60 1065-84).
Nonlinear control for global stabilization of multiple-integrator system by bounded controls
Bin ZHOU; Guangren DUAN; Liu ZHANG
2008-01-01
The global stabilization problem of the multiple-integrator system by bounded controls is considered.A nonlinear feedback law consisting of nested saturation functions is proposed.This type of nonlinear feedback law that is a modification and generalization of the result given in[1] needs only[(n+1)/2](n is the dimensions of the system)saturation elements,which is fewer than that which the other nonlinear laws need.Funhermore.the poles of the closedloop system Can be placed on any location on the left real axis when none of the saturafion elements in the control laws is saturated.This type of nonlinear control law exhibits a simpler structure and call significantly improve the transient performances of the closed-loop system,and is very superior to the other existing methods.Simulation on a fourth-order system is used to validate the proposed method.
Global stability of a two-mediums rumor spreading model with media coverage
Huo, Liang'an; Wang, Li; Song, Guoxiang
2017-09-01
Rumor spreading is a typical form of social communication and plays a significant role in social life, and media coverage has a great influence on the spread of rumor. In this paper, we present a new model with two media coverage to investigate the impact of the different mediums on rumor spreading. Then, we calculate the equilibria of the model and construct the reproduction number ℜ0. And we prove the global asymptotic stability of equilibria by using Lyapunov functions. Finally, we can conclude that the transition rate of the ignorants between two mediums has a direct effect on the scale of spreaders, and different media coverage has significant effects on the dynamics behaviors of rumor spreading.
Global stabilization of linear systems by bounded controls with guaranteed poles
ZHOU Bin; DUAN GuangRen
2008-01-01
The global stabilization of asymptotically null controllable linear systems by bounded control is considered. A nested type saturation control law is proposed which is a generalization of the existing results reported in the literature. The primary characteristic of this modified control law is that more design parameters, which are the closed-loop eigenvalues when the system is operating in linear form, are intro-duced and which can be well designed to achieve better system performance. Using this law, the pole locations of the closed-loop systems depending on a linear trans-formation can be placed arbitrarily within certain areas. Numerical example shows that the performance of the closed-loop system under this control law can be signif-icantly improved if the free parameters are properly chosen.
SIMULTANEOUS SHAPE AND TOPOLOGY OPTIMIZATION OF TRUSS UNDER LOCAL AND GLOBAL STABILITY CONSTRAINTS
GuoXu; LiuWei; LiHongyan
2003-01-01
A new approach for the solution of truss shape and topology optimization problem sunder local and global stability constraints is proposed. By employing the cross sectional areas of each bar and some shape parameters as topology design variables, the difficulty arising from the jumping of buckling length phenomenon can be easily overcome without the necessity of introducing the overlapping bars into the initial ground structure. Therefore computational efforts can be saved for the solution of this kind of problem. By modifying the elements of the stiffness matrix using Sigmoid function, the continuity of the objective and constraint functions with respect to shape design parameters can be restored to some extent. Some numerical examples demonstrate the effectiveness of the proposed method.
Global stability and optimisation of a general impulsive biological control model
Mailleret, Ludovic
2008-01-01
An impulsive model of augmentative biological control consisting of a general continuous predator-prey model in ordinary differential equations augmented by a discrete part describing periodic introductions of predators is considered. It is shown that there exists an invariant periodic solution that corresponds to prey eradication and a condition ensuring its global asymptotic stability is given. An optimisation problem related to the preemptive use of augmentative biological control is then considered. It is assumed that the per time unit budget of biological control (i.e. the number of predators to be released) is fixed and the best deployment of this budget is sought after in terms of release frequency. The cost function to be minimised is the time taken to reduce an unforeseen prey (pest) invasion under some harmless level. The analysis shows that the optimisation problem admits a countable infinite number of solutions. An argumentation considering the required robustness of the optimisation result is the...
Local and global stability analysis methods of multitime scale neural networks
Meyer-Baese, Anke
1996-03-01
The dynamics of complex neural networks modeling the self-organization process in cortical maps must include the aspects of long and short-term memory. The behavior of the network is such characterized by an equation of neural activity as a fast phenomenon and an equation of synaptic modification as a slow part of the neural system. We present new methods of analyzing the dynamics of a competitive neural system with different time scales: the K- monotone system theory developed by Kamke in 1932 as a global analysis technique and the theory of singular perturbations as a local analysis method. We also show the consequences of the stability analysis on the neural net parameters.
Robust exponential control of a class of systems with uncertainties
无
2002-01-01
The robust exponential stabilization problem for uncertain systems is studied. Based on the solution for a nominal linear quadratic regulator problem with a prescribed degree of stability, the methods of constructing state feedback controllers are developed to ensure the robust stability of the closed loop system under the conditions weaker than the matching condition. Also, the cases where the matching condition is satisfied are considered in detail. Some examples are included to show the solution methods.
Global stability behaviour for the BEK family of rotating boundary layers
Davies, Christopher; Thomas, Christian
2016-09-01
Numerical simulations were conducted to investigate the linear global stability behaviour of the Bödewadt, Ekman, von Kármán (BEK) family of flows, for cases where a disc rotates beneath an incompressible fluid that is also rotating. This extends the work reported in recent studies that only considered the rotating-disc boundary layer with a von Kármán configuration, where the fluid that lies above the boundary layer remains stationary. When a homogeneous flow approximation is made, neglecting the radial variation of the basic state, it can be shown that linearised disturbances are susceptible to absolute instability. We shall demonstrate that, despite this prediction of absolute instability, the disturbance development exhibits globally stable behaviour in the BEK boundary layers with a genuine radial inhomogeneity. For configurations where the disc rotation rate is greater than that of the overlying fluid, disturbances propagate radially outwards and there is only a convective form of instability. This replicates the behaviour that had previously been documented when the fluid did not rotate beyond the boundary layer. However, if the fluid rotation rate is taken to exceed that of the disc, then the propagation direction reverses and disturbances grow while convecting radially inwards. Eventually, as they approach regions of smaller radii, where stability is predicted according to the homogeneous flow approximation, the growth rates reduce until decay takes over. Given sufficient time, such disturbances can begin to diminish at every radial location, even those which are positioned outwards from the radius associated with the onset of absolute instability. This leads to the confinement of the disturbance development within a finitely bounded region of the spatial-temporal plane.
Zhang, Xian-Ming; Han, Qing-Long
2014-06-01
This paper is concerned with global asymptotic stability for a class of generalized neural networks with interval time-varying delays by constructing a new Lyapunov-Krasovskii functional which includes some integral terms in the form of ∫(t-h)(t)(h-t-s)(j)ẋ(T)(s)Rjẋ(s)ds(j=1,2,3). Some useful integral inequalities are established for the derivatives of those integral terms introduced in the Lyapunov-Krasovskii functional. A matrix-based quadratic convex approach is introduced to prove not only the negative definiteness of the derivative of the Lyapunov-Krasovskii functional, but also the positive definiteness of the Lyapunov-Krasovskii functional. Some novel stability criteria are formulated in two cases, respectively, where the time-varying delay is continuous uniformly bounded and where the time-varying delay is differentiable uniformly bounded with its time-derivative bounded by constant lower and upper bounds. These criteria are applicable to both static neural networks and local field neural networks. The effectiveness of the proposed method is demonstrated by two numerical examples.
Universality in stochastic exponential growth.
Iyer-Biswas, Srividya; Crooks, Gavin E; Scherer, Norbert F; Dinner, Aaron R
2014-07-11
Recent imaging data for single bacterial cells reveal that their mean sizes grow exponentially in time and that their size distributions collapse to a single curve when rescaled by their means. An analogous result holds for the division-time distributions. A model is needed to delineate the minimal requirements for these scaling behaviors. We formulate a microscopic theory of stochastic exponential growth as a Master Equation that accounts for these observations, in contrast to existing quantitative models of stochastic exponential growth (e.g., the Black-Scholes equation or geometric Brownian motion). Our model, the stochastic Hinshelwood cycle (SHC), is an autocatalytic reaction cycle in which each molecular species catalyzes the production of the next. By finding exact analytical solutions to the SHC and the corresponding first passage time problem, we uncover universal signatures of fluctuations in exponential growth and division. The model makes minimal assumptions, and we describe how more complex reaction networks can reduce to such a cycle. We thus expect similar scalings to be discovered in stochastic processes resulting in exponential growth that appear in diverse contexts such as cosmology, finance, technology, and population growth.
Conditions for global dynamic stability of a class of resource-bounded model ecosystems.
Seymour, Robert M; Knight, Gwenan; Fung, Tak
2010-11-01
This paper studies a class of dynamical systems that model multi-species ecosystems. These systems are 'resource bounded' in the sense that species compete to utilize an underlying limiting resource or substrate. This boundedness means that the relevant state space can be reduced to a simplex, with coordinates representing the proportions of substrate utilized by the various species. If the vector field is inward pointing on the boundary of the simplex, the state space is forward invariant under the system flow, a requirement that can be interpreted as the presence of non-zero exogenous recruitment. We consider conditions under which these model systems have a unique interior equilibrium that is globally asymptotically stable. The systems we consider generalize classical multi-species Lotka-Volterra systems, the behaviour of which is characterized by properties of the community (or interaction) matrix. However, the more general systems considered here are not characterized by a single matrix, but rather a family of matrices. We develop a set of 'explicit conditions' on the basis of a notion of 'uniform diagonal dominance' for such a family of matrices, that allows us to extract a set of sufficient conditions for global asymptotic stability based on properties of a single, derived matrix. Examples of these explicit conditions are discussed.
Global stability analysis of axisymmetric boundary layer over a circular cone
Vinod, N
2016-01-01
This paper presents the linear Global stability analysis of the incompressible axisymmetric boundary layer on a circular cone. The base flow is considered parallel to the axis of cone at the inlet. The angle of attack is zero and hence the base flow is axisymmetric. The favorable pressure gradient develops in the stream-wise direction due to cone angle. The Reynolds number is calculated based on the cone radius (a) at the inlet and free-stream velocity ($U_{\\infty}$). The base flow velocity profile is fully non-parallel and non-similar. Linearized Navier-Stokes equations (LNS) are derived for the disturbance flow quantities in the spherical coordinates. The LNS are discretized using Chebyshev spectral collocation method. The discretized LNS along with the homogeneous boundary conditions forms a general eigenvalues problem. Arnoldi's iterative algorithm is used for the numerical solution of the general eigenvalues problem. The Global temporal modes are computed for the range of Reynolds number from 174 to 1046...
Stability analysis of delayed cellular neural networks with and without noise perturbation
ZHANG Xue-juan; WANG Guan-xiang; LIU Hua
2008-01-01
The stability of a class of delayed cellular neural networks (DCNN) with or without noise perturbation is studied.After presenting a simple and easily checkable condition for the global exponential stability of a deterministic system,we further investigate the case with noise perturbation.When DCNN is perturbed by external noise,the system is globally stable.An important fact is that,when the system is perturbed by internal noise,it is globally exponentially stable only if the total noise strength is within a certain bound.This is significant since the stochastic resonance phenomena have been found to exist in many nonlinear systems.
Exponential Expansion in Evolutionary Economics
Frederiksen, Peter; Jagtfelt, Tue
2013-01-01
concepts are described in detail. Taken together it provides the rudimentary aspects of an economic system within an analytical perspective. It is argued that the main dynamic processes of the evolutionary perspective can be reduced to these four concepts. The model and concepts are evaluated in the light...... of Thomas Kuhn’s notion of scientific paradigms and criteria for a good theory (1977, 1996). The paper thus aims to augment and assimilate the fragmented and scattered body of concepts presently residing within the field of evolutionary economics, by presenting an intuitive framework, applicable within...... to this problem is proposed in the form of a model of exponential expansion. The model outlines the overall structure and function of the economy as exponential expansion. The pictographic model describes four axiomatic concepts and their exponential nature. The interactive, directional, emerging and expanding...
Chen, Jiyang; Li, Chuandong; Huang, Tingwen; Yang, Xujun
2017-02-01
In this paper, the memristor-based fractional-order neural networks (MFNN) with delay and with two types of stabilizing control are described in detail. Based on the Lyapunov direct method, the theories of set-value maps, differential inclusions and comparison principle, some sufficient conditions and assumptions for global stabilization of this neural network model are established. Finally, two numerical examples are presented to demonstrate the effectiveness and practicability of the obtained results.
Ji, Yu
2015-06-01
In this paper, the dynamical behavior of a viral infection model with general incidence rate and two time delays is studied. By using the Lyapunov functional and LaSalle invariance principle, the global stabilities of the infection-free equilibrium and the endemic equilibrium are obtained. We obtain a threshold of the global stability for the uninfected equilibrium, which means the disease will be under control eventually. These results can be applied to a variety of viral infections of disease that would make it possible to devise optimal treatment strategies. Numerical simulations with application to HIV infection are given to verify the analytical results.
Gao, Fangzheng; Wu, Yuqiang
2015-03-01
This paper considers the problem of global stabilization by state feedback for a class of high-order nonlinear systems with time-varying delays. Comparing with the existing relevant literature, the systems under investigation allow more uncertainties, to which the existing control methods are inapplicable. By introducing sign function and necessarily modifying the method of adding a power integrator, a state feedback controller is successfully constructed to preserve the equilibrium at the origin and guarantee the global asymptotic stability of the resulting closed-loop system. Finally, two simulation examples are provided to illustrate the effectiveness of the proposed approach.
Real-Time Exponential Curve Fits Using Discrete Calculus
Rowe, Geoffrey
2010-01-01
An improved solution for curve fitting data to an exponential equation (y = Ae(exp Bt) + C) has been developed. This improvement is in four areas -- speed, stability, determinant processing time, and the removal of limits. The solution presented avoids iterative techniques and their stability errors by using three mathematical ideas: discrete calculus, a special relationship (be tween exponential curves and the Mean Value Theorem for Derivatives), and a simple linear curve fit algorithm. This method can also be applied to fitting data to the general power law equation y = Ax(exp B) + C and the general geometric growth equation y = Ak(exp Bt) + C.
Vortex structures in exponentially shaped Josephson junctions
Shukrinov, Yu. M.; Semerdjieva, E. G.; Boyadjiev, T. L.
2005-04-01
We report the numerical calculations of the static vortex structure and critical curves in exponentially shaped long Josephson junctions for in-line and overlap geometries. Stability of the static solutions is investigated by checking the sign of the smallest eigenvalue of the associated Sturm-Liouville problem. The change in the junction width leads to the renormalization of the magnetic flux in comparison with the case of a linear one-dimensional model. We study the influence of the model's parameters, and particularly, the shape parameter on the stability of the states of the magnetic flux. We compare the vortex structure and critical curves for the in-line and overlap geometries. Our numerically constructed critical curve of the Josephson junction matches well with the experimental one.
Nungesser, Ernesto
2014-01-01
We show future global non-linear stability of surface symmetric solutions of the Einstein-Vlasov system with a positive cosmological constant. Estimates of higher derivatives of the metric and the matter terms are obtained using an inductive argument. In a recent research monograph Ringstr\\"{o}m shows future non-linear stability of (not necessarily symmetric) solutions of the Einstein-Vlasov system with a non-linear scalar field if certain local estimates on the geometry and the matter terms are fulfilled. We show that these assumptions are satisfied at late times for the case under consideration here which together with Cauchy stability leads to our main conclusion.
