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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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 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.
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.
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.
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.
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.
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.
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.
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.
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.
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...
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.
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.
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).
Anh Tuan Trinh
2013-11-01
Full Text Available The existence of positive periodic solutions of a periodic Lotka-Volterra type competition system with delays and feedback controls is studied by applying the continuation theorem of coincidence degree theory. By contracting a suitable Liapunov functional, a set of sufficient conditions for the global asymptotic stability of the positive periodic solution of the system is given. A counterexample is given to show that the result on the existence of positive periodic solution in [4] is incorrect.
Linearized asymptotic stability for fractional differential equations
Nguyen Cong
2016-06-01
Full Text Available We prove the theorem of linearized asymptotic stability for fractional differential equations. More precisely, we show that an equilibrium of a nonlinear Caputo fractional differential equation is asymptotically stable if its linearization at the equilibrium is asymptotically stable. As a consequence we extend Lyapunov's first method to fractional differential equations by proving that if the spectrum of the linearization is contained in the sector $\\{\\lambda \\in \\mathbb{C} : |\\arg \\lambda| > \\frac{\\alpha \\pi}{2}\\}$ where $\\alpha > 0$ denotes the order of the fractional differential equation, then the equilibrium of the nonlinear fractional differential equation is asymptotically stable.
ASYMPTOTIC STABILITIES OF STOCHASTIC FUNCTIONAL DIFFERENTIAL EQUATIONS
SHEN Yi; JIANG Ming-hui; LIAO Xiao-xin
2006-01-01
Asymptotic characteristic of solution of the stochastic functional differential equation was discussed and sufficient condition was established by multiple Lyapunov functions for locating the limit set of t he solution. Moreover, from them many effective criteria on stochastic asymptotic stability, which enable us to construct the Lyapunov functions much more easily in application, were obtained. The results show that the wellknown classical theorem on stochastic asymptotic stability is a special case of our more general results. In the end, application in stochastic Hopfield neural networks is given to verify our results.
Nonsymmetric gravity does have acceptable global asymptotics
Cornish, N J
1994-01-01
"Reports of my death are greatly exaggerated" - Mark Twain. We consider the claim by Damour, Deser and McCarthy that nonsymmetric gravity theory has unacceptable global asymptotics. We explain why this claim is incorrect.
Asymptotic stability of singularly perturbed differential equations
Artstein, Zvi
2017-02-01
Asymptotic stability is examined for singularly perturbed ordinary differential equations that may not possess a natural split into fast and slow motions. Rather, the right hand side of the equation is comprised of a singularly perturbed component and a regular one. The limit dynamics consists then of Young measures, with values being invariant measures of the fast contribution, drifted by the slow one. Relations between the asymptotic stability of the perturbed system and the limit dynamics are examined, and a Lyapunov functions criterion, based on averaging, is established.
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.
Delay-dependent asymptotic stability for neural networks with time-varying delays
Xiaofeng Liao
2006-01-01
ensure local and global asymptotic stability of the equilibrium of the neural network. Our results are applied to a two-neuron system with delayed connections between neurons, and some novel asymptotic stability criteria are also derived. The obtained conditions are shown to be less conservative and restrictive than those reported in the known literature. Some numerical examples are included to demonstrate our results.
Asymptotic Linear Stability of Solitary Water Waves
Pego, Robert L.; Sun, Shu-Ming
2016-12-01
We prove an asymptotic stability result for the water wave equations linearized around small solitary waves. The equations we consider govern irrotational flow of a fluid with constant density bounded below by a rigid horizontal bottom and above by a free surface under the influence of gravity neglecting surface tension. For sufficiently small amplitude waves, with waveform well-approximated by the well-known sech-squared shape of the KdV soliton, solutions of the linearized equations decay at an exponential rate in an energy norm with exponential weight translated with the wave profile. This holds for all solutions with no component in (that is, symplectically orthogonal to) the two-dimensional neutral-mode space arising from infinitesimal translational and wave-speed variation of solitary waves. We also obtain spectral stability in an unweighted energy norm.
Park Jong Yeoul
2007-01-01
Full Text Available We study the existence of global weak solutions for a hyperbolic differential inclusion with a source term, and then investigate the asymptotic stability of the solutions by using Nakao lemma.
Asymptotic stability of steady compressible fluids
Padula, Mariarosaria
2011-01-01
This volume introduces a systematic approach to the solution of some mathematical problems that arise in the study of the hyperbolic-parabolic systems of equations that govern the motions of thermodynamic fluids. It is intended for a wide audience of theoretical and applied mathematicians with an interest in compressible flow, capillarity theory, and control theory. The focus is particularly on recent results concerning nonlinear asymptotic stability, which are independent of assumptions about the smallness of the initial data. Of particular interest is the loss of control that sometimes results when steady flows of compressible fluids are upset by large disturbances. The main ideas are illustrated in the context of three different physical problems: (i) A barotropic viscous gas in a fixed domain with compact boundary. The domain may be either an exterior domain or a bounded domain, and the boundary may be either impermeable or porous. (ii) An isothermal viscous gas in a domain with free boundaries. (iii) A h...
李玉洁
2012-01-01
We consider the lotka-volterra system of the periolic coefficents for five species. There are predator and competition in five species. A sufficient condition is obtained for existence of periodic solution and global asymptotic stability.%考虑周期系数的五种群Lotka-Volterra模型,种群间既有捕食关系又有竞争关系,得到该系统的正周期解的存在性及全局渐近稳定性的条件.
Asymptotical Stability of Nonlinear Fractional Differential System with Caputo Derivative
2011-01-01
This paper deals with the stability of nonlinear fractional differential systems equipped with the Caputo derivative. At first, a sufficient condition on asymptotical stability is established by using a Lyapunov-like function. Then, the fractional differential inequalities and comparison method are applied to the analysis of the stability of fractional differential systems. In addition, some other sufficient conditions on stability are also presented.
EVANS FUNCTIONS AND ASYMPTOTIC STABILITY OF TRAVELING WAVE SOLUTIONS
无
2001-01-01
This paper studies the asymptotic stability of traveling wave solutions of nonlinear systems of integral-differential equations. It has been established that linear stability of traveling waves is equivalent to nonlinear stability and some “nice structure” of the spectrum of an associated operator implies the linear stability. By using the method of variation of parameter, the author defines some complex analytic function, called the Evans function. The zeros of the Evans function corresponds to the eigenvalues of the associated linear operator. By calculating the zeros of the Evans function, the asymptotic stability of the travling wave solutions is established.
Asymptotical stability analysis of linear fractional differential systems
LI Chang-pin; ZHAO Zhen-gang
2009-01-01
It has been recently found that many models were established with the aid of fractional derivatives, such as viscoelastic systems, colored noise, electrode-electrolyte polarization, dielectric polarization, boundary layer effects in ducts,electromagnetic waves, quantitative finance, quantum evolution of complex systems, and fractional kinetics. In this paper, the asymptotical stability of higher-dimensional linear fractional differential systems with the Riemann-Liouville fractional order and Caputo fractional order were studied. The asymptotical stability theorems were also derived.
Asymptotic Stability of Uniformly Bounded Nonlinear Switched Systems
Jouan, Philippe; Naciri, Said
2012-01-01
We study the asymptotic stability properties of nonlinear switched systems under the assumption of the existence of a common weak Lyapunov function. We consider the class of nonchaotic inputs, which generalize the different notions of inputs with dwell-time, and the class of general ones. For each of them we provide some sufficient conditions for asymptotic stability in terms of the geometry of certain sets. The results, which extend those of Balde, Jouan about linear systems, are illustrated...
Asymptotic Stability of Interconnected Passive Non-Linear Systems
Isidori, A.; Joshi, S. M.; Kelkar, A. G.
1999-01-01
This paper addresses the problem of stabilization of a class of internally passive non-linear time-invariant dynamic systems. A class of non-linear marginally strictly passive (MSP) systems is defined, which is less restrictive than input-strictly passive systems. It is shown that the interconnection of a non-linear passive system and a non-linear MSP system is globally asymptotically stable. The result generalizes and weakens the conditions of the passivity theorem, which requires one of the systems to be input-strictly passive. In the case of linear time-invariant systems, it is shown that the MSP property is equivalent to the marginally strictly positive real (MSPR) property, which is much simpler to check.
Global asymptotical ω-periodicity of a fractional-order non-autonomous neural networks.