Ardela, A.; Cooper, W.A. [Ecole Polytechnique Federale, Lausanne (Switzerland). Centre de Recherche en Physique des Plasma (CRPP)
1996-09-01
In this paper we resume a numerical study of the global stability of plasma with helical boundary deformation and non null net toroidal current. The aim was to see whether external modes with n=1,2 (n toroidal mode number) can be stabilized at values of {beta} inaccessible to the tokamak. L=2,3 configurations with several aspect ratios and different numbers of equilibrium field periods are considered. A large variety of toroidal current densities and different pressure profiles are taken into account. Mercier stability is also investigated. (author) 4 figs., 6 refs.
Stabilization of Parametric Roll Resonance with Active U-Tanks via Lyapunov Control Design
Holden, Christian; Galeazzi, Roberto; Fossen, Thor Inge;
2009-01-01
design of an active u-tank stabilizer is carried out using Lyapunov theory. A nonlinear backstepping controller is developed to provide global exponential stability of roll. An extension of commonly used u-tank models is presented to account for large roll angles, and the control design is tested via...
Phenomenology of stochastic exponential growth
Pirjol, Dan; Jafarpour, Farshid; Iyer-Biswas, Srividya
2017-06-01
Stochastic exponential growth is observed in a variety of contexts, including molecular autocatalysis, nuclear fission, population growth, inflation of the universe, viral social media posts, and financial markets. Yet literature on modeling the phenomenology of these stochastic dynamics has predominantly focused on one model, geometric Brownian motion (GBM), which can be described as the solution of a Langevin equation with linear drift and linear multiplicative noise. Using recent experimental results on stochastic exponential growth of individual bacterial cell sizes, we motivate the need for a more general class of phenomenological models of stochastic exponential growth, which are consistent with the observation that the mean-rescaled distributions are approximately stationary at long times. We show that this behavior is not consistent with GBM, instead it is consistent with power-law multiplicative noise with positive fractional powers. Therefore, we consider this general class of phenomenological models for stochastic exponential growth, provide analytical solutions, and identify the important dimensionless combination of model parameters, which determines the shape of the mean-rescaled distribution. We also provide a prescription for robustly inferring model parameters from experimentally observed stochastic growth trajectories.
Bilateral matrix-exponential distributions
Bladt, Mogens; Esparza, Luz Judith R; Nielsen, Bo Friis
2012-01-01
In this article we define the classes of bilateral and multivariate bilateral matrix-exponential distributions. These distributions have support on the entire real space and have rational moment-generating functions. These distributions extend the class of bilateral phasetype distributions of [1]...
Exponential convergence rate in entropy
Mu-Fa Chen
2007-01-01
The exponential convergence rate in entropy is studied for symmetric forms, with a specia! attention to the Markov chain with a state space having two points only. Some upper and lower bounds of the rate are obtained and five examples with precise or qualitatively exact estimates are presented.
Linear or Exponential Number Lines
Stafford, Pat
2011-01-01
Having decided to spend some time looking at one's understanding of numbers, the author was inspired by "Alex's Adventures in Numberland," by Alex Bellos to look at one's innate appreciation of number. Bellos quotes research studies suggesting that an individual's natural appreciation of numbers is more likely to be exponential rather than linear,…
Stability analysis of switched stochastic neural networks with time-varying delays.
Wu, Xiaotai; Tang, Yang; Zhang, Wenbing
2014-03-01
This paper is concerned with the global exponential stability of switched stochastic neural networks with time-varying delays. Firstly, the stability of switched stochastic delayed neural networks with stable subsystems is investigated by utilizing the mathematical induction method, the piecewise Lyapunov function and the average dwell time approach. Secondly, by utilizing the extended comparison principle from impulsive systems, the stability of stochastic switched delayed neural networks with both stable and unstable subsystems is analyzed and several easy to verify conditions are derived to ensure the exponential mean square stability of switched delayed neural networks with stochastic disturbances. The effectiveness of the proposed results is illustrated by two simulation examples.
Yoshiaki MUROYA; Yoichi ENATSU; Toshikazu KUNIYA
2013-01-01
In this article,we establish the global stability of an endemic equilibrium of multi-group SIR epidemic models,which have not only an exchange of individuals between patches through migration but also cross patch infection between different groups.As a result,we partially generalize the recent result in the article [16].
I. M. STAMOVA; T. G. STAMOV
2014-01-01
Sufficient conditions are investigated for the global stability of the solu-tions to models based on nonlinear impulsive differential equations with“supremum”and variable impulsive perturbations. The main tools are the Lyapunov functions and Razu-mikhin technique. Two illustrative examples are given to demonstrate the effectiveness of the obtained results.
Cuimei ZHANG; Wencheng CHEN; Yu YANG
2006-01-01
In this paper, we study the existence and global asymptotic stability of positive periodic solutions of a delayed periodic predator-prey system with Holling Ⅱ type functional response. By use of the continuation theorem of coincidence degree theory and the method of Lyapunov function, some sufficient conditions are obtained.
Linfei Nie
2013-04-01
Full Text Available In this article, a singular perturbation is introduced to analyze the global asymptotic stability of positive equilibria of ratio-dependent predator-prey models with stage structure for the prey. We prove theoretical results and show numerically that the proposed approach is feasible and efficient.
Sato, T.; Kato, S.; Masuda, A.
2016-09-01
This paper presents a resonance-type vibration energy harvester with a Duffing-type nonlinear oscillator which is designed to perform effectively in a wide frequency band. For the conventional linear vibration energy harvester, the maximum performance of the power generation and its bandwidth are in a relation of trade-off. Introducing a Duffing-type nonlinearity can expand the resonance frequency band and enable the harvester to generate larger electric power in a wider frequency range. However, since such nonlinear oscillator may have coexisting multiple steady-state solutions in the resonance band, it is difficult for the nonlinear harvester to maintain the high performance of the power generation constantly. The principle of self-excitation and entrainment has been utilized to give global stability to the high-energy orbit by destabilizing other unexpected low-energy orbits by introducing a switching circuit of the load resistance between positive and the negative values depending on the response amplitude of the oscillator. In this paper, an improved control law that switches the load resistance according to a frequency-dependent threshold is proposed to ensure the oscillator to respond in the high-energy orbit without ineffective power consumption. Numerical study shows that the steady-state responses of the harvester with the proposed control low are successfully kept on the high-energy orbit without repeating activation of the excitationmode.
Global stability-based design optimization of truss structures using multiple objectives
Tugrul Talaslioglu
2013-02-01
This paper discusses the effect of global stability on the optimal size and shape of truss structures taking into account of a nonlinear critical load, truss weight and serviceability at the same time. The nonlinear critical load is computed by arc-length method. In order to increase the accuracy of the estimation of critical load (ignoring material nonlinearity), an eigenvalue analysis is implemented into the arc-length method. Furthermore, a pure pareto-ranking based multi-objective optimization model is employed for the design optimization of the truss structure with multiple objectives. The computational performance of the optimization model is increased by implementing an island model into its evolutionary search mechanism. The proposed design optimization approach is applied for both size and shape optimization of real world trusses including 101, 224 and 444 bars and successful in generating feasible designations in a large and complex design space. It is observed that the computational performance of pareto-ranking based island model is better than the pure pareto-ranking based model. Therefore, pareto-ranking based island model is recommended to optimize the design of truss structure possessing geometric nonlinearity
Gordillo, José Manuel; Campo-Cortés, Francisco
2014-01-01
In this paper we reveal the physics underlying the conditions needed for the generation of emulsions composed of uniformly sized drops of micrometric or submicrometric diameters when two immiscible streams flow in parallel under the so-called tip streaming regime after Suryo & Basaran (2006). Indeed, when inertial effects in both liquid streams are negligible, the inner to outer flow-rate and viscosity ratios are small enough and the capillary number is above an experimentally determined threshold which is predicted by our theoretical results with small relative errors, a steady micron-sized jet is issued from the apex of a conical drop. Under these conditions, the jet disintegrates into drops with a very well defined mean diameter, giving rise to a monodisperse micro-emulsion. Here, we demonstrate that the regime in which uniformly-sized drops are produced corresponds to values of the capillary number for which the cone-jet system is globally stable. Interestingly enough, our general stability theory rev...
Einstein Static Universe in Exponential $f(T)$ Gravity
Li, Jung-Tsung; Geng, Chao-Qiang
2013-01-01
We analyze the stability of the Einstein static closed and open universe in two types of exponential $f(T)$ gravity theories. We show that the stable solutions exist in these two models. In particular, we find that large regions of parameter space in equation of state $w=p/\\rho$ for the stable universe are allowed in the $f(T)$ theories.
Einstein static universe in exponential f(T) gravity
Li, Jung-Tsung; Lee, Chung-Chi; Geng, Chao-Qiang [National Tsing Hua University, Department of Physics, Hsinchu (China); National Center for Theoretical Sciences, Physics Division, Hsinchu (China)
2013-02-15
We analyze the stability of the Einstein static closed and open universe in two types of exponential f(T) gravity theory. We show that stable solutions exist in these two models. In particular, we find that large regions of parameter space in equation of state w=p/{rho} for the stable universe are allowed in the f(T) theories. (orig.)
The universe evolution in exponential $F(R)$-gravity
Bamba, K; Myrzakulov, R; Odintsov, S D; Sebastiani, L
2013-01-01
A generic feature of viable exponential $F(R)$-gravity is investigated. An additional modification to stabilize the effective dark energy oscillations during matter era is proposed and applied to two viable models. An analysis on the future evolution of the universe is performed. Furthermore, a unified model for early and late-time acceleration is proposed and studied.
Limit laws for exponential families
Balkema, August A.; Klüppelberg, Claudia; Resnick, Sidney I.
1999-01-01
For a real random variable [math] with distribution function [math] , define ¶ [math] ¶ The distribution [math] generates a natural exponential family of distribution functions [math] , where ¶ [math] ¶ We study the asymptotic behaviour of the distribution functions [math] as [math] increases to [math] . If [math] then [math] pointwise on [math] . It may still be possible to obtain a non-degenerate weak limit law [math] by choosing suitable scaling and centring constants [math] an...
Limit laws for exponential families
Balkema, August A.; Klüppelberg, Claudia; Resnick, Sidney I.
1999-01-01
For a real random variable [math] with distribution function [math] , define ¶ [math] ¶ The distribution [math] generates a natural exponential family of distribution functions [math] , where ¶ [math] ¶ We study the asymptotic behaviour of the distribution functions [math] as [math] increases to [math] . If [math] then [math] pointwise on [math] . It may still be possible to obtain a non-degenerate weak limit law [math] by choosing suitable scaling and centring constants [math] an...
On exponential stabilizability of linear neutral systems
Dusser Xavier
2001-01-01
Full Text Available In this paper, we deal with linear neutral functional differential systems. Using an extended state space and an extended control operator, we transform the initial neutral system in an infinite dimensional linear system. We give a sufficient condition for admissibility of the control operator B , conditions under which operator B can be acceptable in order to work with controllability and stabilizability. Necessary and sufficient conditions for exact controllability are provided; in terms of a gramian of controllability N ( μ . Assuming admissibility and exact controllability, a feedback control law is defined from the inverse of the operator N ( μ in order to stabilize exponentially the closed loop system. In this case, the semigroup generated by the closed loop system has an arbitrary decay rate.
Controlling chaos using an exponential control
Gadre, S D; Gadre, Sangeeta D; Varma, V S
1995-01-01
We demonstrate that chaos can be controlled using a multiplicative exponential feedback control. All three types of unstable orbits - unstable fixed points, limit cycles and chaotic trajectories can be stabilized using this control. The control is effective both for maps and flows. The control is significant, particularly for systems with several degrees of freedom, as knowledge of only one variable on the desired unstable orbit is sufficient to settle the system on to that orbit. We find, that in all the cases studied, the transient time is a decreasing function of the stiffness of control. But increasing the stiffness beyond an optimum value can increase the transient time. The control can also be used to create suitable new stable attractors in a map, which did not exist in the original system.
Generalized exponential function and discrete growth models
Souto Martinez, Alexandre; Silva González, Rodrigo; Lauri Espíndola, Aquino
2009-07-01
Here we show that a particular one-parameter generalization of the exponential function is suitable to unify most of the popular one-species discrete population dynamic models into a simple formula. A physical interpretation is given to this new introduced parameter in the context of the continuous Richards model, which remains valid for the discrete case. From the discretization of the continuous Richards’ model (generalization of the Gompertz and Verhulst models), one obtains a generalized logistic map and we briefly study its properties. Notice, however that the physical interpretation for the introduced parameter persists valid for the discrete case. Next, we generalize the (scramble competition) θ-Ricker discrete model and analytically calculate the fixed points as well as their stabilities. In contrast to previous generalizations, from the generalized θ-Ricker model one is able to retrieve either scramble or contest models.
Black Hole Instabilities and Exponential Growth
Prabhu, Kartik
2015-01-01
Recently, a general analysis has been given of the stability with respect to axisymmetric perturbations of stationary-axisymmetric black holes and black branes in vacuum general relativity in arbitrary dimensions. It was shown that positivity of canonical energy on an appropriate space of perturbations is necessary and sufficient for stability. However, the notions of both "stability" and "instability" in this result are significantly weaker than one would like to obtain. In this paper, we prove that if a perturbation of the form $\\pounds_t \\delta g$---with $\\delta g$ a solution to the linearized Einstein equation---has negative canonical energy, then that perturbation must, in fact, grow exponentially in time. The key idea is to make use of the $t$- or ($t$-$\\phi$)-reflection isometry, $i$, of the background spacetime and decompose the initial data for perturbations into their odd and even parts under $i$. We then write the canonical energy as $\\mathscr E\\ = \\mathscr K + \\mathscr U$, where $\\mathscr K$ and $...
Jean Bosco Mbede
2014-01-01
Full Text Available This paper addresses the design of exponential tracking control using backstepping approach for voltage-based control of a flexible joint electrically driven robot (EFJR, to cope with the difficulty introduced by the cascade structure in EFJR dynamic model, to deal with flexibility in joints, and to ensure fast tracking performance. Backstepping approach is used to ensure global asymptotic stability and its common algorithm is modified such that the link position and velocity errors converge to zero exponentially fast. In contrast with the other backstepping controller for electrically driven flexible joint robot manipulators control problem, the proposed controller is robust with respect to stiffness uncertainty and allows tracking fast motions. Simulation results are presented for both single link flexible joint electrically driven manipulator and 2-DOF flexible joint electrically driven robot manipulator. These simulations show very satisfactory tracking performances and the superiority of the proposed controller to those performed in the literature using simple backstepping methodology.
Desjardins, Tiffany
2015-11-01
Various bias electrodes have been inserted into the Helicon-Cathode (HelCat) device at the University of New Mexico, in order to affect intrinsic drift-wave turbulence and flows. The goal of the experiments was to suppress and effect the intrinsic turbulence and with detailed measurements, understand the changes that occur during biasing. The drift-mode in HelCat varies from coherent at low magnetic field (1kG). The first electrode consists of 6 concentric rings set in a ceramic substrate; these rings act as a boundary condition, sitting at the end of the plasma column 2-m away from the source. A negative bias has been found to have no effect on the fluctuations, but a positive bias (Vr>5Te) is required in order to suppress the drift-mode. Two molybdenum grids can also be inserted into the plasma and sit close to the source. Floating or grounding a grid results in suppressing the drift-mode of the system. A negative bias (>-5Te) is found to return the drift-mode, and it is possible to drive a once coherent mode into a broad-band turbulent one. From a bias voltage of -5Tenew mode, which is identified as a parallel-driven Kelvin-Helmholtz mode. At high positive bias, Vg>10Te, a new large-scale global mode is excited. This mode exhibits fluctuations in the ion saturation current, as well as in the potential, with a magnitude >50%. This mode has been identified as the potential relaxation instability (PRI). In order to better understand the modes and changes observed in the plasma, a linear stability code, LSS, was employed. As well, a 1D3V-PIC code utilizing Braginskii's equations was also utilized to understand the high-bias instability.
Global Stability and Hopf Bifurcation of a Predator-Prey Model with Time Delay and Stage Structure
Lingshu Wang
2014-01-01
Full Text Available A delayed predator-prey system with Holling type II functional response and stage structure for both the predator and the prey is investigated. By analyzing the corresponding characteristic equations, the local stability of each of the feasible equilibria of the system is addressed and the existence of a Hopf bifurcation at the coexistence equilibrium is established. By means of persistence theory on infinite dimensional systems, it is proved that the system is permanent. By using Lyapunov functions and the LaSalle invariant principle, the global stability of each of the feasible equilibria of the model is discussed. Numerical simulations are carried out to illustrate the main theoretical results.
Nang, Roberto N; Monahan, Felicia; Diehl, Glendon B; French, Daniel
2015-04-01
Many institutions collect reports in databases to make important lessons-learned available to their members. The Uniformed Services University of the Health Sciences collaborated with the Peacekeeping and Stability Operations Institute to conduct a descriptive and qualitative analysis of global health engagements (GHEs) contained in the Stability Operations Lessons Learned and Information Management System (SOLLIMS). This study used a summative qualitative content analysis approach involving six steps: (1) a comprehensive search; (2) two-stage reading and screening process to identify first-hand, health-related records; (3) qualitative and quantitative data analysis using MAXQDA, a software program; (4) a word cloud to illustrate word frequencies and interrelationships; (5) coding of individual themes and validation of the coding scheme; and (6) identification of relationships in the data and overarching lessons-learned. The individual codes with the most number of text segments coded included: planning, personnel, interorganizational coordination, communication/information sharing, and resources/supplies. When compared to the Department of Defense's (DoD's) evolving GHE principles and capabilities, the SOLLIMS coding scheme appeared to align well with the list of GHE capabilities developed by the Department of Defense Global Health Working Group. The results of this study will inform practitioners of global health and encourage additional qualitative analysis of other lessons-learned databases.
On an Asymptotic Behavior of Exponential Functional Equation
Soon Mo JUNG
2006-01-01
The stability problems of the exponential (functional) equation on a restricted domain will be investigated, and the results will be applied to the study of an asymptotic property of that equation. More precisely, the following asymptotic property is proved: Let X be a real (or complex)normed space. A mapping f : X → C is exponential if and only if f(x + y) - f(x)f(y) → 0 as ‖x‖ + ‖y‖→∞ under some suitable conditions.
On uniform exponential growth for solvable groups
Breuillard, Emmanuel
2006-01-01
Using a theorem of J. Groves we give a ping-pong proof of Osin's uniform exponential growth for solvable groups. We discuss slow exponential growth and show that this phenomenon disappears as one passes to a finite index subgroup.
Teaching about Exponential Growth in Social Studies.
Allen, Rodney F.; LaHart, David E.
1984-01-01
Characteristics of exponential growth which should be taught in social studies classes are listed, and learning activities dealing with exponential growth which can be used in secondary social studies classes are provided. (RM)
Fang-Xiang Wu
2011-08-01
The study of stability is essential for designing or controlling genetic regulatory networks. This paper addresses global and robust stability of genetic regulatory networks with time delays and parameter uncertainties. Most existing results on this issue are based on the linear matrix inequalities (LMIs) approach, which results in checking the existence of a feasible solution to high dimensional LMIs. Based on M-matrix theory, we will present several novel global stability conditions for genetic regulatory networks with time-varying and time-invariant delays. All of these stability conditions are given in terms of M-matrices, for which there are many and very easy ways to be verified. Then, we extend these results to genetic regulatory networks with time delays and parameter uncertainties. To illustrate the effectiveness of our theoretical results, several genetic regulatory networks are analyzed. Compared with existing results in the literature, we also show that our results are less conservative than existing ones with these illustrative genetic regulatory networks.
Notes on the Stochastic Exponential and Logarithm
Larsson, Martin; Ruf, Johannes
2017-01-01
Stochastic exponentials are defined for semimartingales on stochastic intervals, and stochastic logarithms are defined for nonnegative semimartingales, up to the first time the semimartingale hits zero continuously. In the case of (nonnegative) local supermartingales, these two stochastic transformations are inverse to each other. The reciprocal of a stochastic exponential is again a stochastic exponential on a stochastic interval.
Zhang, Wei
2016-03-31
We perform two-dimensional unsteady Navier-Stokes simulation and global linear stability analysis of flow past a heated circular cylinder to investigate the effect of aided buoyancy on the stabilization of the flow. The Reynolds number of the incoming flow is fixed at 100, and the Richardson number characterizing the buoyancy is varied from 0.00 (buoyancy-free case) to 0.10 at which the flow is still unsteady. We investigate the effect of aided buoyancy in stabilizing the wake flow, identify the temporal and spatial characteristics of the growth of the perturbation, and quantify the contributions from various terms comprising the perturbed kinetic energy budget. Numerical results reveal that the increasing Ri decreases the fluctuation magnitude of the characteristic quantities monotonically, and the momentum deficit in the wake flow decays rapidly so that the flow velocity recovers to that of the free-stream; the strain on the wake flow is reduced in the region where the perturbation is the most greatly amplified. Global stability analysis shows that the temporal growth rate of the perturbation decreases monotonically with Ri, reflecting the stabilization of the flow due to aided buoyancy. The perturbation grows most significantly in the free shear layer separated from the cylinder. As Ri increases, the location of maximum perturbation growth moves closer to the cylinder and the perturbation decays more rapidly in the far wake. The introduction of the aided buoyancy alters the base flow, and destabilizes the near wake shear layer mainly through the strain-induced transfer term and the pressure term of the perturbed kinetic energy, whereas the flow is stabilized in the far wake as the strain is alleviated. © 2016 Elsevier Ltd. All rights reserved.
范玮丽
2008-01-01
This paper mainly talks about the currently hot topic-globalization. Firstly, it brings out the general trend about globalization and how to better understand its implication. Secondly, it largely focuses on how to deal with it properly, especially for international marketers. Then, facing with the overwhelming trend, it is time for us to think about seriously what has globalization brought to us. Last but not least, it summarized the author's personal view about the future of globalization and how should we go.
Tulio Rosembuj
2006-12-01
Full Text Available There is no singular globalization, nor is the result of an individual agent. We could start by saying that global action has different angles and subjects who perform it are different, as well as its objectives. The global is an invisible invasion of materials and immediate effects.
New explicit global asymptotic stability criteria for higher order difference equations
El-Morshedy, Hassan A.
2007-12-01
New explicit sufficient conditions for the asymptotic stability of the zero solution of higher order difference equations are obtained. These criteria can be applied to autonomous and nonautonomous equations. The celebrated Clark asymptotic stability criterion is improved. Also, applications to models from mathematical biology and macroeconomics are given.
Robertson, Stanley L
2016-01-01
Magnetic Eternally Collapsing Objects (MECO) have been proposed as the central engines of galactic black hole candidates (GBHC) and supermassive active galactic nuclei (AGN). Previous work has shown that their luminosities and spectral and timing characteristics are in good agreement with observations. These features and the formation of jets are generated primarily by the interactions of accretion disks with an intrinsically magnetic central MECO. The interaction of accretion disks with the anchored magnetic fields of the central objects permits a unified description of properties for GBHC, AGN, neutron stars in low mass x-ray binaries and dwarf novae systems. The previously published MECO models have been based on a quasistatic Schwarzschild metric of General Relativity; however, the only essential feature of this metric is its ability to produce extreme gravitational redshifts. For reasons discussed in this article, an alternative development based on a quasistatic exponential metric is considered here.
Observational Constraints on Exponential Gravity
Yang, Louis; Luo, Ling-Wei; Geng, Chao-Qiang
2010-01-01
We study the observational constraints on the exponential gravity model of f(R)=-beta*Rs(1-e^(-R/Rs)). We use the latest observational data including Supernova Cosmology Project (SCP) Union2 compilation, Two-Degree Field Galaxy Redshift Survey (2dFGRS), Sloan Digital Sky Survey Data Release 7 (SDSS DR7) and Seven-Year Wilkinson Microwave Anisotropy Probe (WMAP7) in our analysis. From these observations, we obtain a lower bound on the model parameter beta at 1.27 (95% CL) but no appreciable upper bound. The constraint on the present matter density parameter is 0.245< Omega_m^0<0.311 (95% CL). We also find out the best-fit value of model parameters on several cases.
UCB Algorithm for Exponential Distributions
Jouini, Wassim
2012-01-01
We introduce in this paper a new algorithm for Multi-Armed Bandit (MAB) problems. A machine learning paradigm popular within Cognitive Network related topics (e.g., Spectrum Sensing and Allocation). We focus on the case where the rewards are exponentially distributed, which is common when dealing with Rayleigh fading channels. This strategy, named Multiplicative Upper Confidence Bound (MUCB), associates a utility index to every available arm, and then selects the arm with the highest index. For every arm, the associated index is equal to the product of a multiplicative factor by the sample mean of the rewards collected by this arm. We show that the MUCB policy has a low complexity and is order optimal.
PARAMETER ESTIMATION OF EXPONENTIAL DISTRIBUTION
XU Haiyan; FEI Heliang
2005-01-01
Because of the importance of grouped data, many scholars have been devoted to the study of this kind of data. But, few documents have been concerned with the threshold parameter. In this paper, we assume that the threshold parameter is smaller than the first observing point. Then, on the basis of the two-parameter exponential distribution, the maximum likelihood estimations of both parameters are given, the sufficient and necessary conditions for their existence and uniqueness are argued, and the asymptotic properties of the estimations are also presented, according to which approximate confidence intervals of the parameters are derived. At the same time, the estimation of the parameters is generalized, and some methods are introduced to get explicit expressions of these generalized estimations. Also, a special case where the first failure time of the units is observed is considered.
Yang Dai; YunZe Cai; Xiao-Ming Xu
2009-01-01
Exponential estimates and sufficient conditions for the exponential synchronization of complex dynamical networks with bounded time-varying delays are given in terms of linear matrix inequalities (LMIs). A generalized complex networks model involving both neutral delays and retarded ones is presented. The exponential synchronization problem of the complex networks is converted equivalently into the exponential stability problem of a group of uncorrelated delay functional differential equations with mixed time-varying delays. By utilizing the free weighting matrix technique, a less conservative delay-dependent synchronization criterion is derived. An illustrative example is provided to demonstrate the effectiveness of the proposed method.
Growing Up to Stability? Financial Globalization, Financial Development and Financial Crises
Bordo, Michael D.; Christopher M. Meissner
2015-01-01
Why did some countries learn to grow up to financial stability and others not? We explore this question by surveying the key determinants and major policy responses to banking, currency, and debt crises between 1880 and present. We divide countries into three groups: leaders, learners, and non-learners. Each of these groups had very different experiences in terms of long-run economic outcomes, financial development, financial stability, crisis frequency, and their policy responses to crises. ...
Global stability analysis of a delayed susceptible-infected-susceptible epidemic model.
Paulhus, Calah; Wang, Xiang-Sheng
2015-01-01
We study a susceptible-infected-susceptible model with distributed delays. By constructing suitable Lyapunov functionals, we demonstrate that the global dynamics of this model is fully determined by the basic reproductive ratio R0. To be specific, we prove that if R0 ≤ 1, then the disease-free equilibrium is globally asymptotically stable. On the other hand, if R0>1, then the endemic equilibrium is globally asymptotically stable. It is remarkable that the model dynamics is independent of the probability of immunity lost.
Convective and global stability analysis of a Mach 5.8 boundary layer grazing a compliant surface
Dettenrieder, Fabian; Bodony, Daniel
2016-11-01
Boundary layer transition on high-speed vehicles is expected to be affected by unsteady surface compliance. The stability properties of a Mach 5.8 zero-pressure-gradient laminar boundary layer grazing a nominally-flat thermo-mechanically compliant panel is considered. The linearized compressible Navier-Stokes equations describe small amplitude disturbances in the fluid while the panel deformations are described by the Kirchhoff-Love plate equation and its thermal state by the transient heat equation. Compatibility conditions that couple disturbances in the fluid to those in the solid yield simple algebraic and robin boundary conditions for the velocity and thermal states, respectively. A local convective stability analysis shows that the panel can modify both the first and second Mack modes when, for metallic-like panels, the panel thickness exceeds the lengthscale δ99 Rex- 0 . 5 . A global stability analysis, which permits finite panel lengths with clamped-clamped boundary conditions, shows a rich eigenvalue spectrum with several branches. Unstable modes are found with streamwise-growing panel deformations leading to Mach wave-type radiation. Stable global modes are also found and have distinctly different panel modes but similar radiation patterns. Air Force Office of Scientific Research.
Yingwei Li
2013-01-01
Full Text Available The global exponential stability issues are considered for almost periodic solution of the neural networks with mixed time-varying delays and discontinuous neuron activations. Some sufficient conditions for the existence, uniqueness, and global exponential stability of almost periodic solution are achieved in terms of certain linear matrix inequalities (LMIs, by applying differential inclusions theory, matrix inequality analysis technique, and generalized Lyapunov functional approach. In addition, the existence and asymptotically almost periodic behavior of the solution of the neural networks are also investigated under the framework of the solution in the sense of Filippov. Two simulation examples are given to illustrate the validity of the theoretical results.
Global stability for delay-dependent HTLV-I model with CTL immune response
Wang, Yan; Liu, Jun
2016-06-01
We present a delay-dependent HTLV-I model with CTL immune response. The basic reproduction number is obtained for the existence of positive steady state. By constructing suitable Lyapunov functions, when the basic reproduction number is less than one, the infection-free steady state is globally asymptotically stable; when the basic reproduction number is greater than one, the infected steady state is globally asymptotically stable.
An exponential polynomial observer for synchronization of chaotic systems
Mata-Machuca, J. L.; Martínez-Guerra, R.; Aguilar-López, R.
2010-12-01
In this paper, we consider the synchronization problem via nonlinear observer design. A new exponential polynomial observer for a class of nonlinear oscillators is proposed, which is robust against output noises. A sufficient condition for synchronization is derived analytically with the help of Lyapunov stability theory. The proposed technique has been applied to synchronize chaotic systems (Rikitake and Rössler systems) by means of numerical simulation.