Chen, Boshan; Chen, Jiejie
2015-08-01
We study the global asymptotic ω-periodicity for a fractional-order non-autonomous neural networks. Firstly, based on the Caputo fractional-order derivative it is shown that ω-periodic or autonomous fractional-order neural networks cannot generate exactly ω-periodic signals. Next, by using the contraction mapping principle we discuss the existence and uniqueness of S-asymptotically ω-periodic solution for a class of fractional-order non-autonomous neural networks. Then by using a fractional-order differential and integral inequality technique, we study global Mittag-Leffler stability and global asymptotical periodicity of the fractional-order non-autonomous neural networks, which shows that all paths of the networks, starting from arbitrary points and responding to persistent, nonconstant ω-periodic external inputs, asymptotically converge to the same nonconstant ω-periodic function that may be not a solution.
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.
Asymptotical Stability of Nonlinear Fractional Differential System with Caputo Derivative
Fengrong Zhang
2011-01-01
Full Text Available This paper deals with the stability of nonlinear fractional differential systems equipped with the Caputo derivative. At first, a sufficient condition on asymptotical stability is established by using a Lyapunov-like function. Then, the fractional differential inequalities and comparison method are applied to the analysis of the stability of fractional differential systems. In addition, some other sufficient conditions on stability are also presented.
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.
On a new approach to asymptotic stabilization problems
Ivanchikov, A. A.; Kornev, A. A.; Ozeritskii, A. V.
2009-12-01
A numerical algorithm for solving the asymptotic stabilization problem by the initial data to a fixed hyperbolic point with a given rate is proposed and justified. The stabilization problem is reduced to projecting the resolving operator of the given evolution process on a strongly stable manifold. This approach makes it possible to apply the results to a wide class of semidynamical systems including those corresponding to partial differential equations. By way of example, a numerical solution of the problem of the asymptotic stabilization of unstable trajectories of the two-dimensional Chafee-Infante equation in a circular domain by the boundary conditions is given.
郑秀亮; 柳洁冰
2016-01-01
研究了一类连续型时滞与离散型变时滞的非自治n种群Gilpin-Ayala型竞争系统,分别利用比较原理和构造Lyapunov函数得到了系统持久生存与全局渐近稳定性的充分条件,通过数值举例验证了定理的可行性.%In this paper, a class of nonautonomous n species Gilpin-Ayala competition system with continuous delays and discrete varying delays is studied, respectively, the sufficient conditions are obtained for the permanence and global asymp-totic stability of the system by using the comparison theorem and constructing a suitable Lyapunov functional, theorems are realized by giving a numerical example.
ASYMPTOTIC STABILITY OF A SINGULAR SYSTEM WITH DISTRIBUTED DELAYS
无
2010-01-01
Based on the stability theory of functional differential equations, this paper studies the asymptotic stability of a singular system with distributed delays by constructing suitable Lyapunov functionals and applying the linear matrix inequalities. A numerical example is given to show the effectiveness of the main results.
ASYMPTOTIC STABILITY OF SINGULAR NONLINEAR DIFFERENTIAL SYSTEMS WITH UNBOUNDED DELAYS
无
2012-01-01
In this paper,the asymptotic stability of singular nonlinear differential systems with unbounded delays is considered.The stability criteria are derived based on a kind of Lyapunov-functional and some technique of matrix inequalities.The criteria are described as matrix equation and matrix inequalities,which are computationally flexible and efficient.Two examples are given to illustrate the results.
Asymptotic stability estimates near an equilibrium point
Dumas, H. Scott; Meyer, Kenneth R.; Palacián, Jesús F.; Yanguas, Patricia
2017-07-01
We use the error bounds for adiabatic invariants found in the work of Chartier, Murua and Sanz-Serna [3] to bound the solutions of a Hamiltonian system near an equilibrium over exponentially long times. Our estimates depend only on the linearized system and not on the higher order terms as in KAM theory, nor do we require any steepness or convexity conditions as in Nekhoroshev theory. We require that the equilibrium point where our estimate applies satisfy a type of formal stability called Lie stability.
Asymptotic stability of solutions to elastic systems with structural damping
Hongxia Fan
2014-11-01
Full Text Available In this article, we study the asymptotic stability of solutions for the initial value problems of second order evolution equations in Banach spaces, which can model elastic systems with structural damping. The discussion is based on exponentially stable semigroups theory. Applications to the vibration equation of elastic beams with structural damping are also considered.
Asymptotic stability and stabilizability of nonlinear systems with delay.
Srinivasan, V; Sukavanam, N
2016-11-01
This paper is concerned with asymptotic stability and stabilizability of a class of nonlinear dynamical systems with fixed delay in state variable. New sufficient conditions are established in terms of the system parameters such as the eigenvalues of the linear operator, delay parameter, and bounds on the nonlinear parts. Finally, examples are given to testify the effectiveness of the proposed theory.
On global asymptotic controllability of planar affine nonlinear systems
SUN Yimin; GUO Lei
2005-01-01
In this paper, we present a necessary and sufficient condition for globally asymptotic controllability of the general planar affine nonlinear systems with single-input.This result is obtained by introducing a new method in the analysis, which is based on the use of some basic results in planar topology and in the geometric theory of ordinary differential equations.
Wang Shaoli; Feng Xinlong; He Yinnian
2011-01-01
This article proposes a diffused hepatitis B virus (HBV) model with CTLimmune response and nonlinear incidence for the control of viral infections.By means of different Lyapunov functions,the global asymptotical properties of the viral-free equilibrium and immune-free equilibrium of the model are obtained.Global stability of the positive equilibrium of the model is also considered.The results show that the free diffusion of the virus has no effect on the global stability of such HBV infection problem with Neumann homogeneous boundary conditions.
Global asymptotic stabilisation in probability of nonlinear stochastic systems via passivity
Florchinger, Patrick
2016-07-01
The purpose of this paper is to develop a systematic method for global asymptotic stabilisation in probability of nonlinear control stochastic systems with stable in probability unforced dynamics. The method is based on the theory of passivity for nonaffine stochastic differential systems combined with the technique of Lyapunov asymptotic stability in probability for stochastic differential equations. In particular, we prove that a nonlinear stochastic differential system whose unforced dynamics are Lyapunov stable in probability is globally asymptotically stabilisable in probability provided some rank conditions involving the affine part of the system coefficients are satisfied. In this framework, we show that a stabilising smooth state feedback law can be designed explicitly. A dynamic output feedback compensator for a class of nonaffine stochastic systems is constructed as an application of our analysis.
Gerbi, Stéphane
2011-12-01
In this paper we consider a multi-dimensional wave equation with dynamic boundary conditions, related to the KelvinVoigt damping. Global existence and asymptotic stability of solutions starting in a stable set are proved. Blow up for solutions of the problem with linear dynamic boundary conditions with initial data in the unstable set is also obtained. © 2011 Elsevier Ltd. All rights reserved.
Delay-Dependent Asymptotic Stability of Cohen-Grossberg Models with Multiple Time-Varying Delays
Xiaofeng Liao
2007-01-01
Full Text Available Dynamical behavior of a class of Cohen-Grossberg models with multiple time-varying delays is studied in detail. Sufficient delay-dependent criteria to ensure local and global asymptotic stabilities of the equilibrium of this network are derived by constructing suitable Lyapunov functionals. The obtained conditions are shown to be less conservative and restrictive than those reported in the known literature. Some numerical examples are included to demonstrate our results.
Asymptotic stability properties of θ-methods for delay differential equations
无
2001-01-01
Deals with the asymptotic stability properties of θ- methods for the pantograph equation and the linear delay differential-algebraic equation with emphasis on the linear θ- methods with variable stepsize schemes for the pantograph equation, proves that asymptotic stability is obtained if and only if θ ＞ 1/2, and studies further the one-leg θ- method for the linear delay differential-algebraic equation and establishes the sufficient asymptotic-ally differential-algebraic stable condition θ = 1.
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.
Wu, Ailong; Zeng, Zhigang
2016-02-01
We show that the ω-periodic fractional-order fuzzy neural networks cannot generate non-constant ω-periodic signals. In addition, several sufficient conditions are obtained to ascertain the boundedness and global Mittag-Leffler stability of fractional-order fuzzy neural networks. Furthermore, S-asymptotical ω-periodicity and global asymptotical ω-periodicity of fractional-order fuzzy neural networks is also characterized. The obtained criteria improve and extend the existing related results. To illustrate and compare the theoretical criteria, some numerical examples with simulation results are discussed in detail.
Zhanhua Yu
2011-01-01
Full Text Available We study the almost surely asymptotic stability of exact solutions to neutral stochastic pantograph equations (NSPEs, and sufficient conditions are obtained. Based on these sufficient conditions, we show that the backward Euler method (BEM with variable stepsize can preserve the almost surely asymptotic stability. Numerical examples are demonstrated for illustration.