Chaos and Exponentially Localized Eigenstates in Smooth Hamiltonian Systems
Santhanam, M S; Lakshminarayan, A
1998-01-01
We present numerical evidence to show that the wavefunctions of smooth classically chaotic Hamiltonian systems scarred by certain simple periodic orbits are exponentially localized in the space of unperturbed basis states. The degree of localization, as measured by the information entropy, is shown to be correlated with the local phase space structure around the scarring orbit; indicating sharp localization when the orbit undergoes a pitchfork bifurcation and loses stability.
A Spectral Lyapunov Function for Exponentially Stable LTV Systems
Zhu, J. Jim; Liu, Yong; Hang, Rui
2010-01-01
This paper presents the formulation of a Lyapunov function for an exponentially stable linear timevarying (LTV) system using a well-defined PD-spectrum and the associated PD-eigenvectors. It provides a bridge between the first and second methods of Lyapunov for stability assessment, and will find significant applications in the analysis and control law design for LTV systems and linearizable nonlinear time-varying systems.
Wang, Bin; Shao, Yanchun; Chen, Tao; Chen, Wanping; Chen, Fusheng
2015-12-22
Acetobacter pasteurianus (Ap) CICC 20001 and CGMCC 1.41 are two acetic acid bacteria strains that, because of their strong abilities to produce and tolerate high concentrations of acetic acid, have been widely used to brew vinegar in China. To globally understand the fermentation characteristics, acid-tolerant mechanisms and genetic stabilities, their genomes were sequenced. Genomic comparisons with 9 other sequenced Ap strains revealed that their chromosomes were evolutionarily conserved, whereas the plasmids were unique compared with other Ap strains. Analysis of the acid-tolerant metabolic pathway at the genomic level indicated that the metabolism of some amino acids and the known mechanisms of acetic acid tolerance, might collaboratively contribute to acetic acid resistance in Ap strains. The balance of instability factors and stability factors in the genomes of Ap CICC 20001 and CGMCC 1.41 strains might be the basis for their genetic stability, consistent with their stable industrial performances. These observations provide important insights into the acid resistance mechanism and the genetic stability of Ap strains and lay a foundation for future genetic manipulation and engineering of these two strains.
Wang, Bin; Shao, Yanchun; Chen, Tao; Chen, Wanping; Chen, Fusheng
2015-12-01
Acetobacter pasteurianus (Ap) CICC 20001 and CGMCC 1.41 are two acetic acid bacteria strains that, because of their strong abilities to produce and tolerate high concentrations of acetic acid, have been widely used to brew vinegar in China. To globally understand the fermentation characteristics, acid-tolerant mechanisms and genetic stabilities, their genomes were sequenced. Genomic comparisons with 9 other sequenced Ap strains revealed that their chromosomes were evolutionarily conserved, whereas the plasmids were unique compared with other Ap strains. Analysis of the acid-tolerant metabolic pathway at the genomic level indicated that the metabolism of some amino acids and the known mechanisms of acetic acid tolerance, might collaboratively contribute to acetic acid resistance in Ap strains. The balance of instability factors and stability factors in the genomes of Ap CICC 20001 and CGMCC 1.41 strains might be the basis for their genetic stability, consistent with their stable industrial performances. These observations provide important insights into the acid resistance mechanism and the genetic stability of Ap strains and lay a foundation for future genetic manipulation and engineering of these two strains.
Hua Chen
2015-11-01
Full Text Available In this paper, the global finite-time partial stabilization problem is discussed for a class of nonholonomic mobile wheeled robots with continuous pure state feedback and subject to input saturation. Firstly, for the mobile robot kinematic model, a “3 inputs, 2 chains, 1 generator" nonholonomic chained form systems can be obtained by using a state and input transformation. The continuous, saturated pure state feedback control law is proposed such that the special chained form systems can be stabilized to zero (except an angle variable in a finite time, i.e., finite-time partial stabilization. Secondly, the rigorous stability analysis of the corresponding closed-loop system is presented by applying Lyapunov theorem combined with the finite-time control theory, and the angle variable can be proved to converge to a constant, moreover, its convergent limit may be accurately estimated in advance. Finally, the simulation results show the correctness and the validity of the proposed controller not only for the chained system but also for the original mobile robots system.
Muhammad H. Al-Malack
2016-07-01
Full Text Available Fuel oil flyash (FFA produced in power and water desalination plants firing crude oils in the Kingdom of Saudi Arabia is being disposed in landfills, which increases the burden on the environment, therefore, FFA utilization must be encouraged. In the current research, the effect of adding FFA on the engineering properties of two indigenous soils, namely sand and marl, was investigated. FFA was added at concentrations of 5%, 10% and 15% to both soils with and without the addition of Portland cement. Mixtures of the stabilized soils were thoroughly evaluated using compaction, California Bearing Ratio (CBR, unconfined compressive strength (USC and durability tests. Results of these tests indicated that stabilized sand mixtures could not attain the ACI strength requirements. However, marl was found to satisfy the ACI strength requirement when only 5% of FFA was added together with 5% of cement. When the FFA was increased to 10% and 15%, the mixture’s strength was found to decrease to values below the ACI requirements. Results of the Toxicity Characteristics Leaching Procedure (TCLP, which was performed on samples that passed the ACI requirements, indicated that FFA must be cautiously used in soil stabilization.
Theory, computation, and application of exponential splines
Mccartin, B. J.
1981-01-01
A generalization of the semiclassical cubic spline known in the literature as the exponential spline is discussed. In actuality, the exponential spline represents a continuum of interpolants ranging from the cubic spline to the linear spline. A particular member of this family is uniquely specified by the choice of certain tension parameters. The theoretical underpinnings of the exponential spline are outlined. This development roughly parallels the existing theory for cubic splines. The primary extension lies in the ability of the exponential spline to preserve convexity and monotonicity present in the data. Next, the numerical computation of the exponential spline is discussed. A variety of numerical devices are employed to produce a stable and robust algorithm. An algorithm for the selection of tension parameters that will produce a shape preserving approximant is developed. A sequence of selected curve-fitting examples are presented which clearly demonstrate the advantages of exponential splines over cubic splines.
无
2008-01-01
A ratio-dependent predator-prey system with stage structure and time delays for both prey and predator is considered in this paper. Both the predator and prey have two stages,immature stage and mature stage,and the growth of them is of Lotka-Volterra nature. It is assumed that immature individuals and mature individuals of each species are divided by a fixed age,and that mature predators attack immature prey only. The global stability of three nonnegative equilibria and permanence are presented.
Xu, Jian-Jun; Chen, Yong-Qiang
2011-06-01
The present paper investigates the global instability mechanisms of arrayed-cellular growth with asymptotic approach. We find that the system of directional solidification involves two types of global instability mechanisms: the low-frequency instability and the global oscillatory instability, which are profoundly similar to that found in the system of viscous fingering and free dendritic growth. Based on these global instabilities, the neutral mode selection principle for the limiting state of growth is proposed; the origin and essence of side branching on the interface are elucidated with the so-called global trapped wave mechanism, which involves the interfacial wave reflection and amplification along the interface. It is demonstrated that side branching is self-sustaining and can persist without continuously applying the external noise; the effect of the anisotropy of interfacial energy is not essential for the selection of steady cellular growth and for the origin and formation of side branching at the interface. The comparisons of theoretical results are made with the most recent experimental works and the numerical simulations which show very good quantitative agreement.
Global dynamic modeling of electro-hydraulic 3-UPS/S parallel stabilized platform by bond graph
Zhang, Lijie; Guo, Fei; Li, Yongquan; Lu, Wenjuan
2016-08-01
Dynamic modeling of a parallel manipulator(PM) is an important issue. A complete PM system is actually composed of multiple physical domains. As PMs are widely used in various fields, the importance of modeling the global dynamic model of the PM system becomes increasingly prominent. Currently there lacks further research in global dynamic modeling. A unified modeling approach for the multi-energy domains PM system is proposed based on bond graph and a global dynamic model of the 3-UPS/S parallel stabilized platform involving mechanical and electrical-hydraulic elements is built. Firstly, the screw bond graph theory is improved based on the screw theory, the modular joint model is modeled and the normalized dynamic model of the mechanism is established. Secondly, combined with the electro-hydraulic servo system model built by traditional bond graph, the global dynamic model of the system is obtained, and then the motion, force and power of any element can be obtained directly. Lastly, the experiments and simulations of the driving forces, pressure and flow are performed, and the results show that, the theoretical calculation results of the driving forces are in accord with the experimental ones, and the pressure and flow of the first limb and the third limb are symmetry with each other. The results are reasonable and verify the correctness and effectiveness of the model and the method. The proposed dynamic modeling method provides a reference for modeling of other multi-energy domains system which contains complex PM.
Xungao Zhong
2013-10-01
Full Text Available In this paper, a global-state-space visual servoing scheme is proposed for uncalibrated model-independent robotic manipulation. The scheme is based on robust Kalman filtering (KF, in conjunction with Elman neural network (ENN learning techniques. The global map relationship between the vision space and the robotic workspace is learned using an ENN. This learned mapping is shown to be an approximate estimate of the Jacobian in global space. In the testing phase, the desired Jacobian is arrived at using a robust KF to improve the ENN learning result so as to achieve robotic precise convergence of the desired pose. Meanwhile, the ENN weights are updated (re-trained using a new input-output data pair vector (obtained from the KF cycle to ensure robot global stability manipulation. Thus, our method, without requiring either camera or model parameters, avoids the corrupted performances caused by camera calibration and modeling errors. To demonstrate the proposed scheme’s performance, various simulation and experimental results have been presented using a six-degree-of-freedom robotic manipulator with eye-in-hand configurations.
Generalised Exponential Families and Associated Entropy Functions
Jan Naudts
2008-07-01
Full Text Available A generalised notion of exponential families is introduced. It is based on the variational principle, borrowed from statistical physics. It is shown that inequivalent generalised entropy functions lead to distinct generalised exponential families. The well-known result that the inequality of CramÃ‚Â´er and Rao becomes an equality in the case of an exponential family can be generalised. However, this requires the introduction of escort probabilities.
Exponential Observers for Lotka-Volterra Systems
Dr. V. Sundarapandian
2011-03-01
Full Text Available This paper solves the exponential observer design problem for Lotka-Volterra systems. Explicitly, Sundarapandian’s theorem (2002 for observer design for exponential observer design is used to solve the nonlinear observer design problem for 2-species, 3-species and 4-species Lotka-Volterra systems. Numerical examples are provided to illustrate the effectiveness of the proposed exponential observer design for the Lotka-Volterra systems.
On the exponentials of some structured matrices
Ramakrishna, Viswanath; Costa, F [Department of Mathematical Sciences and Center for Signals, Systems and Communications, University of Texas at Dallas, PO Box 830688, Richardson, TX 75083 (United States)
2004-12-03
This paper provides explicit techniques to compute the exponentials of a variety of structured 4 x 4 matrices. The procedures are fully algorithmic and can be used to find the desired exponentials in closed form. With one exception, they require no spectral information about the matrix being exponentiated. They rely on a mixture of Lie theory and one particular Clifford algebra isomorphism. These can be extended, in some cases, to higher dimensions when combined with techniques such as Givens rotations.
Global asymptotic stability of a delayed SEIRS epidemic model with saturation incidence
Zhang Tailei [College of Mathematics and System Sciences, Xinjiang University, Urumqi 830046 (China)], E-mail: t.l.zhang@126.com; Teng Zhidong [College of Mathematics and System Sciences, Xinjiang University, Urumqi 830046 (China)
2008-09-15
In this paper, the asymptotic behavior of solutions of an autonomous SEIRS epidemic model with the saturation incidence is studied. Using the method of Liapunov-LaSalle invariance principle, we obtain the disease-free equilibrium is globally stable if the basic reproduction number is not greater than one. Moreover, we show that the disease is permanent if the basic reproduction number is greater than one. Furthermore, the sufficient conditions of locally and globally asymptotically stable convergence to an endemic equilibrium are obtained base on the permanence.
van de Merbel, Nico; Savoie, Natasha; Yadav, Manish; Ohtsu, Yoshiaki; White, Joleen; Riccio, Maria Francesca; Dong, Kelly; de Vries, Ronald; Diancin, Julie
2014-01-01
This paper provides a comprehensive overview of stability-related aspects of quantitative bioanalysis and recommends science-based best practices, covering small and large molecules as well as chromatographic and ligand-binding assays. It addresses general aspects, such as the use of reference value
Stability of Global Alfven Waves (Tae, Eae) in Jet Tritium Discharges
Kerner, W.; Borba, D.; Huysmans, G. T. A.; Porcelli, F.; Poedts, S.; Goedbloed, J. P.; Betti, R.
1994-01-01
The interaction of alpha-particles in JET tritium discharges with global Alfven waves via inverse Landau damping is analysed. It is found that alpha-particle driven eigenmodes were stable in the PTE1 and should also be stable in a future 50:50 deuterium-tritium mix discharge aiming at Q(DT) = 1,
Global stabilization of the new chaotic system based on small-gain theorem
Liu Debin [Department of Mathematics, Huazhong University of Science and Technology, Wuhan 430074 (China); Yang Xiaosong [Department of Mathematics, Huazhong University of Science and Technology, Wuhan 430074 (China)], E-mail: yangxs@cqupt.edu.cn
2008-05-15
In this paper, we study chaos control of the new chaotic system. Based on small-gain theorem, a class of nonlinear feedback controllers are designed such that the equilibria of the controlled systems are globally asymptotically stable, thus eliminating chaos.
Minimal data rate stabilization of nonlinear systems over networks with large delays
Persis, Claudio De
2007-01-01
We consider the problem of designing encoders, decoders and controllers which stabilize feedforward nonlinear systems over a communication network with finite bandwidth and large delay. The control scheme guarantees minimal data-rate semi-global asymptotic and local exponential stabilizatioln of the
Stability of Delayed Hopfield Neural Networks with Variable-Time Impulses
Yangjun Pei
2014-01-01
Full Text Available In this paper the globally exponential stability criteria of delayed Hopfield neural networks with variable-time impulses are established. The proposed criteria can also be applied in Hopfield neural networks with fixed-time impulses. A numerical example is presented to illustrate the effectiveness of our theoretical results.
Do, H. Q.; Massa, F.; Tison, T.; Lallemand, B.
2017-02-01
This paper presents a numerical strategy to reanalyze the modified frequency stability analysis of friction induced vibration problem. The stability analysis of a mechanical system relies on several coupling steps, namely a non-linear static analysis followed by linear and complex eigenvalue problems. We thus propose a numerical strategy to perform more rapidly multiple complex eigenvalue analyses. This strategy couples three methods namely, Fuzzy Logic Controllers to manage frictional contact problem, homotopy developments and projection techniques to reanalyze the projection matrices and component mode synthesis to calculate the modified eigensolutions. A numerical application is performed to highlight the efficiency of the strategy and a discussion is proposed in terms of precision and computational time.
The Matrix exponential, Dynamic Systems and Control
Poulsen, Niels Kjølstad
2004-01-01
The matrix exponential can be found in various connections in analysis and control of dynamic systems. In this short note we are going to list a few examples. The matrix exponential usably pops up in connection to the sampling process, whatever it is in a deterministic or a stochastic setting...
The Ronkin number of an exponential sum
Silipo, James
2011-01-01
We give an intrinsic estimate of the number of connected components of the complementary set to the amoeba of an exponential sum with real spectrum improving the result of Forsberg, Passare and Tsikh in the polynomial case and that of Ronkin in the exponential one.
The Matrix exponential, Dynamic Systems and Control
Poulsen, Niels Kjølstad
2004-01-01
The matrix exponential can be found in various connections in analysis and control of dynamic systems. In this short note we are going to list a few examples. The matrix exponential usably pops up in connection to the sampling process, whatever it is in a deterministic or a stochastic setting...
On level-transitivity and exponential growth
Klimann, Ines
2016-01-01
We prove that if the group generated by a Mealy automaton acts level-transitively on a regular rooted tree, then the semigroup generated by the dual automaton has exponential growth, hence giving a decision procedure of exponential growth for a restricted family of automaton semigroups.
q-exponentials on quantum spaces
Wachter, H. [Ludwig-Maximilians-Universitaet, Sektion Physik, Muenchen (Germany)
2004-10-01
We present explicit formulae for q-exponentials on quantum spaces which could be of particular importance in physics, i.e. the q-deformed Minkowski space and the q-deformed Euclidean space with two, three or four dimensions. Furthermore, these formulae can be viewed as 2-, 3- or 4-dimensional analogues of the well-known q-exponential function. (orig.)
Global Stability Analysis of SEIR Model with Holling Type II Incidence Function
Mohammad A. Safi
2012-01-01
Full Text Available A deterministic model for the transmission dynamics of a communicable disease is developed and rigorously analysed. The model, consisting of five mutually exclusive compartments representing the human dynamics, has a globally asymptotically stable disease-free equilibrium (DFE whenever a certain epidemiological threshold, known as the basic reproduction number (ℛ0, is less than unity; in such a case the endemic equilibrium does not exist. On the other hand, when the reproduction number is greater than unity, it is shown, using nonlinear Lyapunov function of Goh-Volterra type, in conjunction with the LaSalle's invariance principle, that the unique endemic equilibrium of the model is globally asymptotically stable under certain conditions. Furthermore, the disease is shown to be uniformly persistent whenever ℛ0>1.
Global stability of trajectories of inertial particles within domains of instability
Sudarsanam, Senbagaraman; Tallapragada, Phanindra
2017-01-01
Finite sized particles exhibit complex dynamics that differ from that of the underlying fluid flow. These dynamics such as chaotic motion, size dependent clustering and separation can have important consequences in many natural and engineered settings. Though fluid streamlines are global attractors for the inertial particles, regions of local instability can exist where the inertial particle can move away from the fluid streamlines. Identifying and manipulating the location of the so called stable and unstable regions in the fluid flow can find important applications in microfluidics. Research in the last two decades has identified analytical criteria that can partition the fluid domain into locally stable and unstable regions. In this paper, we identify two new mechanisms by which neutrally buoyant inertial particles could exhibit globally stable dynamics in the regions of the fluid flow that are thought to be locally unstable and demonstrate this with examples. The examples we use are restricted to the simpler case of time independent fluid flows.
Balsara, Dinshaw S.; Käppeli, Roger
2017-05-01
In this paper we focus on the numerical solution of the induction equation using Runge-Kutta Discontinuous Galerkin (RKDG)-like schemes that are globally divergence-free. The induction equation plays a role in numerical MHD and other systems like it. It ensures that the magnetic field evolves in a divergence-free fashion; and that same property is shared by the numerical schemes presented here. The algorithms presented here are based on a novel DG-like method as it applies to the magnetic field components in the faces of a mesh. (I.e., this is not a conventional DG algorithm for conservation laws.) The other two novel building blocks of the method include divergence-free reconstruction of the magnetic field and multidimensional Riemann solvers; both of which have been developed in recent years by the first author. Since the method is linear, a von Neumann stability analysis is carried out in two-dimensions to understand its stability properties. The von Neumann stability analysis that we develop in this paper relies on transcribing from a modal to a nodal DG formulation in order to develop discrete evolutionary equations for the nodal values. These are then coupled to a suitable Runge-Kutta timestepping strategy so that one can analyze the stability of the entire scheme which is suitably high order in space and time. We show that our scheme permits CFL numbers that are comparable to those of traditional RKDG schemes. We also analyze the wave propagation characteristics of the method and show that with increasing order of accuracy the wave propagation becomes more isotropic and free of dissipation for a larger range of long wavelength modes. This makes a strong case for investing in higher order methods. We also use the von Neumann stability analysis to show that the divergence-free reconstruction and multidimensional Riemann solvers are essential algorithmic ingredients of a globally divergence-free RKDG-like scheme. Numerical accuracy analyses of the RKDG
DARIUSZ ELIGIUSZ STASZCZAK
2015-03-01
Full Text Available This paper analyses reasons of the instability of the world monetary system. The author considers this problem from historical and contemporary perspectives. According to presented point of view banknotes and electronic money which replaced gold and silver coins in popular circulation are the most important reason of the instability. There are also proven positive and negative consequences of money instability. Reforms of the world monetary system need agreement within the global collective hegemony of state-powers and transnational corporations.
Stability analysis of discrete-time BAM neural networks based on standard neural network models
ZHANG Sen-lin; LIU Mei-qin
2005-01-01
To facilitate stability analysis of discrete-time bidirectional associative memory (BAM) neural networks, they were converted into novel neural network models, termed standard neural network models (SNNMs), which interconnect linear dynamic systems and bounded static nonlinear operators. By combining a number of different Lyapunov functionals with S-procedure, some useful criteria of global asymptotic stability and global exponential stability of the equilibrium points of SNNMs were derived. These stability conditions were formulated as linear matrix inequalities (LMIs). So global stability of the discrete-time BAM neural networks could be analyzed by using the stability results of the SNNMs. Compared to the existing stability analysis methods, the proposed approach is easy to implement, less conservative, and is applicable to other recurrent neural networks.
Wen, Sun; Chen, Shihua; Wang, Changping
2008-04-01
Recently a large set of dynamical systems have been intensively investigated as models of complex networks in which there exist a class of very common systems with the property of x-leading asymptotic stability [R. Zhang, M. Hu, Z. Xu, Phys. Lett. A 368 (2007) 276]. In this Letter, we introduced a new complex network model consisted of this systems, then considered its global synchronization. Based on Lasalle invariance principle, global synchronization criteria is derived. We also do not assume coupling matrix is symmetric and irreducible, so our model is more general than that of [R. Zhang, M. Hu, Z. Xu, Phys. Lett. A 368 (2007) 276]. What is more, our assumption f∈Quad(θ,P,α) is weaker than the assumption f∈Quad(D,P,α) in [W. Lu, T. Chen, Physica D 213 (2006) 214], but it improves synchronization results greatly. Numerical simulations of Lorenz systems as the nodes are given to show the effectiveness of the proposed global asymptotic synchronization criteria.
Wen Sun [College of Mathematics and Statistics, Wuhan University, Wuhan 430072 (China)], E-mail: sunwen_2201@163.com; Chen Shihua [College of Mathematics and Statistics, Wuhan University, Wuhan 430072 (China); Wang Changping [Department of Mathematics and Statistics, Dalhousie University, Halifax NS, B3H 3J5 (Canada)
2008-04-21
Recently a large set of dynamical systems have been intensively investigated as models of complex networks in which there exist a class of very common systems with the property of x{sub k}-leading asymptotic stability [R. Zhang, M. Hu, Z. Xu, Phys. Lett. A 368 (2007) 276]. In this Letter, we introduced a new complex network model consisted of this systems, then considered its global synchronization. Based on Lasalle invariance principle, global synchronization criteria is derived. We also do not assume coupling matrix is symmetric and irreducible, so our model is more general than that of [R. Zhang, M. Hu, Z. Xu, Phys. Lett. A 368 (2007) 276]. What is more, our assumption f element of Quad*({theta},P,{alpha}) is weaker than the assumption f element of Quad(D,P,{alpha}) in [W. Lu, T. Chen, Physica D 213 (2006) 214], but it improves synchronization results greatly. Numerical simulations of Lorenz systems as the nodes are given to show the effectiveness of the proposed global asymptotic synchronization criteria.
Erb, Karl-Heinz; Haberl, Helmut; Plutzar, Christoph
2012-08-01
The future bioenergy crop potential depends on (1) changes in the food system (food demand, agricultural technology), (2) political stability and investment security, (3) biodiversity conservation, (4) avoidance of long carbon payback times from deforestation, and (5) energy crop yields. Using a biophysical biomass-balance model, we analyze how these factors affect global primary bioenergy potentials in 2050. The model calculates biomass supply and demand balances for eleven world regions, eleven food categories, seven food crop types and two livestock categories, integrating agricultural forecasts and scenarios with a consistent global land use and NPP database. The TREND scenario results in a global primary bioenergy potential of 77 EJ/yr, alternative assumptions on food-system changes result in a range of 26-141 EJ/yr. Exclusion of areas for biodiversity conservation and inaccessible land in failed states reduces the bioenergy potential by up to 45%. Optimistic assumptions on future energy crop yields increase the potential by up to 48%, while pessimistic assumptions lower the potential by 26%. We conclude that the design of sustainable bioenergy crop production policies needs to resolve difficult trade-offs such as food vs. energy supply, renewable energy vs. biodiversity conservation or yield growth vs. reduction of environmental problems of intensive agriculture.
Plum, Maja
Globalization is often referred to as external to education - a state of affair facing the modern curriculum with numerous challenges. In this paper it is examined as internal to curriculum; analysed as a problematization in a Foucaultian sense. That is, as a complex of attentions, worries, ways...... of reasoning, producing curricular variables. The analysis is made through an example of early childhood curriculum in Danish Pre-school, and the way the curricular variable of the pre-school child comes into being through globalization as a problematization, carried forth by the comparative practices of PISA...
Nada S. Abdelwahab
2017-05-01
Full Text Available The present work concerns with the development of stability indicating the RP-HPLC method for simultaneous determination of guaifenesin (GUF and pseudoephedrine hydrochloride (PSH in the presence of guaifenesin related substance (Guaiacol. GUC, and in the presence of syrup excepients with minimum sample pre-treatment. In the developed RP-HPLC method efficient chromatographic separation was achieved for GUF, PSH, GUC and syrup excepients using ODS column as a stationary phase and methanol: water (50:50, v/v, pH = 4 with orthophosphoric acid as a mobile phase with a flow rate of 1 mL min−1 and UV detection at 210 nm. The chromatographic run time was approximately 10 min. Calibration curves were drawn relating the integrated area under peak to the corresponding concentrations of PSH, GUF and GUC in the range of 1–8, 1–20, 0.4–8 μg mL−1, respectively. The developed method has been validated and met the requirements delineated by ICH guidelines with respect to linearity, accuracy, precision, specificity and robustness. The validated method was successfully applied for determination of the studied drugs in triaminic chest congestion® syrup; moreover its results were statistically compared with those obtained by the official method and no significant difference was found between them.
Jensen, Tom Nørgaard; Wisniewski, Rafal
2014-01-01
An industrial case study involving a large-scale hydraulic network underlying a district heating system subject to structural changes is considered. The problem of controlling the pressure drop across the so-called end-user valves in the network to a designated vector of reference values under......-users. Furthermore, by a proper design of controller gains the closed-loop equilibrium point can be designed to belong to an arbitrarily small neighborhood of the desired equilibrium point. Since there exists a globally asymptotically stable equilibrium point independently on the number of end-users in the system...
A Novel Organic Rankine Cycle System with Improved Thermal Stability and Low Global Warming Fluids
Panesar Angad S
2014-07-01
Full Text Available This paper proposes a novel Organic Rankine Cycle (ORC system for long haul truck application. Rather than typical tail pipe heat recovery configurations, the proposed setup exploits the gaseous streams that are already a load on the engine cooling module. The system uses dual loops connected only by the Exhaust Gas Recirculation (EGR stream. A water blend study is conducted to identify suitable mixtures for the High Temperature (HT loop, while the Low Temperature (LT loop utilises a Low Global Warming (GWP Hydrofluoroether.
Global asymptotic stability of a tracking sectorial fuzzy controller for robot manipulators.
Santibañez, Victor; Kelly, Rafael; Llama, Miguel A
2004-02-01
This paper shows that fuzzy control systems satisfying sectorial properties are effective for motion tracking control of robot manipulators. We propose a controller whose structure is composed by a sectorial fuzzy controller plus a full nonlinear robot dynamics compensation, in such a way that this structure leads to a very simple closed-loop system represented by an autonomous nonlinear differential equation. We demonstrate via Lyapunov theory, that the closed-loop system is globally asymptotically stable. Experimental results show the feasibility of the proposed controller.
Allareddy, Veerasathpurush; Allareddy, Veeratrishul; Rampa, Sankeerth; Nalliah, Romesh P; Elangovan, Satheesh
2015-09-01
The objective of this study is to examine the associations between country level factors (such as human development, economic productivity, and political stability) and their dental research productivity. This study is a cross-sectional analysis of bibliometric data from Scopus search engine. Human Development Index (HDI), Gross National Income per capita (GNI), and Failed State Index measures were the independent variables. Outcomes were "Total number of publications (articles or articles in press) in the field of dentistry" and "Total number of publications in the field of dentistry per million population." Non-parametric tests were used to examine the association between the independent and outcome variables. During the year 2013, a total of 11,952 dental research articles were published across the world. The top 5 publishing countries were United States, Brazil, India, Japan, and United Kingdom. "Very High" HDI countries had significantly higher number of total dental research articles and dental research articles per million population when compared to the "High HDI," "Medium HDI," and "Low HDI" countries (p human development and economic development of a country are linearly correlated with dental research productivity. Dental research productivity also increases with increasing political stability of a country. Copyright © 2015 Elsevier Inc. All rights reserved.
Global stability analysis for cosmological models with non-minimally coupled scalar fields
Skugoreva, Maria A; Vernov, Sergey Yu
2014-01-01
We explorer dynamics of cosmological models with a non-minimally coupled scalar field evolving on a spatially flat Friedmann-Lemaitre-Robertson-Walker background. We consider cosmological models including the Hilbert-Einstein curvature term and the $N$ degree monomial of the scalar field non-minimally coupled to gravity. The potential of the scalar field is the $n$ degree monomial or polynomial.We describe several qualitatively different types of dynamics depending on values of power indices $N$ and $n$. We identify that three main possible pictures correspond to $n2N$ cases. Some special features connected with the important cases of $N=n$ (including quadratic potential with quadratic coupling) and $n=2N$ (which share its asymptotics with the potential of the Higgs-driven inflation) are described separately. A global qualitative analysis allows us to cover most interesting cases of small $N$ and $n$ by a limiting number of phase-space diagrams. The influence of the cosmological constant to the global feature...