Asymptotic stabilization via control by interconnection of port-Hamiltonian systems
Castaños, Fernando; Ortega, Romeo; Schaft, Arjan van der; Astolfi, Alessandro
2009-01-01
We study the asymptotic properties of control by interconnection, a passivity-based controller design methodology for stabilization of port-Hamiltonian systems. It is well-known that the method, in its basic form, imposes some unnatural controller initialization to yield asymptotic stability of the
Asymptotic stability for a class of boundary control systems with non-linear damping
Zwart, Heiko J.; Ramirez, Hector; Le Gorrec, Yann
2016-01-01
The asymptotic stability of boundary controlled port-Hamiltonian systems defined on a 1D spatial domain interconnected to a class of non-linear boundary damping is addressed. It is shown that if the port-Hamiltonian system is approximately observable, then any boundary damping which behaves linear for small velocities asymptotically stabilizes the system.
Hernández-Guzmán, Victor M.; Santibáñez, Victor; Silva-Ortigoza, Ramón
2010-10-01
In this note we prove, for the first time, that indirect field-oriented control of voltage-fed induction motors achieves global asymptotic stability when used to regulate position in rigid robots. This results in the simplest controller proposed until now to solve this problem. Our stability analysis considers inner current loops driven by linear PI controllers and an external position loop driven by a saturated PD controller.
Asymptotic Stability of High-dimensional Zakharov-Kuznetsov Solitons
Côte, Raphaël; Muñoz, Claudio; Pilod, Didier; Simpson, Gideon
2016-05-01
We prove that solitons (or solitary waves) of the Zakharov-Kuznetsov (ZK) equation, a physically relevant high dimensional generalization of the Korteweg-de Vries (KdV) equation appearing in Plasma Physics, and having mixed KdV and nonlinear Schrödinger (NLS) dynamics, are strongly asymptotically stable in the energy space. We also prove that the sum of well-arranged solitons is stable in the same space. Orbital stability of ZK solitons is well-known since the work of de Bouard [Proc R Soc Edinburgh 126:89-112, 1996]. Our proofs follow the ideas of Martel [SIAM J Math Anal 157:759-781, 2006] and Martel and Merle [Math Ann 341:391-427, 2008], applied for generalized KdV equations in one dimension. In particular, we extend to the high dimensional case several monotonicity properties for suitable half-portions of mass and energy; we also prove a new Liouville type property that characterizes ZK solitons, and a key Virial identity for the linear and nonlinear part of the ZK dynamics, obtained independently of the mixed KdV-NLS dynamics. This last Virial identity relies on a simple sign condition which is numerically tested for the two and three dimensional cases with no additional spectral assumptions required. Possible extensions to higher dimensions and different nonlinearities could be obtained after a suitable local well-posedness theory in the energy space, and the verification of a corresponding sign condition.
Impulsive control of stochastic system under the sense of stochastic asymptotical stability
Niu Yu-Jun; Ma Ge
2010-01-01
This paper studies the stochastic asymptotical stability of stochastic impulsive differential equations,and establishes a comparison theory to ensure the trivial solution's stochastic asymptotical stability.From the comparison theory,it can find out whether the stochastic impulsive differential system is stable just by studying the stability of a deterimpulsive control method,and numerical simulations are employed to verify the feasibility of this method.
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 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 Asymptotic Behavior of a Nonautonomous Competitor-Competitor-Mutualist Model
Shengmao Fu
2013-01-01
Full Text Available The global asymptotic behavior of a nonautonomous competitor-competitor-mutualist model is investigated, where all the coefficients are time-dependent and asymptotically approach periodic functions, respectively. Under certain conditions, it is shown that the limit periodic system of this asymptotically periodic model admits two positive periodic solutions (u1T,u2T,u3T, (u1T,u2T,u3T such that uiT≤uiT (i=1,2,3, and the sector {(u1,u2,u3:uiT≤ui≤uiT, i=1,2,3} is a global attractor of the asymptotically periodic model. In particular, we derive sufficient conditions that guarantee the existence of a positive periodic solution which is globally asymptotically stable.
Ergodicity and asymptotic stability of Feller semigroups on Polish metric spaces
Gong, FuZhou; Liu, Yuan
2015-06-01
We provide some sharp criteria for studying the ergodicity and asymptotic stability of general Feller semigroups on Polish metric spaces. As application, the 2D Navier-Stokes equations with degenerate stochastic forcing will be simply revisited.
Asymptotic Stability and Balanced Growth Solution of the Singular Dynamic Input-Output System＊
ChonghuiGuo; HuanwenTang
2004-01-01
The dynamic input-output system is well known in economic theory and practice. In this paper the asymptotic stability and balanced growth solution of the dynamic input-output system are considered. Under three natural assumptions, we obtain four theorems about asymptotic stability and balanced growth solution of the dynamic input-output system and bring together in a unified manner some contributions scattered in the literature.
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.
ASYMPTOTIC STABILITY OF RAREFACTION WAVE FOR GENERALIZED BURGERS EQUATION
Xu Yanling; Jiang Mina
2005-01-01
This paper is concerned with the stability of the rarefaction wave for the Burgers equation{ ut+f(u)x=μtαuxx, μ＞0, x∈R, t＞0, (Ⅰ)u|t=o = u0(x) →u± , x →∞ ,where 0 ≤α＜ 1/4q (q is determined by (2.2)). Roughly speaking, under the assumption that u- ＜ u+, the authors prove the existence of the global smooth solution to the Cauchy problem (Ⅰ), also find the solution u(x, t) to the Cauchy problem (Ⅰ) satisfying sup |u(x, t)-x∈RuR(x/t)| → 0 as t →∞, where uR(x/t) is the rarefaction wave of the non-viscous Burgers equation ut + f(u)x = 0 with Riemann initial data u(x, 0) ={u_,x＜0, u+, x＞0.
Global existence and asymptotic behavior for a nonlinear degenerate SIS model
Tarik Ali Ziane
2013-01-01
Full Text Available In this paper we investigate the global existence and asymptotic behavior of a reaction diffusion system with degenerate diffusion arising in the modeling and the spatial spread of an epidemic disease.
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.
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...
Asymptotic stability of monostable wavefronts in discrete-time integral recursions
无
2010-01-01
The aim of this work is to study the traveling wavefronts in a discrete-time integral recursion with a Gauss kernel in R2.We first establish the existence of traveling wavefronts as well as their precise asymptotic behavior.Then,by employing the comparison principle and upper and lower solutions technique,we prove the asymptotic stability and uniqueness of such monostable wavefronts in the sense of phase shift and circumnutation.We also obtain some similar results in R.
Hai Zhang
2014-01-01
Full Text Available We discuss the delay-independent asymptotic stability of Caputo type fractional-order neutral differential systems with multiple discrete delays. Based on the algebraic approach and matrix theory, the sufficient conditions are derived to ensure the asymptotic stability for all time-delay parameters. By applying the stability criteria, one can avoid solving the roots of transcendental equations. The results obtained are computationally flexible and convenient. Moreover, an example is provided to illustrate the effectiveness and applicability of the proposed theoretical results.
A GLOBALLY UNIFORM ASYMPTOTIC EXPANSION OF THE HERMITE POLYNOMIALS
Shi Wei
2008-01-01
In this article, the author extends the validity of a uniform asymptotic ex-pansion of the Hermite polynomials HN(√2n+1α) to include all positive values of a.His method makes use of the rational functions introduced by Olde Daalhuis and Temme (SIAM J. Math. Anal., (1994), 25: 304-321). A new estimate for the remainder is given.
A Lyapunov-Krasovskii methodology for asymptotic stability of discrete time delay systems
Stojanović Sreten B.
2007-01-01
Full Text Available This paper presents a Lyapunov-Krasovskii methodology for asymptotic stability of discrete time delay systems. Based on the methods, delay-independent stability condition is derived. A numerical example has been working out to show the applicability of results derived.
ASYMPTOTIC STABILITY OF A CLASS OF NONLINEAR NEUTRAL-TYPE SYSTEMS
无
2009-01-01
By Lyapunov functional method, sufficient conditions for the asymptotic stability of a class of neutral-type systems are discussed in this paper. This work extends some results on the stability of neutral-type systems in the previous papers. Several numerical examples are listed in the end of this paper to confirm our results.
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)
Asymptotic Stability of Neutral Differential Equations with Unbounded Delay
YE Hai-ping; GAO Guo-zhu
2002-01-01
Consider the neutral differential equation with positive and negative coefficients and unbounded delay ddt [x(t)- P(t)x(h(t))] + Q(t)x(q(t)) -R(t)x(r(t))= 0, t ≥ t0,where P(t)∈ C([t0, ∞), R), Q(t), R(t) ∈ C([t0,∞ ), R+ ), and h, q, r: [ t0, ∞ ) → R are continuously differentiable and strictly increasing, h( t) ＜ t, q( t) ＜t, r(t) ＜ t for all t ≥ t0. In this paper, the authors obtain sufficient conditions for the zero solution of this equation with unbounded delay to be uniformly stable as well as asymptotically stable.
Asymptotic Behavior of Global Solution for Nonlinear Generalized Euler-Possion-Darboux Equation
LIANGBao-song; CHENZhen
2004-01-01
J. L Lions and W. A. Stranss [1] have proved the existence of a global solution of the initial boundary value problem for nonlinear generalized Euler-Possion-Darboux equation. In this paper we are going to investigate the asymptotic behavior of the global solution by a difference inequality.
Vacuum stability of asymptotically safe gauge-Yukawa theories
Litim, Daniel F.; Mojaza, Matin; Sannino, Francesco
2016-01-01
We study the phase diagram and the stability of the ground state for certain four-dimensional gauge-Yukawa theories whose high-energy behaviour is controlled by an interacting fixed point. We also provide analytical and numerical results for running couplings, their crossover scales, the separatrix......, and the Coleman-Weinberg effective potential. Classical and quantum stability of the vacuum is established....
Vacuum stability of asymptotically safe gauge-Yukawa theories
Litim, Daniel F; Sannino, Francesco
2016-01-01
We study the phase diagram and the stability of the ground state for certain four-dimensional gauge-Yukawa theories whose high-energy behaviour is controlled by an interacting fixed point. We also provide analytical and numerical results for running couplings, their crossover scales, the separatrix, and the Coleman-Weinberg effective potential. Classical and quantum stability of the vacuum is established.
Asymptotic Stabilization of Non-holonomic Port-controlled Hamiltonian Systems
Sørensen, Mathias Jesper; Bendtsen, Jan Dimon; Andersen, Palle
2004-01-01
A novel method for asymptotic stabilization of a class of non-holonomic systems is presented. The method is based on the port-controlled Hamiltonian description of electro-mechanical systems. The general system is augmented with so-called kinematic inputs, thus representing a special class...... of mobile robots. The asymptotic stability guarantees are obtained by applying a passivity based control design, based on energy shaping and damping injection. The method has been successfully applied to a particular four wheel steered, four wheel driven robot....
Asymptotic Stabilization of Continuous-Time Linear Systems with Input and State Quantizations
Sung Wook Yun
2014-01-01
Full Text Available This paper discusses the asymptotic stabilization problem of linear systems with input and state quantizations. In order to achieve asymptotic stabilization of such systems, we propose a state-feedback controller comprising two control parts: the main part is used to determine the fundamental characteristics of the system associated with the cost, and the additional part is employed to eliminate the effects of input and state quanizations. In particular, in order to implement the additional part, we introduce a quantizer with a region-decision making process (RDMP for a certain linear switching surface. The simulation results show the effectiveness of the proposed controller.
Luo, Tao; Xin, Zhouping; Zeng, Huihui
2016-11-01
The nonlinear asymptotic stability of Lane-Emden solutions is proved in this paper for spherically symmetric motions of viscous gaseous stars with the density dependent shear and bulk viscosities which vanish at the vacuum, when the adiabatic exponent {γ} lies in the stability regime {(4/3, 2)}, by establishing the global-in-time regularity uniformly up to the vacuum boundary for the vacuum free boundary problem of the compressible Navier-Stokes-Poisson systems with spherical symmetry, which ensures the global existence of strong solutions capturing the precise physical behavior that the sound speed is {C^{{1}/{2}}}-Hölder continuous across the vacuum boundary, the large time asymptotic uniform convergence of the evolving vacuum boundary, density and velocity to those of Lane-Emden solutions with detailed convergence rates, and the detailed large time behavior of solutions near the vacuum boundary. Those uniform convergence are of fundamental importance in the study of vacuum free boundary problems which are missing in the previous results for global weak solutions. Moreover, the results obtained in this paper apply to much broader cases of viscosities than those in Fang and Zhang (Arch Ration Mech Anal 191:195-243, 2009) for the theory of weak solutions when the adiabatic exponent {γ} lies in the most physically relevant range. Finally, this paper extends the previous local-in-time theory for strong solutions to a global-in-time one.
Conditions of asymptotic stability for linear homogeneous switched systems
Ivanov, Gennady; Alferov, Gennady; Sharlay, Artem; Efimova, Polina
2017-07-01
In this article the authors prove the theorems giving the necessary and sufficient conditions for stability of robotic and mechatronic systems motion in terms of Lyapunov functions theory with the use of set-theoretic approach.
Polynomial asymptotic stability of damped stochastic differential equations
John Appleby
2004-08-01
Full Text Available The paper studies the polynomial convergence of solutions of a scalar nonlinear It\\^{o} stochastic differential equation\\[dX(t = -f(X(t\\,dt + \\sigma(t\\,dB(t\\] where it is known, {\\it a priori}, that $\\lim_{t\\rightarrow\\infty} X(t=0$, a.s. The intensity of the stochastic perturbation $\\sigma$ is a deterministic, continuous and square integrable function, which tends to zero more quickly than a polynomially decaying function. The function $f$ obeys $\\lim_{x\\rightarrow 0}\\mbox{sgn}(xf(x/|x|^\\beta = a$, for some $\\beta>1$, and $a>0$.We study two asymptotic regimes: when $\\sigma$ tends to zero sufficiently quickly the polynomial decay rate of solutions is the same as for the deterministic equation (when $\\sigma\\equiv0$. When $\\sigma$ decays more slowly, a weaker almost sure polynomial upper bound on the decay rate of solutions is established. Results which establish the necessity for $\\sigma$ to decay polynomially in order to guarantee the almost sure polynomial decay of solutions are also proven.
Vacuum stability of asymptotically safe gauge-Yukawa theories
Litim, Daniel F.; Mojaza, Matin; Sannino, Francesco
2016-01-01
We study the phase diagram and the stability of the ground state for certain four-dimensional gauge-Yukawa theories whose high-energy behaviour is controlled by an interacting fixed point. We also provide analytical and numerical results for running couplings, their crossover scales, the separatrix...
An Enhanced Asymptotic Expansion for the Stability of Nonlinear Elastic Structures
Christensen, Claus Dencker; Byskov, Esben
2010-01-01
A new, enhanced asymptotic expansion applicable to stability of structures made of nonlinear elastic materials is established. The method utilizes “hyperbolic” terms instead of the conventional polynomial terms, covers full kinematic nonlinearity and is applied to nonlinear elastic Euler columns ...
Zhanhua Yu
2011-01-01
convergence theorem. It is shown that the Euler method and the backward Euler method can reproduce the almost surely asymptotic stability of exact solutions to NSDDEs under additional conditions. Numerical examples are demonstrated to illustrate the effectiveness of our theoretical results.
Asymptotic stability and periodic solutions of vector Li\\'enard equations
Briata, F.; Sabatini, M.
2010-01-01
We prove the asymptotic stability of the equilibrium solution of a class of vector Li\\'enard equations by means of LaSalle invariance principle. The key hypothesis consists in assuming that the intersections of the manifolds in $\\{\\dot V = 0\\}$ be isolated. We deduce an existence theorem for periodic solutions of periodically perturbed vector Li\\'enard equations.
Asymptotic stability for a class of boundary control systems with non-linear damping
Zwart, Heiko J.; Ramirez, Hector; Le Gorrec, Yann
2016-01-01
The asymptotic stability of boundary controlled port-Hamiltonian systems defined on a 1D spatial domain interconnected to a class of non-linear boundary damping is addressed. It is shown that if the port-Hamiltonian system is approximately observable, then any boundary damping which behaves linear
Asymptotic stability of solutions to the nonisentropic hydrodynamic model for semiconductors
XU Jiang; FANG Da-yuan
2008-01-01
In this paper, the asymptotic stability of smooth solutions to the multidimensional nonisentropic hydrodynamic model for semiconductors is established, under the assumption that the initial data are a small perturbation of the stationary solutions for the thermal equilibrium state, whose proofs mainly depend on the basic energy methods.
Chung Jae-Young
2010-01-01
Full Text Available Let be the set of positive real numbers, a Banach space, and , with . We prove the Hyers-Ulam stability of the Jensen type logarithmic functional inequality in restricted domains of the form for fixed with or and . As consequences of the results we obtain asymptotic behaviors of the inequality as .
Oscillation and asymptotic stability of a delay differential equation with Richard's nonlinearity
Leonid Berezansky
2005-04-01
Full Text Available We obtain sufficient conditions for oscillation of solutions, and for asymptotical stability of the positive equilibrium, of the scalar nonlinear delay differential equation $$ frac{dN}{dt} = r(tN(tBig[a-Big(sum_{k=1}^m b_k N(g_k(tBig^{gamma}Big], $$ where $ g_k(tleq t$.