He, Lihua; Kota, Pradeep; Aleksandrov, Andrei A; Cui, Liying; Jensen, Tim; Dokholyan, Nikolay V; Riordan, John R
2013-02-01
Most cystic fibrosis is caused by the deletion of a single amino acid (F508) from CFTR and the resulting misfolding and destabilization of the protein. Compounds identified by high-throughput screening to improve ΔF508 CFTR maturation have already entered clinical trials, and it is important to understand their mechanisms of action to further improve their efficacy. Here, we showed that several of these compounds, including the investigational drug VX-809, caused a much greater increase (5- to 10-fold) in maturation at 27 than at 37°C (CFTR can be completely assembled and evade cellular quality control systems, while remaining thermodynamically unstable. He, L., Kota, P., Aleksandrov, A. A., Cui, L., Jensen, T., Dokholyan, N. V., Riordan, J. R. Correctors of ΔF508 CFTR restore global conformational maturation without thermally stabilizing the mutant protein.
Comparing exponential and exponentiated models of drug demand in cocaine users.
Strickland, Justin C; Lile, Joshua A; Rush, Craig R; Stoops, William W
2016-12-01
Drug purchase tasks provide rapid and efficient measurement of drug demand. Zero values (i.e., prices with zero consumption) present a quantitative challenge when using exponential demand models that exponentiated models may resolve. We aimed to replicate and advance the utility of using an exponentiated model by demonstrating construct validity (i.e., association with real-world drug use) and generalizability across drug commodities. Participants (N = 40 cocaine-using adults) completed Cocaine, Alcohol, and Cigarette Purchase Tasks evaluating hypothetical consumption across changes in price. Exponentiated and exponential models were fit to these data using different treatments of zero consumption values, including retaining zeros or replacing them with 0.1, 0.01, or 0.001. Excellent model fits were observed with the exponentiated model. Means and precision fluctuated with different replacement values when using the exponential model but were consistent for the exponentiated model. The exponentiated model provided the strongest correlation between derived demand intensity (Q0) and self-reported free consumption in all instances (Cocaine r = .88; Alcohol r = .97; Cigarette r = .91). Cocaine demand elasticity was positively correlated with alcohol and cigarette elasticity. Exponentiated parameters were associated with real-world drug use (e.g., weekly cocaine use) whereas these correlations were less consistent for exponential parameters. Our findings show that selection of zero replacement values affects demand parameters and their association with drug-use outcomes when using the exponential model but not the exponentiated model. This work supports the adoption of the exponentiated demand model by replicating improved fit and consistency and demonstrating construct validity and generalizability. (PsycINFO Database Record (c) 2016 APA, all rights reserved).
Exponential stabilization of a Rayleigh beam using collocated control
Weiss, George; Curtain, Ruth F.
We consider a hinged elastic beam described by the Rayleigh beam equation on the interval [0, pi]. We assume the presence of two sensors: one measures the angular velocity of the beam at a point xi is an element of [0, pi] and the other measures the bending (curvature) of the beam at the same point.
Stabilization of model-based networked control systems
Miranda, Francisco; Abreu, Carlos; Mendes, Paulo M.
2016-06-01
A class of networked control systems called Model-Based Networked Control Systems (MB-NCSs) is considered. Stabilization of MB-NCSs is studied using feedback controls and simulation of stabilization for different feedbacks is made with the purpose to reduce the network trafic. The feedback control input is applied in a compensated model of the plant that approximates the plant dynamics and stabilizes the plant even under slow network conditions. Conditions for global exponential stabilizability and for the choosing of a feedback control input for a given constant time between the information moments of the network are derived. An optimal control problem to obtain an optimal feedback control is also presented.
Gogoi, Bidyut B.
2016-07-01
We have recently analyzed the global two-dimensional (2D) stability of the staggered lid-driven cavity (LDC) flow with a higher order compact (HOC) approach. In the analysis, critical parameters are determined for both the parallel and anti-parallel motion of the lids and a detailed analysis has been carried out on either side of the critical values. In this article, we carry out an investigation of flow stabilities inside a two-sided cross lid-driven cavity with a pair of opposite lids moving in both parallel and anti-parallel directions. On discretization, the governing 2D Navier-Stokes (N-S) equations describing the steady flow and flow perturbations results in a generalized eigenvalue problem which is solved for determining the critical parameters on four different grids. Elaborate computation is performed for a wide range of Reynolds numbers (Re) on either side of the critical values in the range 200 ⩽ Re ⩽ 10000. For flows below the critical Reynolds number Rec, our numerical results are compared with established steady-state results and excellent agreement is obtained in all the cases. For Reynolds numbers above Rec, phase plane and spectral density analysis confirmed the existence of periodic, quasi-periodic, and stable flow patterns.
An Exponential Bound for Cox Regression☆
Kosorok, M. R.
2012-01-01
We present an asymptotic exponential bound for the deviation of the survival function estimator of the Cox model. We show that the bound holds even when the proportional hazards assumption does not hold. PMID:23565013
An Exponential Bound for Cox Regression.
Goldberg, Y; Kosorok, M R
2012-07-01
We present an asymptotic exponential bound for the deviation of the survival function estimator of the Cox model. We show that the bound holds even when the proportional hazards assumption does not hold.
Ebola Viral Disease in West Africa: A Threat to Global Health, Economy and Political Stability.
Omoleke, Semeeh Akinwale; Mohammed, Ibrahim; Saidu, Yauba
2016-08-17
The West African sub-continent is currently experiencing its first, and ironically, the largest and longest Ebola viral diseases (EVD) outbreak ever documented in modern medical history. The current outbreak is significant in several ways, including longevity, magnitude of morbidity and mortality, occurrence outside the traditional niches, rapid spread and potential of becoming a global health tragedy. The authors provided explicit insights into the current and historical background, drivers of the epidemic, societal impacts, status of vaccines and drugs development and proffered recommendations to halt and prevent future occurrences. The authors reviewed mainly five databases and a hand search of key relevant literature. We reviewed 51 articles that were relevant up until the 18(th) of August 2014. The authors supplemented the search with reference list of relevant articles and grey literature as well as relevant Internet websites. Article searches were limited to those published either in English or French. There are strong indications that the EVD may have been triggered by increased human activities and encroachment into the forest ecosystem spurred by increasing population and poverty-driven forest-dependent local economy. Containment efforts are being hampered by weak and fragile health systems, including public health surveillance and weak governance, certain socio-anthropological factors, fast travels (improved transport systems) and globalization. The societal impacts of the EBV outbreak are grave, including economic shutdown, weakening of socio-political systems, psychological distress, and unprecedented consumption of scarce health resources. The research and development (R&D) pipeline for product against EBV seems grossly insufficient. The outbreak of Ebola and the seeming difficulty to contain the epidemic is simply a reflection of the weak health system, poor surveillance and emergency preparedness/response, poverty and disconnect between the
Ebola viral disease in West Africa: a threat to global health, economy and political stability
Semeeh Akinwale Omoleke
2016-08-01
Full Text Available The West African sub-continent is currently experiencing its first, and ironically, the largest and longest Ebola viral diseases (EVD outbreak ever documented in modern medical history. The current outbreak is significant in several ways, including longevity, magnitude of morbidity and mortality, occurrence outside the traditional niches, rapid spread and potential of becoming a global health tragedy. The authors provided explicit insights into the current and historical background, drivers of the epidemic, societal impacts, status of vaccines and drugs development and proffered recommendations to halt and prevent future occurrences. The authors reviewed mainly five databases and a hand search of key relevant literature. We reviewed 51 articles that were relevant up until the 18th of August 2014. The authors supplemented the search with reference list of relevant articles and grey literature as well as relevant Internet websites. Article searches were limited to those published either in English or French. There are strong indications that the EVD may have been triggered by increased human activities and encroachment into the forest ecosystem spurred by increasing population and povertydriven forest-dependent local economy. Containment efforts are being hampered by weak and fragile health systems, including public health surveillance and weak governance, certain socio-anthropological factors, fast travels (improved transport systems and globalization. The societal impacts of the EBV outbreak are grave, including economic shutdown, weakening of socio-political systems, psychological distress, and unprecedented consumption of scarce health resources. The research and development (R&D pipeline for product against EBV seems grossly insufficient. The outbreak of Ebola and the seeming difficulty to contain the epidemic is simply a reflection of the weak health system, poor surveillance and emergency preparedness/ response, poverty and disconnect
Exponential Attractor for the Boussinesq Equation with Strong Damping and Clamped Boundary Condition
Fan Geng; Ruizhai Li; Xiaojun Zhang; Xiangyu Ge
2016-01-01
The paper studies the existence of exponential attractor for the Boussinesq equation with strong damping and clamped boundary condition utt-Δu+Δ2u-Δut-Δg(u)=f(x). The main result is concerned with nonlinearities g(u) with supercritical growth. In that case, we construct a bounded absorbing set with further regularity and obtain quasi-stability estimates. Then the exponential attractor is established in natural energy space V2×H.
When economic growth is less than exponential
Groth, Christian; Koch, Karl-Josef; Steger, Thomas
2010-01-01
This paper argues that growth theory needs a more general notion of "regularity" than that of exponential growth. We suggest that paths along which the rate of decline of the growth rate is proportional to the growth rate itself deserve attention. This opens up for considering a richer set of par......) serves as illustration that a continuum of "regular" growth processes fill the whole range between exponential growth and complete stagnation....
When economic growth is less than exponential
Groth, Christian; Koch, Karl-Josef; Steger, Thomas M.
2009-01-01
This paper argues that growth theory needs a more general notion of “regularity” than that of exponential growth. We suggest that paths along which the rate of decline of the growth rate is proportional to the growth rate itself deserve attention. This opens up for considering a richer set of parameter combinations than in standard growth models. And it avoids the usual oversimplistic dichotomy of either exponential growth or stagnation. Allowing zero population growth in three ...
Continued Fraction Algorithm for Matrix Exponentials
无
2001-01-01
A recursive rational algorithm for matrix exponentials was obtained by making use of the generalized inverse of a matrix in this paper. On the basis of the n-th convergence of Thiele-type continued fraction expansion, a new type of the generalized inverse matrix-valued Padé approximant (GMPA) for matrix exponentials was defined and its remainder formula was proved. The results of this paper were illustrated by some examples.
Environmental stability affects phenotypic evolution in a globally distributed marine picoplankton
Schaum, C-Elisa; Rost, Björn; Collins, Sinéad
2016-01-01
Marine phytoplankton can evolve rapidly when confronted with aspects of climate change because of their large population sizes and fast generation times. Despite this, the importance of environment fluctuations, a key feature of climate change, has received little attention—selection experiments with marine phytoplankton are usually carried out in stable environments and use single or few representatives of a species, genus or functional group. Here we investigate whether and by how much environmental fluctuations contribute to changes in ecologically important phytoplankton traits such as C:N ratios and cell size, and test the variability of changes in these traits within the globally distributed species Ostreococcus. We have evolved 16 physiologically distinct lineages of Ostreococcus at stable high CO2 (1031±87 μatm CO2, SH) and fluctuating high CO2 (1012±244 μatm CO2, FH) for 400 generations. We find that although both fluctuation and high CO2 drive evolution, FH-evolved lineages are smaller, have reduced C:N ratios and respond more strongly to further increases in CO2 than do SH-evolved lineages. This indicates that environmental fluctuations are an important factor to consider when predicting how the characteristics of future phytoplankton populations will have an impact on biogeochemical cycles and higher trophic levels in marine food webs. PMID:26125683
Beretta, E; Capasso, V; Rinaldi, F
1988-01-01
The paper contains an extension of the general ODE system proposed in previous papers by the same authors, to include distributed time delays in the interaction terms. The new system describes a large class of Lotka-Volterra like population models and epidemic models with continuous time delays. Sufficient conditions for the boundedness of solutions and for the global asymptotic stability of nontrivial equilibrium solutions are given. A detailed analysis of the epidemic system is given with respect to the conditions for global stability. For a relevant subclass of these systems an existence criterion for steady states is also given.
Active Flow Control and Global Stability Analysis of Separated Flow Over a NACA 0012 Airfoil
Munday, Phillip M.
definition of the coefficient of momentum, which successfully characterizes suppression of separation and lift enhancement. The effect of angular momentum is incorporated into the modified coefficient of momentum by introducing a characteristic swirling jet velocity based on the non-dimensional swirl number. With the modified coefficient of momentum, this single value is able to categorize controlled flows into separated, transitional, and attached flows. With inadequate control input (separated flow regime), lift decreased compared to the baseline flow. Increasing the modified coefficient of momentum, flow transitions from separated to attached and accordingly results in improved aerodynamic forces. Modifying the spanwise spacing, it is shown that the minimum modified coefficient of momentum input required to begin transitioning the flow is dependent on actuator spacing. The growth (or decay) of perturbations can facilitate or inhibit the influence of flow control inputs. Biglobal stability analysis is considered to further analyze the behavior of control inputs on separated flow over a symmetric airfoil. Assuming a spanwise periodic waveform for the perturbations, the eigenvalues and eigenvectors about a base flow are solved to understand the influence of spanwise variation on the development of the flow. Two algorithms are developed and validated to solve for the eigenvalues of the flow: an algebraic eigenvalue solver (matrix based) and a time-stepping algorithm. The matrix based approach is formulated without ever storing the matrices, creating a computationally memory efficient algorithm. Increasing the Reynolds number to Re = 23,000 over a NACA 0012 airfoil, the time-stepper method is implemented due to rising computational cost of the matrix-based method. Stability analysis about the time-averaged flow is performed for spanwise wavenumbers of beta = 1/c, 10pi/ c and 20pi/c, which the latter two wavenumbers are representative of the spanwise spacing between the
Practical stabilization of a class of uncertain time-varying nonlinear delay systems
Bassem Ben HAMED; Mohamed Ali HAMMAMI
2009-01-01
In this paper we deal with a class of uncertain time-varying nonlinear systems with a state delay. Under some assumptions, we construct some stabilizing continuous feedback, i.e. linear and nonlinear in the state, which can guarantee global uniform exponential stability and global uniform practical convergence of the considered system. The quadratic Lyapunov function for the nominal stable system is used as a Lyapunov candidate function for the global system. The results developed in this note are applicable to a class of dynamical systems with uncertain time-delay. Our result is illustrated by a numerical example.
„STABILITY AND GROWTH PACT, COMMUNITY DOCUMENT „REVIVED” IN THE CURRENT GLOBAL ECONOMIC CRISIS”
ROXANA-DANIELA PAUN
2011-04-01
Full Text Available The article proposes to make a reasoned radiography Stability and Growth Pact, EU document revived therefore need to strengthen financial discipline and budget 6 to 7 September 2010 meeting of the Economic and Financial Affairs Council (ECOFIN. He talked about the introduction of the Stability and Growth in a 'European quarter' which will be monitored in structural and fiscal policies of the Member States. He also held a first exchange of views about the possible introduction of a levy on banks and a tax on financial transactions. Thus, the European Union has moved to create the world's first supranational system of control over the financial markets, particularly in order to reduce the risk of global financial crisis. The system will act in early 2011. For the first time in history, European financial control agencies will have more seats than national governments. In addition, the European Central Bank will see a branch that will track the emergence of crisis risk.The financial crisis has diminished the EU's growth potential, and made it clear just how interdependent its members' economies are, particularly inside the eurozone. The most important priority now is to restore growth and create effective mechanisms for regulating financial markets - in Europe and internationally. In strengthening its system of economic governance, Europe must learn from previous shortcomings which have put the financial stability of the whole eurozone at risk:- poor observance of the EU's sound rules and procedures for economic policy coordination- insufficient reduction in public debt during the good times – with peer pressure proving an adequate incentive- failure to deal effectively with the build-up of macroeconomic imbalances - despite the Commission's warnings – resulting in high current account deficits, large external indebtedness and high public debt levels in a number of countries (above the official 60% limit for eurozone countries. Greater economic
van de Vyver, Hans
2006-04-01
This paper provides an investigation of the stability properties of a family of exponentially fitted Runge-Kutta-Nystrom (EFRKN) methods. P-stability is a very important property usually demanded for the numerical solution of stiff oscillatory second-order initial value problems. P-stable EFRKN methods with arbitrary high order are presented in this work. We have proved our results based on a symmetry argument.
Dynamic Transcriptional Regulation of Fis in Salmonella During the Exponential Phase.
Wang, Hui; Wang, Lei; Li, Ping; Hu, Yilang; Zhang, Wei; Tang, Bo
2015-12-01
Fis is one of the most important global regulators and has attracted extensive research attention. Many studies have focused on comparing the Fis global regulatory networks for exploring Fis function during different growth stages, such as the exponential and stationary stages. Although the Fis protein in bacteria is mainly expressed in the exponential phase, the dynamic transcriptional regulation of Fis during the exponential phase remains poorly understood. To address this question, we used RNA-seq technology to identify the Fis-regulated genes in the S. enterica serovar Typhimurium during the early exponential phase, and qRT-PCR was performed to validate the transcriptional data. A total of 1495 Fis-regulated genes were successfully identified, including 987 Fis-repressed genes and 508 Fis-activated genes. Comparing the results of this study with those of our previous study, we found that the transcriptional regulation of Fis was diverse during the early- and mid-exponential phases. The results also showed that the strong positive regulation of Fis on Salmonella pathogenicity island genes in the mid-exponential phase transitioned into insignificant effect in the early exponential phase. To validate these results, we performed a cell infection assay and found that Δfis only exhibited a 1.49-fold decreased capacity compared with the LT2 wild-type strain, indicating a large difference from the 6.31-fold decrease observed in the mid-exponential phase. Our results provide strong evidence for a need to thoroughly understand the dynamic transcriptional regulation of Fis in Salmonella during the exponential phase.
Small data global existence for a fluid-structure model
Ignatova, Mihaela; Kukavica, Igor; Lasiecka, Irena; Tuffaha, Amjad
2017-02-01
We address the system of partial differential equations modeling motion of an elastic body inside an incompressible fluid. The fluid is modeled by the incompressible Navier-Stokes equations while the structure is represented by the damped wave equation with interior damping. The additional boundary stabilization γ, considered in our previous paper, is no longer necessary. We prove the global existence and exponential decay of solutions for small initial data in a suitable Sobolev space.
BiGlobal linear stability analysis on low-Re flow past an airfoil at high angle of attack
Zhang, Wei
2016-04-04
We perform BiGlobal linear stability analysis on flow past a NACA0012 airfoil at 16° angle of attack and Reynolds number ranging from 400 to 1000. The steady-state two-dimensional base flows are computed using a well-tested finite difference code in combination with the selective frequency damping method. The base flow is characterized by two asymmetric recirculation bubbles downstream of the airfoil whose streamwise extent and the maximum reverse flow velocity increase with the Reynolds number. The stability analysis of the flow past the airfoil is carried out under very small spanwise wavenumber β = 10−4 to approximate the two-dimensional perturbation, and medium and large spanwise wavenumbers (β = 1–8) to account for the three-dimensional perturbation. Numerical results reveal that under small spanwise wavenumber, there are at most two oscillatory unstable modes corresponding to the near wake and far wake instabilities; the growth rate and frequency of the perturbation agree well with the two-dimensional direct numerical simulation results under all Reynolds numbers. For a larger spanwise wavenumber β = 1, there is only one oscillatory unstable mode associated with the wake instability at Re = 400 and 600, while at Re = 800 and 1000 there are two oscillatory unstable modes for the near wake and far wake instabilities, and one stationary unstable mode for the monotonically growing perturbation within the recirculation bubble via the centrifugal instability mechanism. All the unstable modes are weakened or even suppressed as the spanwise wavenumber further increases, among which the stationary mode persists until β = 4.
徐瑞; 陈兰荪
2002-01-01
A three-species ratio-dependent predator-prey diffusion model with time delays is investigated. It is shown that the system is uniformly persistent under some appropriate conditions, and sufficient conditions are obtained for the global stability of the positive equilibrium of the system.
袁堃; 费树岷; 曹进德
2012-01-01
分析了Cohen-Grossberg神经网络的指数稳定性(局部指数稳定和全局指数稳定).给出了基于矩阵测度的判定Cohen-Grossberg神经网络的指数稳定的充分条件.并且对于局部指数稳定的平衡点,给出了其吸引域的估计；对于全局指数稳定的平衡点,给出了其指数收敛的速率.该结果可以用于神经网络容错能力的估计以及其指数收敛速率的估计,因此在设计Cohen-Grossberg神经网络中具有很重要的现实意义.%Exponential stability (local exponential stability and global exponential stability) was analyzed for Cohen-Grossberg neural networks.Simple sufficient conditions in the form of matrix measure were derived for ascertaining the local exponential stability or the global exponential stability for Cohen-Grossberg neural networks.Moreover,for the locally exponentially stable equilibrium point,its attraction region was estimated; for the globally exponentially stable equilibrium point,its convergence rate was assessed.The proposed results can be used for the evaluation of fault-tolerance capability and the estimation of exponential decay rate of the networks,and are hence of practical significance for designing Cohen-Grossberg neural networks.
ESTIMATION ACCURACY OF EXPONENTIAL DISTRIBUTION PARAMETERS
muhammad zahid rashid
2011-04-01
Full Text Available The exponential distribution is commonly used to model the behavior of units that have a constant failure rate. The two-parameter exponential distribution provides a simple but nevertheless useful model for the analysis of lifetimes, especially when investigating reliability of technical equipment.This paper is concerned with estimation of parameters of the two parameter (location and scale exponential distribution. We used the least squares method (LSM, relative least squares method (RELS, ridge regression method (RR, moment estimators (ME, modified moment estimators (MME, maximum likelihood estimators (MLE and modified maximum likelihood estimators (MMLE. We used the mean square error MSE, and total deviation TD, as measurement for the comparison between these methods. We determined the best method for estimation using different values for the parameters and different sample sizes
Modeling aftershocks as a stretched exponential relaxation
Mignan, A.
2015-11-01
The decay rate of aftershocks has been modeled as a power law since the pioneering work of Omori in the late nineteenth century. Although other expressions have been proposed in recent decades to describe the temporal behavior of aftershocks, the number of model comparisons remains limited. After reviewing the aftershock models published from the late nineteenth century until today, I solely compare the power law, pure exponential and stretched exponential expressions defined in their simplest forms. By applying statistical methods recommended recently in applied mathematics, I show that all aftershock sequences tested in three regional earthquake catalogs (Southern and Northern California, Taiwan) and with three declustering techniques (nearest-neighbor, second-order moment, window methods) follow a stretched exponential instead of a power law. These results infer that aftershocks are due to a simple relaxation process, in accordance with most other relaxation processes observed in Nature.
Unification modulo a partial theory of exponentiation
Kapur, Deepak; Narendran, Paliath; 10.4204/EPTCS.42.2
2010-01-01
Modular exponentiation is a common mathematical operation in modern cryptography. This, along with modular multiplication at the base and exponent levels (to different moduli) plays an important role in a large number of key agreement protocols. In our earlier work, we gave many decidability as well as undecidability results for multiple equational theories, involving various properties of modular exponentiation. Here, we consider a partial subtheory focussing only on exponentiation and multiplication operators. Two main results are proved. The first result is positive, namely, that the unification problem for the above theory (in which no additional property is assumed of the multiplication operators) is decidable. The second result is negative: if we assume that the two multiplication operators belong to two different abelian groups, then the unification problem becomes undecidable.
ESTIMATION ACCURACY OF EXPONENTIAL DISTRIBUTION PARAMETERS
muhammad zahid rashid
2011-04-01
Full Text Available The exponential distribution is commonly used to model the behavior of units that have a constant failure rate. The two-parameter exponential distribution provides a simple but nevertheless useful model for the analysis of lifetimes, especially when investigating reliability of technical equipment.This paper is concerned with estimation of parameters of the two parameter (location and scale exponential distribution. We used the least squares method (LSM, relative least squares method (RELS, ridge regression method (RR, moment estimators (ME, modified moment estimators (MME, maximum likelihood estimators (MLE and modified maximum likelihood estimators (MMLE. We used the mean square error MSE, and total deviation TD, as measurement for the comparison between these methods. We determined the best method for estimation using different values for the parameters and different sample sizes
When Economic Growth is Less than Exponential
Groth, Christian; Koch, Karl-Josef; Steger, Thomas M.
This paper argues that growth theory needs a more general notion of "regularity" than that of exponential growth. We suggest that paths along which the rate of decline of the growth rate is proportional to the growth rate itself deserve attention. This opens up for considering a richer set...... of parameter combinations than in standard growth models. And it avoids the usual oversimplistic dichotomy of either exponential growth or stagnation. Allowing zero population growth in three different growth models (the Jones R&D-based model, a learning-by-doing model, and an embodied technical change model......) serve as illustrations that a continuum of "regular" growth processes fill the whole range between exponential growth and complete stagnation....
The technological singularity and exponential medicine
Iraj Nabipour
2016-01-01
Full Text Available The "technological singularity" is forecasted to occur in 2045. It is a point when non-biological intelligence becomes more intelligent than humans and each generation of intelligent machines re-designs itself smarter. Beyond this point, there is a symbiosis between machines and humans. This co-existence will produce incredible impacts on medicine that its sparkles could be seen in healthcare industry and the future medicine since 2025. Ray Kurzweil, the great futurist, suggested that three revolutions in science and technology consisting genetic and molecular science, nanotechnology, and robotic (artificial intelligence provided an exponential growth rate for medicine. The "exponential medicine" is going to create more disruptive technologies in healthcare industry. The exponential medicine shifts the paradigm of medical philosophy and produces significant impacts on the healthcare system and patient-physician relationship.
Static vortices in long Josephson junctions of exponentially varying width
Semerdjieva, E. G.; Boyadjiev, T. L.; Shukrinov, Yu. M.
2004-06-01
A numerical simulation is carried out for static vortices in a long Josephson junction with an exponentially varying width. At specified values of the parameters the corresponding boundary-value problem admits more than one solution. Each solution (distribution of the magnetic flux in the junction) is associated to a Sturm-Liouville problem, the smallest eigenvalue of which can be used, in a first approximation, to assess the stability of the vortex against relatively small spatiotemporal perturbations. The change in width of the junction leads to a renormalization of the magnetic flux in comparison with the case of a linear one-dimensional model. The influence of the model parameters on the stability of the states of the magnetic flux is investigated in detail, particularly that of the shape parameter. The critical curve of the junction is constructed from pieces of the critical curves for the different magnetic flux distributions having the highest critical currents for the given magnetic field.
Zheng, Cheng-De; Shan, Qi-He; Zhang, Huaguang; Wang, Zhanshan
2013-05-01
The globally exponential stabilization problem is investigated for a general class of stochastic Cohen-Grossberg neural networks with both Markovian jumping parameters and mixed mode-dependent time-delays. The mixed time-delays consist of both discrete and distributed delays. This paper aims to design a memoryless state feedback controller such that the closed-loop system is stochastically exponentially stable in the mean square sense. By introducing a new Lyapunov-Krasovskii functional that accounts for the mode-dependent mixed delays, stochastic analysis is conducted in order to derive delay-dependent criteria for the exponential stabilization problem. Three numerical examples are carried out to demonstrate the feasibility of our delay-dependent stabilization criteria.
Exponential Polynomial Approximation with Unrestricted Upper Density
Xiang Dong YANG
2011-01-01
We take a new approach to obtaining necessary and sufficient conditions for the incompleteness of exponential polynomials in Lp/α, where Lp/α is the weighted Banach space of complex continuous functions f defined on the real axis (R)satisfying (∫+∞/-∞|f(t)|pe-α(t)dt)1/p, 1 < p < ∞, and α(t) is a nonnegative continuous function defined on the real axis (R). In this paper, the upper density of the sequence which forms the exponential polynomials is not required to be finite. In the study of weighted polynomial approximation, consideration of the case is new.
Metastability of exponentially perturbed Markov chains
陈大岳; 冯建峰; 钱敏平
1996-01-01
A family of irreducible Markov chains on a finite state space is considered as an exponential perturbation of a reducible Markov chain. This is a generalization of the Freidlin-Wentzell theory, motivated by studies of stochastic Ising models, neural network and simulated annealing. It is shown that the metastability is a universal feature for this wide class of Markov chains. The metastable states are simply those recurrent states of the reducible Markov chain. Higher level attractors, related attractive basins and their pyramidal structure are analysed. The logarithmic asymptotics of the hitting time of various sets are estimated. The hitting time over its mean converges in law to the unit exponential distribution.
Exponential Operators, Dobinski Relations and Summability
Blasiak, P; Horzela, A; Penson, K A; Solomon, A I
2005-01-01
We investigate properties of exponential operators preserving the particle number using combinatorial methods developed in order to solve the boson normal ordering problem. In particular, we apply generalized Dobinski relations and methods of multivariate Bell polynomials which enable us to understand the meaning of perturbation-like expansions of exponential operators. Such expansions, obtained as formal power series, are everywhere divergent but the Pade summation method is shown to give results which very well agree with exact solutions got for simplified quantum models of the one mode bosonic systems.
Exponential Data Fitting and its Applications
Pereyra, Victor
2010-01-01
Real and complex exponential data fitting is an important activity in many different areas of science and engineering, ranging from Nuclear Magnetic Resonance Spectroscopy and Lattice Quantum Chromodynamics to Electrical and Chemical Engineering, Vision and Robotics. The most commonly used norm in the approximation by linear combinations of exponentials is the l2 norm (sum of squares of residuals), in which case one obtains a nonlinear separable least squares problem. A number of different methods have been proposed through the years to solve these types of problems and new applications appear
Nonuniform exponential dichotomies and Lyapunov functions
Barreira, Luis; Dragičević, Davor; Valls, Claudia
2017-05-01
For the nonautonomous dynamics defined by a sequence of bounded linear operators acting on an arbitrary Hilbert space, we obtain a characterization of the notion of a nonuniform exponential dichotomy in terms of quadratic Lyapunov sequences. We emphasize that, in sharp contrast with previous results, we consider the general case of possibly noninvertible linear operators, thus requiring only the invertibility along the unstable direction. As an application, we give a simple proof of the robustness of a nonuniform exponential dichotomy under sufficiently small linear perturbations.
Phani Y.