Scheduling in a random environment: stability and asymptotic optimality
Ayesta, U; Jonckheere, M; Verloop, I M
2011-01-01
We investigate the scheduling of a common resource between several concurrent users when the feasible transmission rate of each user varies randomly over time. Time is slotted and users arrive and depart upon service completion. This may model for example the flow-level behavior of end-users in a narrowband HDR wireless channel (CDMA 1xEV-DO). As performance criteria we consider the stability of the system and the mean delay experienced by the users. Given the complexity of the problem we investigate the fluid-scaled system, which allows to obtain important results and insights for the original system: (1) We characterize for a large class of scheduling policies the stability conditions and identify a set of maximum stable policies, giving in each time slot preference to users being in their best possible channel condition. We find in particular that many opportunistic scheduling policies like Score-Based, Proportionally Best or Potential Improvement are stable under the maximum stability conditions, whereas ...
New asymptotic stability criteria for neural networks with time-varying delay
Tian Junkang, E-mail: tianjunkang1980@163.co [School of Sciences, Southwest Petroleum University, Chengdu, Sichuan 610500 (China); Xie Xiangjun [School of Sciences, Southwest Petroleum University, Chengdu, Sichuan 610500 (China)
2010-02-01
The problem of delay-dependent asymptotic stability criteria for neural networks with time-varying delay is investigated. A new class of Lyapunov functional is constructed to derive some new delay-dependent stability criteria.The obtained criterion are less conservative because free-weighting matrices method and a convex optimization approach are considered. Finally, numerical examples are given to demonstrate the effectiveness of the proposed method.
On the Conditions for the Orbitally Asymptotical Stability of the Almost
无
2000-01-01
@@This paper studies the behaviors of the solutions in the vicinity of a givenalmost periodic solution of the autonomous system x′=f(x), x Rn , (1) where f C1 (Rn ,Rn ). Since the periodic solutions of the autonomous system are not Liapunov asymptotic stable, we consider the weak orbitally stability. For the planar autonomous systems (n=2), the classical result of orbitally stability about its periodic solution with period w belongs to Poincare, i.e.
Asymptotic stability of the Boltzmann equation with Maxwell boundary conditions
Briant, Marc; Guo, Yan
2016-12-01
In a general C1 domain, we study the perturbative Cauchy theory for the Boltzmann equation with Maxwell boundary conditions with an accommodation coefficient α in (√{ 2 / 3 } , 1 ], and discuss this threshold. We consider polynomial or stretched exponential weights m (v) and prove existence, uniqueness and exponential trend to equilibrium around a global Maxwellian in Lx,v∞ (m). Of important note is the fact that the methods do not involve contradiction arguments.
Global dynamics and asymptotics for monomial scalar field potentials and perfect fluids
Alho, Artur; Uggla, Claes
2015-01-01
We consider a minimally coupled scalar field with a monomial potential and a perfect fluid in flat FLRW cosmology. We apply local and global dynamical systems techniques to a new three-dimensional dynamical systems reformulation of the field equations on a compact state space. This leads to a visual global description of the solution space and asymptotic behavior. At late times we employ averaging techniques to prove statements about how the relationship between the equation of state of the fluid and the monomial exponent of the scalar field affects asymptotic source dominance and asymptotic manifest self-similarity breaking. We also situate the `attractor' solution in the three-dimensional state space and show that it corresponds to the one-dimensional unstable center manifold of a de Sitter fixed point, located on an unphysical boundary associated with the dynamics at early times. By deriving a center manifold expansion we obtain approximate expressions for the attractor solution. We subsequently improve th...
Komech, A I; Stuart, D
2008-01-01
The long-time asymptotics is analyzed for finite energy solutions of the 1D Schr\\"odinger equation coupled to a nonlinear oscillator; mathematically the system under study is a nonlinear Schr\\"odinger equation, whose nonlinear term includes a Dirac delta. The coupled system is invariant with respect to the phase rotation group U(1). This article, which extends the results of a previous one, provides a proof of asymptotic stability of solitary wave solutions in the case that the linearization contains a single discrete oscillatory mode satisfying a non-degeneracy assumption of the type known as the Fermi Golden Rule.
Ploberger, W.; Bierens, H.J.
1995-01-01
In this paper we study further the asymptotic power properties of the integrated conditional moment (ICM) test of Bierens (1982) and Bierens and Ploberger (1994). First, we establish the relation between consistency against global alternatives and nontrivial local power, using the concept of
黎勇; 陈丽
2002-01-01
In this paper, we study the asymptotic behavior of global smooth solution to the initial boundary problem for the 1-D energy transport model in semiconductor science. We prove that the smooth solution of the problem converges to a stationary solution exponentially fast as t - ∞ when the initial data is a small perturbation of the stationary solution.
ASYMPTOTIC BEHAVIOR OF GLOBAL SMOOTH SOLUTIONS TO THE EULER-POISSON SYSTEM IN SEMICONDUCTORS
琚强昌
2002-01-01
In this paper, we establish the global existence and the asymptotic behavior of smooth solution to the initial-boundary value problem of Euler-Poisson system which is used as the bipolar hydrodynamic model for semiconductors with the nonnegative constant doping profile.
Stabilization and asymptotic behavior of a generalized telegraph equation
Nicaise, Serge
2015-12-01
We analyze the stability of different models of the telegraph equation set in a real interval. They correspond to the coupling between a first-order hyperbolic system and a first-order differential equation of parabolic type. We show that some models have an exponential decay rate, while other ones are only polynomially stable. When the parameters are constant, we show that the obtained polynomial decay is optimal and in the case of an exponential decay that the decay rate is equal to the spectral abscissa. These optimality results are based on a careful spectral analysis of the operator. In particular, we characterize its full spectrum that is made of a discrete set of eigenvalues and an essential spectrum reduced to one point.
Asymptotic stability for a class of Markov semigroups
Prunaru, Bebe
2011-01-01
Let $U\\subset K$ be an open and dense subset of a compact metric space and let $\\{\\Phi_t\\}_{t\\ge0}$ be a Markov semigroup on the space of bounded Borel measurable functions on $U$ with the strong Feller property. Suppose that for each $x\\in\\bdu$ there exists a barrier $h\\in C(K)$ at $x$ such that $\\Phi_t(h)\\ge h$ for all $t\\ge0$. Suppose also that every real-valued $g\\in C(K)$ with $\\Phi_t(g)\\ge g$ for all $t\\ge0$ and which attains its global maximum at a point inside $U$ is constant. Then for each $f\\in C(K)$ there exists the uniform limit $F=\\lim_{t\\to\\infty}\\Phi_t(f)$. Moreover $F$ is continuous on $K$, agrees with $f$ on $\\partial{U}$ and $\\Phi_t(F)=F$ for all $t\\ge0$.
Global Asymptotics of Krawtchouk Polynomials——a Riemann-Hilbert Approach
Dan DAI; Roderick WONG
2007-01-01
In this paper, we study the asymptotics of the Krawtchouk polynomials KnN(z;p,q) as the degree n becomes large. Asymptotic expansions are obtained when the ratio of the parameters n/N tends to a limit c ∈ (0, 1) as n →∞. The results are globally valid in one or two regions in the complex z-plane depending on the values of c and p;in particular, they are valid in regions containing the interval on which these polynomials are orthogonal. Our method is based on the Riemann-Hilbert approach introduced by Deift and Zhou.
Asymptotical stability of stochastic neural networks with multiple time-varying delays
Zhou, Xianghui; Zhou, Wuneng; Dai, Anding; Yang, Jun; Xie, Lili
2015-03-01
The stochastic neural networks can be considered as an expansion of cellular neural networks and Hopfield neural networks. In real world, the neural networks are prone to be instable due to time delay and external disturbance. In this paper, we consider the asymptotic stability for the stochastic neural networks with multiple time-varying delays. By employing a Lyapunov-Krasovskii function, a sufficient condition which guarantees the asymptotic stability of the state trajectory in the mean square is obtained. The criteria proposed can be verified readily by utilising the linear matrix inequality toolbox in Matlab, and no parameters to be tuned. In the end, two numerical examples are provided to demonstrate the effectiveness of the proposed method.
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.
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.
The asymptotic form of non-global logarithms, black disc saturation, and gluonic deserts
Neill, Duff
2017-01-01
We develop an asymptotic perturbation theory for the large logarithmic behavior of the non-linear integro-differential equation describing the soft correlations of QCD jet measurements, the Banfi-Marchesini-Smye (BMS) equation. This equation captures the late-time evolution of radiating color dipoles after a hard collision. This allows us to prove that at large values of the control variable (the non-global logarithm, a function of the infra-red energy scales associated with distinct hard jets in an event), the distribution has a gaussian tail. We compute the decay width analytically, giving a closed form expression, and find it to be jet geometry independent, up to the number of legs of the dipole in the active jet. Enabling the asymptotic expansion is the correct perturbative seed, where we perturb around an anzats encoding formally no real emissions, an intuition motivated by the buffer region found in jet dynamics. This must be supplemented with the correct application of the BFKL approximation to the BMS equation in collinear limits. Comparing to the asymptotics of the conformally related evolution equation encountered in small-x physics, the Balitisky-Kovchegov (BK) equation, we find that the asymptotic form of the non-global logarithms directly maps to the black-disc unitarity limit of the BK equation, despite the contrasting physical pictures. Indeed, we recover the equations of saturation physics in the final state dynamics of QCD.
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.
阮炯; 王军平; 郭德典
2004-01-01
In this paper, we first introduce the model of discrete-time neural networks with generalized input-output function and present a proof of the existence of a fixed point by Schauder fixed-point principle. Secondly, we study the uniformly asymptotical stability of equilibrium in non-autonomous discrete-time neural networks and give some sufficient conditions that guarantee the stability of it by using the converse theorem of Lyapunov function. Finally, several examples and numerical simulations are given to illustrate and reinforce our theories.
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.
郭柏灵; 苗长兴
1995-01-01
The final value problem for the classical coupled Klein-Gordon-Schrodinger equations is studied in . This leads to the construction of the modified wave operator Ω, for certain scattered data. When initial functions belong to (Ω) which denotes the range domain of Ω, the global existence and asymptotic behavior of solutions of Cauchy problem tor the coupled Klein-Gordon-Schrodinger equations are proved.
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.
Global Existence and Asymptotic Behavior of Affine Motion of 3D Ideal Fluids Surrounded by Vacuum
Sideris, Thomas C.
2017-07-01
The 3D compressible and incompressible Euler equations with a physical vacuum free boundary condition and affine initial conditions reduce to a globally solvable Hamiltonian system of ordinary differential equations for the deformation gradient in {GL^+(3, R)}. The evolution of the fluid domain is described by a family of ellipsoids whose diameter grows at a rate proportional to time. Upon rescaling to a fixed diameter, the asymptotic limit of the fluid ellipsoid is determined by a positive semi-definite quadratic form of rank r = 1, 2, or 3, corresponding to the asymptotic degeneration of the ellipsoid along 3- r of its principal axes. In the compressible case, the asymptotic limit has rank r = 3, and asymptotic completeness holds, when the adiabatic index {γ} satisfies {4/3 adiabatic index {γ}. In the incompressible case, affine motion reduces to geodesic flow in {SL(3, R)} with the Euclidean metric. For incompressible affine swirling flow, there is a structural instability. Generically, when the vorticity is nonzero, the domains degenerate along only one axis, but the physical vacuum boundary condition fails over a finite time interval. The rescaled fluid domains of irrotational motion can collapse along two axes.
Xia ZHOU; Shou Ming ZHONG
2011-01-01
In this paper the asymptotical stability in p-moment of neutral stochastic differential equations with discrete and distributed time-varying delays is discussed. The authors apply the fixed-point theory rather than the Lyapunov functions. We give a sufficient condition for asymptotical stability in p-moment when the coefficient functions of equations are not required to be fixed values. Since more general form of system is considered, this paper improves Luo Jiaowan's results.
Asymptotic Stability for an Axis-Symmetric Ohmic Heating Model in Thermal Electricity
Anyin Xia
2013-01-01
Full Text Available The asymptotic behavior of the solution for the Dirichlet problem of the parabolic equation with nonlocal term ut=urr+ur/r+f(u/(a+2πb∫01f(urdr2, for 00,u1,t=u′(0,t=0, for t>0, ur,0=u0r, for 0≤r≤1. The model prescribes the dimensionless temperature when the electric current flows through two conductors, subject to a fixed potential difference. One of the electrical resistivity of the axis-symmetric conductor depends on the temperature and the other one remains constant. The main results show that the temperature remains uniformly bounded for the generally decreasing function f(s, and the global solution of the problem converges asymptotically to the unique equilibrium.
Asymptotic theory of neutral stability of the Couette flow of a vibrationally excited gas
Grigor'ev, Yu. N.; Ershov, I. V.
2017-01-01
An asymptotic theory of the neutral stability curve for a supersonic plane Couette flow of a vibrationally excited gas is developed. The initial mathematical model consists of equations of two-temperature viscous gas dynamics, which are used to derive a spectral problem for a linear system of eighth-order ordinary differential equations within the framework of the classical linear stability theory. Unified transformations of the system for all shear flows are performed in accordance with the classical Lin scheme. The problem is reduced to an algebraic secular equation with separation into the "inviscid" and "viscous" parts, which is solved numerically. It is shown that the thus-calculated neutral stability curves agree well with the previously obtained results of the direct numerical solution of the original spectral problem. In particular, the critical Reynolds number increases with excitation enhancement, and the neutral stability curve is shifted toward the domain of higher wave numbers. This is also confirmed by means of solving an asymptotic equation for the critical Reynolds number at the Mach number M ≤ 4.
ASYMPTOTIC STABILITY PROPERTIES OF θ-METHODS FOR THE MULTI-PANTOGRAPH DELAY DIFFERENTIAL EQUATION
Dong-song Li; Ming-zhu Liu
2004-01-01
This paper deals with the asymptotic stability analysis of θ - methods for multi-pantograph delay differential equation u'(t)=λu(t)+lΣi=1μiu(qit),0＜ql＜ql-1＜…＜ql＜1,/u(0)=u0.Here λ,μ1,…,μl,u0∈C.In recent years stability properties of numerical methods for this kind of equation has been studied by numerous authors. Many papers are concerned with meshes with fixed stepsize. In general the developed techniques give rise to non-ordinary recurrence relation. In this work, instead, we study constrained variable stpesize schemes, suggested by theoretical and computational reasons, which lead to a non-stationary difference equation.A general theorem is presented which can be used to obtain the characterization of the stability regions of θ - methods.
Asymptotic theory of neutral stability curve of the Couette flow of vibrationally excited gas
Grigor'ev, Yu N.; Ershov, I. V.
2016-06-01
The asymptotic theory of neutral stability curve of the supersonic plane Couette flow of vibrationally excited gas is constructed. The system of two-temperature viscous gas dynamics equations was used as original mathematical model. Spectral problem for an eighth order linear system of ordinary differential equations was obtained from the system within framework of classical theory of linear stability. Transformations of the spectral problem universal for all shear flows were carried along the classical Dunn — Lin scheme. As a result the problem was reduced to secular algebraic equation with a characteristic division on “inviscid” and “viscous” parts which was solved numerically. The calculated neutral stability curves coincide in limits of 10% with corresponding results of direct numerical solution of original spectral problem.
Stability Analysis of A Neuro-Identification Scheme with Asymptotic Convergence
José A. R. Vargas
2012-07-01
Full Text Available This paper focuses on the stability and convergence analysis of a neuro-identification scheme for uncertain nonlinear systems. Based on linearly parameterized neural networks and the previous knowledge of upper bounds for the approximation error and disturbances, a robust modification of the descent gradient algorithm is proposed to make the overall identification process stable, and, in addition, the on-line residual prediction error asymptotically null, despite the presence of approximation error and disturbances. A simulation study to show the application and comparative performance of the proposed algorithm is presented.
Delay-dependent asymptotic stability of mobile ad-hoc networks: A descriptor system approach
Yang, Juan; Yang, Dan; Huang, Bin; Zhang, Xiao-Hong; Luo, Jian-Lu
2014-07-01
In order to analyze the capacity stability of the time-varying-propagation and delay-dependent of mobile ad-hoc networks (MANETs), in this paper, a novel approach is proposed to explore the capacity asymptotic stability for the delay-dependent of MANETs based on non-cooperative game theory, where the delay-dependent conditions are explicitly taken into consideration. This approach is based on the Lyapunov—Krasovskii stability theory for functional differential equations and the linear matrix inequality (LMI) technique. A corresponding Lyapunov—Krasovskii functional is introduced for the stability analysis of this system with use of the descriptor and “neutral-type” model transformation without producing any additional dynamics. The delay-dependent stability criteria are derived for this system. Conditions are given in terms of linear matrix inequalities, and for the first time referred to neutral systems with the time-varying propagation and delay-dependent stability for capacity analysis of MANETs. The proposed criteria are less conservative since they are based on an equivalent model transformation. Furthermore, we also provide an effective and efficient iterative algorithm to solve the constrained stability control model. Simulation experiments have verified the effectiveness and efficiency of our algorithm.