2013-05-01
Full Text Available In this paper we make an attempt to construct a new three parameter linear model, we call this new model as Arc Tan-Exponential Type distribution, by applying Stereographic Projection or equivalently Bilinear transformation on Wrapped Exponential distribution, Probability density and cumulative distribution functions of this new model are presented and their graphs are plotted for various values of parameters.
Ellis, Amy B.; Ozgur, Zekiye; Kulow, Torrey; Dogan, Muhammed F.; Amidon, Joel
2016-01-01
This article presents an Exponential Growth Learning Trajectory (EGLT), a trajectory identifying and characterizing middle grade students' initial and developing understanding of exponential growth as a result of an instructional emphasis on covariation. The EGLT explicates students' thinking and learning over time in relation to a set of tasks…
丁楠
2010-01-01
本文研究了模糊变时滞Cohen-Grossberg神经网络的全局指数稳定性,通过构造合适的Lyapunov函数和运用不等式技巧,得到了模糊变时滞Cohen-Grossberg神经网络平衡点的存在唯一性和全局指数稳定性的判别准则.
罗文品; 杨军
2010-01-01
讨论了一类具有时滞的脉冲Cohen-Grossberg神经网络的全局指数稳定性.利用Lyapunov函数和不等式技巧得到了该系统全局指数稳定的一个充分条件,同时给出示例说明结果的有效性.
汪海洋
2008-01-01
本文主要考虑了一类带脉冲的Cohen-Grossberg时滞神经网络模型的全局指数稳定性,通过构造Li-apunov函数,应用M矩阵理论和一些不等式的技巧,给出了模型的平凡解全局指数稳定的充分条件.
Rukes, Lothar; Sieber, Moritz; Paschereit, C. Oliver; Oberleithner, Kilian
2016-10-01
This study investigates the dynamics of non-isothermal swirling jets undergoing vortex breakdown, with an emphasis on helical coherent structures. It is proposed that the dominant helical coherent structure can be suppressed by heating the recirculation bubble. This proposition is assessed with stereo Particle Image Velocimetry (PIV) measurements of the breakdown region of isothermal and heated swirling jets. The coherent kinetic energy of the dominant helical structure was derived from PIV snapshots via proper orthogonal decomposition. For one set of experimental parameters, mild heating is found to increase the energy content of the dominant helical mode. Strong heating leads to a reduction by 30% of the coherent structures energy. For a second set of experimental parameters, no alteration of the dominant coherent structure is detectable. Local linear stability analysis of the time-averaged velocity fields shows that the key difference between the two configurations is the density ratio at the respective wavemaker location. A density ratio of approximately 0.8 is found to correlate to a suppression of the global mode in the experiments. A parametric study with model density and velocity profiles indicates the most important parameters that govern the local absolute growth rate: the density ratio and the relative position of the density profiles and the inner shear layer.
Baba, Isa Abdullahi; Hincal, Evren
2017-05-01
In this article we studied an epidemic model consisting of two strains with different types of incidence rates; bilinear and non-monotone. The model consists of four equilibrium points: disease-free equilibrium, endemic with respect to strain 1, endemic with respect to strain 2, and endemic with respect to both strains. The global stability analysis of the equilibrium points was carried out through the use of Lyapunov functions. Two basic reproduction ratios R 1 0 and R 2 0 are found, and we have shown that if both are less than one, the disease dies out, and if both are greater than one epidemic occurs. Furthermore, epidemics occur with respect to any strain with a basic reproduction ratio greater than one and disease dies out with respect to any strain with a basic reproduction ratio less than one. It was also shown that any strain with highest basic reproduction ratio will automatically outperform the other strain, thereby eliminating it. Numerical simulations were carried out to support the analytic result and to show the effect of the parameter k in the non-monotone incidence rate, which describes the psychological effect of general public towards infection.
On exponential growth [of gas breakdown
McAllister, Iain Wilson
1991-01-01
The agreement obtained between measured breakdown voltages and predicted breakdown values is frequently used as a means of assessing the validity of the theory/model in question. However, owing to the mathematical nature of exponential growth, it is easy to formulate a criterion that provides...
Intersection of the Exponential and Logarithmic Curves
Boukas, Andreas; Valahas, Theodoros
2009-01-01
The study of the number of intersection points of y = a[superscript x] and y = log[subscript a]x can be an interesting topic to present in a single-variable calculus class. In this article, the authors present a classroom presentation outline involving the basic algebra and the elementary calculus of the exponential and logarithmic functions. The…
When Economic Growth is Less than Exponential
Groth, Christian; Koch, Karl-Josef; Steger, Thomas M.
This paper argues that growth theory needs a more general notion of "regularity" than that of exponential growth. We suggest that paths along which the rate of decline of the growth rate is proportional to the growth rate itself deserve attention. This opens up for considering a richer set...
Exponential lifetime improvement in topological quantum memories
Bardyn, Charles-Edouard; Karzig, Torsten
2016-09-01
We propose a simple yet efficient mechanism for passive error correction in topological quantum memories. Our scheme relies on driven-dissipative ancilla systems which couple to local excitations (anyons) and make them "sink" in energy, with no required interaction among ancillae or anyons. Through this process, anyons created by some thermal environment end up trapped in potential "trenches" that they themselves generate, which can be interpreted as a "memory foam" for anyons. This self-trapping mechanism provides an energy barrier for anyon propagation and removes entropy from the memory by favoring anyon recombination over anyon separation (responsible for memory errors). We demonstrate that our scheme leads to an exponential increase of the memory-coherence time with system size L , up to an upper bound Lmax, which can increase exponentially with Δ /T , where T is the temperature and Δ is some energy scale defined by potential trenches. This results in a double exponential increase of the memory time with Δ /T , which greatly improves over the Arrhenius (single-exponential) scaling found in typical quantum memories.
Couplings and Asymptotic Exponentiality of Exit Times
Brassesco, S.; Olivieri, E.; Vares, M. E.
1998-10-01
The goal of this note is simply to call attention to the resulting simplification in the proof of asymptotic exponentiality of exit times in the Freidlin-Wentzell regime (as proved by F. Martinelli et al.) by using the coupling proposed by T. Lindvall and C. Rogers.
A Simple Mechanical Experiment on Exponential Growth
McGrew, Ralph
2015-01-01
With a rod, cord, pulleys, and slotted masses, students can observe and graph exponential growth in the cord tension over a factor of increase as large as several hundred. This experiment is adaptable for use either in algebra-based or calculus-based physics courses, fitting naturally with the study of sliding friction. Significant parts of the…
Exponentially tapered Josephson flux-flow oscillator
Benabdallah, A.; Caputo, J. G.; Scott, Alwyn C.
1996-01-01
We introduce an exponentially tapered Josephson flux-flow oscillator that is tuned by applying a bias current to the larger end of the junction. Numerical and analytical studies show that above a threshold level of bias current the static solution becomes unstable and gives rise to a train of flu......, and (iv) better impedance matching to a load....
Functional Regression for General Exponential Families
Dou, Wei; Zhou, Harrison H
2010-01-01
The paper derives a minimax lower bound for rates of convergence for an infinite-dimensional parameter in an exponential family model. An estimator that achieves the optimal rate is constructed by maximum likelihood on finite-dimensional approximations with parameter dimension that grows with sample size.
Robust decentralized adaptive stabilization for a class of interconnected systems
Zhaojing WU; Xuejun XIE; Siying ZHANG
2004-01-01
The robust decentralized adaptive output-feedback stabilization for a class of interconnected systems with static and dynamic interconnections by using the MT-filters and backstepping design method is studied. By introducing a new filtered tramformation, the adaptive laws were derived for measurement. Under the assumption of the nonlinear growth conditions imposed on the nonlinear interconnections and by constructing the error system and using a new proof method, the global stability of the closed-loop system was effectively analyzed, and the exponential convergence of all the signals except for parameter estimates were guaranteed.
Schneller, Mirjam Simone
2013-08-02
In thermonuclear plasmas, a population of super-thermal particles generated by external heating methods or fusion reactions can lead to the excitation of global instabilities. The transport processes due to nonlinear wave-particle interactions and the consequential particle losses reduce the plasma heating and the efficiency of the fusion reaction rate. Furthermore, these energetic or fast particles may cause severe damages to the wall of the device. This thesis addresses the resonance mechanisms between these energetic particles and global MHD and kinetic MHD waves, employing the hybrid code HAGIS. A systematic investigation of energetic particles resonant with multiple modes (double-resonance) is presented for the first time. The double-resonant mode coupling is modeled for waves with different frequencies in various overlapping scenarios. It is found that, depending on the radial mode distance, double-resonance is able to significantly enhance, both the growth rates and the saturation amplitudes. Small radial mode distances, however can lead to strong nonlinear mode stabilization of a linear dominant mode. For the first time, simulations of experimental conditions in the ASDEX Upgrade fusion device are performed for different plasma equilibria (particularly for different q profiles). An understanding of fast particle behavior for non-monotonic q profiles is important for the development of advanced fusion scenarios. The numerical tool is the extended version of the HAGIS code, which computes the particle motion in the vacuum region between vessel wall in addition to the internal plasma volume. For this thesis, a consistent fast particle distribution function was implemented, to represent the fast particle population generated by the particular heating method (ICRH). Furthermore, HAGIS was extended to use more realistic eigenfunctions, calculated by the gyrokinetic eigenvalue solver LIGKA. One important aim of these simulations is to allow fast ion loss
An exponential ESS model and its application to frequency-dependent selection.
Li, J; Liu, L
1989-10-01
A nonlinear ESS model is put forward, that is, a nonnegative exponential ESS model. For a simple case, we discuss the existence, uniqueness, and stability of an ESS. As an application of the model, we give a quantitative analysis of frequency-dependent selection in population genetics when the rare type has an advantage.
Multi-exponentially Photoelectric Response of Bacteriorhodopsin
姚保利; 徐大纶; 侯洵; 胡坤生; 王敖金
2001-01-01
A thin oriented bacteriorhodopsin (bR) film is deposited on a stainless steel slide by use of the electrophoretic sedimentation method. A junction is made with electrolyte gels having a counterelectrode to construct a bRbased photoelectric detector. The photoelectric response signal to a 10ns laser pulse is measured. A theory on the photoelectric kinetics of bR is developed based on the concept of the charge displacement current and the bR photocycle rate equations. Comparison between the theoretical and experimental results proves that the bR photoelectric response to a short laser pulse is a multi-exponential process. The decay time constants and amplitudes of each exponential component are obtained by data fitting.
Matrix-exponential distributions in applied probability
Bladt, Mogens
2017-01-01
This book contains an in-depth treatment of matrix-exponential (ME) distributions and their sub-class of phase-type (PH) distributions. Loosely speaking, an ME distribution is obtained through replacing the intensity parameter in an exponential distribution by a matrix. The ME distributions can also be identified as the class of non-negative distributions with rational Laplace transforms. If the matrix has the structure of a sub-intensity matrix for a Markov jump process we obtain a PH distribution which allows for nice probabilistic interpretations facilitating the derivation of exact solutions and closed form formulas. The full potential of ME and PH unfolds in their use in stochastic modelling. Several chapters on generic applications, like renewal theory, random walks and regenerative processes, are included together with some specific examples from queueing theory and insurance risk. We emphasize our intention towards applications by including an extensive treatment on statistical methods for PH distribu...
Statistical estimation for truncated exponential families
Akahira, Masafumi
2017-01-01
This book presents new findings on nonregular statistical estimation. Unlike other books on this topic, its major emphasis is on helping readers understand the meaning and implications of both regularity and irregularity through a certain family of distributions. In particular, it focuses on a truncated exponential family of distributions with a natural parameter and truncation parameter as a typical nonregular family. This focus includes the (truncated) Pareto distribution, which is widely used in various fields such as finance, physics, hydrology, geology, astronomy, and other disciplines. The family is essential in that it links both regular and nonregular distributions, as it becomes a regular exponential family if the truncation parameter is known. The emphasis is on presenting new results on the maximum likelihood estimation of a natural parameter or truncation parameter if one of them is a nuisance parameter. In order to obtain more information on the truncation, the Bayesian approach is also considere...
Harmonic analysis on exponential solvable Lie groups
Fujiwara, Hidenori
2015-01-01
This book is the first one that brings together recent results on the harmonic analysis of exponential solvable Lie groups. There still are many interesting open problems, and the book contributes to the future progress of this research field. As well, various related topics are presented to motivate young researchers. The orbit method invented by Kirillov is applied to study basic problems in the analysis on exponential solvable Lie groups. This method tells us that the unitary dual of these groups is realized as the space of their coadjoint orbits. This fact is established using the Mackey theory for induced representations, and that mechanism is explained first. One of the fundamental problems in the representation theory is the irreducible decomposition of induced or restricted representations. Therefore, these decompositions are studied in detail before proceeding to various related problems: the multiplicity formula, Plancherel formulas, intertwining operators, Frobenius reciprocity, and associated alge...
Perturbing Misiurewicz Parameters in the Exponential Family
Dobbs, Neil
2015-04-01
In one-dimensional real and complex dynamics, a map whose post-singular (or post-critical) set is bounded and uniformly repelling is often called a Misiurewicz map. In results hitherto, perturbing a Misiurewicz map is likely to give a non-hyperbolic map, as per Jakobson's Theorem for unimodal interval maps. This is despite genericity of hyperbolic parameters (at least in the interval setting). We show the contrary holds in the complex exponential family Misiurewicz maps are Lebesgue density points for hyperbolic parameters. As a by-product, we also show that Lyapunov exponents almost never exist for exponential Misiurewicz maps. The lower Lyapunov exponent is -∞ almost everywhere. The upper Lyapunov exponent is non-negative and depends on the choice of metric.
Six-Parameter Exponential-Type Potential and the Identity for the Exponential-Type Potentials
JIA Chun-Sheng; ZENG Xiang-Lin; LI Shu-Chuan; SUN Liang-Tian; YANG Qiu-Bo
2002-01-01
We propose a six-parameter exponential-type potential (SPEP), which has been shown to be a shape-invariant potential with a translation of parameters. For this reducible potential, the exact energy levels are obtained byusing the supersymmetric shape invariance technique. Choosing appropriate parameters, four classes of exponential-typepotentials and their exact energy spectra are reduced from the SPEP and a general energy level formula, respectively.Each class shows the identity except for the different definitions of parameters.
Financing exponential growth at H3
2012-01-01
H3 is a fast-food chain that introduced the concept of gourmet hamburgers in the Portuguese market. This case-study illustrates its financing strategy that supported an exponential growth represented by opening 33 restaurants within approximately 3 years of its inception. H3 is now faced with the challenge of structuring its foreign ventures and change its financial approach. The main covered topics are the options an entrepreneur has for financing a new venture and how it evolves along th...
An exponential correction to Starobinsky's inflationary model
Fabris, Júlio C; Piattella, Oliver F
2016-01-01
We analyse $f(R)$ theories of gravity from a dynamical system perspective, showing how the $R^2$ correction in Starobinsky's model plays a crucial role from the viewpoint of the inflationary paradigm. Then, we propose a modification of Starobinsky's model by adding an exponential term in the $f(R)$ Lagrangian. We show how this modification could allow to test the robustness of the model by means of the predictions on the scalar spectral index $n_s$.