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.
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.
Zhang Zhijiun
2008-01-01
By Karamata regular variation theory and constructing comparison functions, the author shows the existence and global optimal asymptotic behaviour of solutions for a semilinear elliptic problem △u = k(x)g(u),u>0, x∈Ω, u|(e)Ω = +∞, where Ω is a bounded domain with smooth boundary in RN; g ∈ C1[0,∞), g(0) = g'(0) = 0, and there exists p > 1, such that lims→∞ g(sξ)/g(s)=ξp, (A)ξ > 0, and k∈Cαloc(Ω) is non-negative non-trivial in Ω which may be singular on the boundary.
Tokuda, Shinji [Japan Atomic Energy Research Inst., Naka, Ibaraki (Japan). Naka Fusion Research Establishment; Watanabe, Tomoko
1996-11-01
A theory and a numerical method are presented for the asymptotic matching analysis of resistive magnetohydrodynamic stability in a negative magnetic shear configuration with two rational surfaces. The theory formulates the problem of solving both the Newcomb equations in the ideal MHD region and the inner-layer equations around rational surfaces as boundary value/eigenvalue problems to which the finite element method and the finite difference method can be applied. Hence, the problem of stability analysis is solved by a numerically stable method. The present numerical method has been applied to model equations having analytic solutions in a negative magnetic shear configuration. Comparison of the numerical solutions with the analytical ones verifies the validity of the numerical method proposed. (author)
Asymptotic formation and orbital stability of phase-locked states for the Kuramoto model
Choi, Young-Pil; Ha, Seung-Yeal; Jung, Sungeun; Kim, Yongduck
2012-04-01
We discuss the asymptotic formation and nonlinear orbital stability of phase-locked states arising from the ensemble of non-identical Kuramoto oscillators. We provide an explicit lower bound for a coupling strength on the formation of phase-locked states, which only depends on the diameters of natural frequencies and initial phase configurations. We show that, when the phases of non-identical oscillators are distributed over the half circle and the coupling strength is sufficiently large, the dynamics of Kuramoto oscillators exhibits two stages (transition and relaxation stages). In a transition stage, initial configurations shrink to configurations whose diameters are strictly less than {π}/{2} in a finite-time, and then the configurations tend to phase-locked states asymptotically. This improves previous results on the formation of phase-locked states by Chopra-Spong (2009) [26] and Ha-Ha-Kim (2010) [27] where their attention were focused only on the latter relaxation stage. We also show that the Kuramoto model is ℓ1-contractive in the sense that the ℓ1-distance along two smooth Kuramoto flows is less than or equal to that of initial configurations. In particular, when two initial configurations have the same averaged phases, the ℓ1-distance between them decays to zero exponentially fast. For the configurations with different phase averages, we use the method of average adjustment and translation-invariant of the Kuramoto model to show that one solution converges to the translation of the other solution exponentially fast. This establishes the orbital stability of the phase-locked states. Our stability analysis does not employ any standard linearization technique around the given phase-locked states, but instead, we use a robust ℓ1-metric functional as a Lyapunov functional. In the formation process of phase-locked states, we estimate the number of collisions between oscillators, and lower-upper bounds of the transversal phase differences.
张映辉; 吴国春
2014-01-01
We investigate the global existence and asymptotic behavior of classical solutions for the 3D compressible non-isentropic damped Euler equations on a periodic domain. The global existence and uniqueness of classical solutions are obtained when the initial data is near an equilibrium. Furthermore, the exponential convergence rates of the pressure and velocity are also proved by delicate energy methods.
ASYMPTOTIC SIMILARITY OF INFINITE-DIMENSIONAL LINEAR SYSTEMS AND APPLICATIONS TO STABILITY
WU Jingbo
2000-01-01
In this note a generalization of the concept of similarity called asymptotic similarity for infinite-dimensional linear systems is introduced. We show that this asymptotic similarity preserves the spectrum and the exponential growth bound.
The Asymptotic Form of Non-Global Logarithms, Black Disc Saturation, and Gluonic Deserts
Neill, Duff
2016-01-01
We develop an asymptotic perturbation theory for the large logarithmic behavior of the non-linear integro-differential equation describing the soft correlations of QCD jet measurements, the Banfi-Marchesini-Smye (BMS) equation. This equation captures the late-time evolution of radiating color dipoles after a hard collision. This allows us to prove that at large values of the control variable (the non-global logarithm, a function of the infra-red energy scales associated with distinct hard jets in an event), the distribution has a gaussian tail. We compute the decay width analytically, giving a closed form expression, and find it to be jet geometry independent, up to the number of legs of the dipole in the active jet. Enabling the asymptotic expansion is the correct perturbative seed, where we perturb around an anzats encoding formally no real emissions, an intuition motivated by the buffer region found in jet dynamics. This must be supplemented with the correct application of the BFKL approximation to the BMS...
Willie, Robert
2016-09-01
In this paper, we study a model system of equations of the time dependent Ginzburg-Landau equations of superconductivity in a Lorentz gauge, in scale of Hilbert spaces E^{α } with initial data in E^{β } satisfying 3α + β ≥ N/2, where N=2,3 is such that the spatial domain of the equations [InlineEquation not available: see fulltext.]. We show in the asymptotic dynamics of the equations, well-posedness of the dynamical system for a global exponential attractor {{U}}subset E^{α } compact in E^{β } if α >β , uniform differentiability of orbits on the attractor in E0\\cong L2, and the existence of an explicit finite bounding estimate on the fractal dimension of the attractor yielding that its Hausdorff dimension is as well finite. Uniform boundedness in (0,∞ )× Ω of solutions in E^{1/2}\\cong H1(Ω ) is in addition investigated.
无
2001-01-01
We theoretically investigate the asymptotical stability, localbifurcations and chaos of discrete-time recurrent neural networks with the form ofwhere the input-output function is defined as a generalized sigmoid function, such as vi=tanh(μiui), etc. Numerical simulations are also provided to demonstrate the theoretical results.
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.
Qin, Yuming; Zhang, Jianlin
2016-12-01
In this paper, we establish the global existence, uniqueness and asymptotic behavior of cylindrically symmetric solutions for the 3D infrarelativistic model with radiation in H^i× (H^i)^3× H^i× H^{i+1}(i=1,2,4) . The key point is that the smallness of initial data is not needed.
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.
Quantum fields from global propagators on asymptotically Minkowski and extended de Sitter spacetimes
Vasy, András
2015-01-01
We consider the wave equation on asymptotically Minkowski spacetimes and the Klein-Gordon equation on even asymptotically de Sitter spaces. In both cases we show that the extreme difference of propagators (i.e. retarded propagator minus advanced, or Feynman minus anti-Feynman), defined as Fredholm inverses, induces a symplectic form on the space of solutions with wave front set confined to the radial sets. Furthermore, we construct isomorphisms between the solution spaces and symplectic spaces of asymptotic data. As an application of this result we obtain distinguished Hadamard two-point functions from asymptotic data. Ultimately, we prove that the corresponding Quantum Field Theory on asymptotically de Sitter spacetimes induces canonically a QFT beyond the future and past conformal horizon, i.e. on two even asymptotically hyperbolic spaces. Specifically, we show this to be true both at the level of symplectic spaces of solutions and at the level of Hadamard two-point functions.
Wenrong DAI
2006-01-01
In this paper, we study the asymptotic behavior of global classical solutions of the Cauchy problem for general quasilinear hyperbolic systems with constant multiple and weakly linearly degenerate characteristic fields. Based on the existence of global classical solution proved by Zhou Yi et al., we show that, when t tends to infinity, the solution approaches a combination of C1 travelling wave solutions, provided that the total variation and the L1 norm of initial data are sufficiently small.
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.
Uniformly Asymptotic Stability and Existence of Periodic Solutions and Almost Periodic Solutions
林发兴
1994-01-01
We introduce the concepts of uniformly stable solutions and uniformly-asymptotically stable solutions, and then give the relation between Lyapunov function and those concepts. Furthermore, we establish the theorem that an almost periodic system or periodic system has uniformly-asymptotically stable solutions and Lipschitz’ condition has an almost periodic solution or periodic solution.
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 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.
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.
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.
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.
Nal, P L
2002-01-01
We consider the asymptotic stability and the boundedness with probability one of solutions of linear lto stochastic differential equations not reduced to the Cauchy form and give some numerical examples to show that our sufficient conditions for the asymptotic stability with probability one of solutions are more general and more effective than those of Korenevskij and Mitropoloshij. Moreover, our results can also be applied to the case when the unperturbed linear deterministic system is not assumed to be stable.
Asymptotic vacua with higher derivatives
Spiros Cotsakis
2016-04-01
Full Text Available We study limits of vacuum, isotropic universes in the full, effective, four-dimensional theory with higher derivatives. We show that all flat vacua as well as general curved ones are globally attracted by the standard, square root scaling solution at early times. Open vacua asymptote to horizon-free, Milne states in both directions while closed universes exhibit more complex logarithmic singularities, starting from initial data sets of a possibly smaller dimension. We also discuss the relation of our results to the asymptotic stability of the passage through the singularity in ekpyrotic and cyclic cosmologies.
Asymptotic vacua with higher derivatives
Cotsakis, Spiros, E-mail: skot@aegean.gr [Department of Mathematics, American University of the Middle East, P.O. Box 220 Dasman, 15453 (Kuwait); Kadry, Seifedine, E-mail: Seifedine.Kadry@aum.edu.kw [Department of Mathematics, American University of the Middle East, P.O. Box 220 Dasman, 15453 (Kuwait); Kolionis, Georgios, E-mail: gkolionis@aegean.gr [Research group of Geometry, Dynamical Systems and Cosmology, University of the Aegean, Karlovassi 83200, Samos (Greece); Tsokaros, Antonios, E-mail: atsok@aegean.gr [Research group of Geometry, Dynamical Systems and Cosmology, University of the Aegean, Karlovassi 83200, Samos (Greece)
2016-04-10
We study limits of vacuum, isotropic universes in the full, effective, four-dimensional theory with higher derivatives. We show that all flat vacua as well as general curved ones are globally attracted by the standard, square root scaling solution at early times. Open vacua asymptote to horizon-free, Milne states in both directions while closed universes exhibit more complex logarithmic singularities, starting from initial data sets of a possibly smaller dimension. We also discuss the relation of our results to the asymptotic stability of the passage through the singularity in ekpyrotic and cyclic cosmologies.
Sarayakar, R.V. (Nagpur Univ. (India). Dept. of Mathematics)
1982-07-01
Using the methods of Choquet-Bruhat, Fischer and Marsden and using weighted Sobolev spaces developed recently by Christodoulou and Choquet-Bruhat, it is proved that the Einstein field equations coupled with self-gravitating scalar fields are linearization stable in asymptotically flat space-times.
Asymptotic behavior and stability of second order neutral delay differential equations
Chen, G.L.; van Gaans, O.W.; Verduyn Lunel, Sjoerd
2014-01-01
We study the asymptotic behavior of a class of second order neutral delay differential equations by both a spectral projection method and an ordinary differential equation method approach. We discuss the relation of these two methods and illustrate some features using examples. Furthermore, a fixed
Zhao, Guangyu; Ruan, Shigui
2011-06-01
We study the existence, uniqueness, and asymptotic stability of time periodic traveling wave solutions to a periodic diffusive Lotka-Volterra competition system. Under certain conditions, we prove that there exists a maximal wave speed c(*) such that for each wave speed c ≤ c(*), there is a time periodic traveling wave connecting two semi-trivial periodic solutions of the corresponding kinetic system. It is shown that such a traveling wave is unique modulo translation and is monotone with respect to its co-moving frame coordinate. We also show that the traveling wave solutions with wave speed c c(*).
Zhao, Guangyu; Ruan, Shigui
2011-01-01
We study the existence, uniqueness, and asymptotic stability of time periodic traveling wave solutions to a periodic diffusive Lotka-Volterra competition system. Under certain conditions, we prove that there exists a maximal wave speed c* such that for each wave speed c ≤ c*, there is a time periodic traveling wave connecting two semi-trivial periodic solutions of the corresponding kinetic system. It is shown that such a traveling wave is unique modulo translation and is monotone with respect to its co-moving frame coordinate. We also show that the traveling wave solutions with wave speed c c*. PMID:21572575
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.
Zhijian, Yang
The paper studies the global existence, asymptotic behavior and blowup of solutions to the initial boundary value problem for a class of nonlinear wave equations with dissipative term. It proves that under rather mild conditions on nonlinear terms and initial data the above-mentioned problem admits a global weak solution and the solution decays exponentially to zero as t→+∞, respectively, in the states of large initial data and small initial energy. In particular, in the case of space dimension N=1, the weak solution is regularized to be a unique generalized solution. And if the conditions guaranteeing the global existence of weak solutions are not valid, then under the opposite conditions, the solutions of above-mentioned problem blow up in finite time. And an example is given.
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...
An asymptotically optimal nonparametric adaptive controller
郭雷; 谢亮亮
2000-01-01
For discrete-time nonlinear stochastic systems with unknown nonparametric structure, a kernel estimation-based nonparametric adaptive controller is constructed based on truncated certainty equivalence principle. Global stability and asymptotic optimality of the closed-loop systems are established without resorting to any external excitations.
Global dynamics of a Yang-Mills field on an asymptotically hyperbolic space
Bizoń, Piotr
2014-01-01
We consider a spherically symmetric (purely magnetic) SU(2) Yang-Mills field propagating on an ultrastatic spacetime with two asymptotically hyperbolic regions connected by a throat of radius $\\alpha$. Static solutions in this model are shown to exhibit an interesting bifurcation pattern in the parameter $\\alpha$. We relate this pattern to the Morse index of the static solution with maximal energy. Using a hyperboloidal approach to the initial value problem, we describe the relaxation to the ground state solution for generic initial data and unstable static solutions for initial data of codimension one, two, and three.
Stability and coherent structures of the asymptotic suction boundary layer over a heated plate
Zammert, Stefan; Eckhardt, Bruno
2016-01-01
The asymptotic suction boundary layer (ASBL) is a parallel shear flow that becomes turbulent in a bypass transition in parameter regions where the laminar profile is stable. We here add a temperature gradient perpendicular to the plate and explore the interaction between convection and shear in determining the transition. We find that the laminar state becomes unstable in a subcritical bifurcation and that the critical Rayleigh number and wave number depend strongly on the Prandtl number. We also track several secondary bifurcations and identify states that are localized in two directions, showing different symmetries. In the subcritical regime, transient turbulent states which are connected to exact coherent states and follow the same transition scenario as found in linearly stable shear flows are identified and analyzed. The study extends the bypass transition scenario from shear flows to thermal boundary layers and shows the intricate interactions between thermal and shear forces in determining critical po...
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 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
The Asymptotic Stability of a Kind of Delay Difference Equations%一类时滞差分方程的渐近稳定性
张红燕; 谢永钦; 秦桂香
2005-01-01
关于种群模型中常见的一类线性时滞差分方程的问题,国内外许多学者进行了一些有效的研究.但大部分讨论的都是确定方程中变系数为正、或常系数的差分方程问题.本文根据种群模型的实际背景,讨论了任意变系数方程利用直接方法获得了所讨论方程的零解的一致稳定和全局渐近稳定的充分条件,并举例说明了这两个充分条件不能相互代替.%Aiming at a kind of linear delay difference equations for species model,many mathematicians at home and abroad have made effective researches.Majority of the problems researched by them were confined to the difference equations with positive variable or constant coefficient.According to the model's actual background,discussing the random variable coefficient equation and using direct method,we obtain sufficient condition for the uniform stability and the globally asymptotic stability of difference equation,and also give examples to show they can not substitute each other.
Dobbs, David E.
2010-01-01
This note develops and implements the theory of polynomial asymptotes to (graphs of) rational functions, as a generalization of the classical topics of horizontal asymptotes and oblique/slant asymptotes. Applications are given to hyperbolic asymptotes. Prerequisites include the division algorithm for polynomials with coefficients in the field of…
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.
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.
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.
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.
Study on Robust Uniform Asymptotical Stability for Uncertain Linear Impulsive Delay Systems
刘斌; 刘新芝; 廖晓昕
2003-01-01
In the area of control theory the time-delay systems have been investigated. It's well known that delays often result in instability, therefore, stability analysis of time-delay systems is an important subject in control theory. As a result, many criteria for testing the stability of linear time-delay systems have been proposed. Significant progress has been made in the theory of impulsive systems and impulsive delay systems in recent years. However, the corresponding theory for uncertain impulsive systems and uncertain impulsive delay systems has not been fully developed. In this paper, robust stability criteria are established for uncertain linear delay impulsive systems by using Lyapunov function, Razumikhin techniques and the results obtained. Some examples are given to illustrate our theory.
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
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.
Tsai, Je-Chiang; Sneyd, James
2007-04-01
Traveling waves of calcium are widely observed under the condition that the free cytosolic calcium is buffered. Thus it is of physiological interest to determine how buffers affect the properties of calcium waves. Here we summarise and extend previous results on the existence, uniqueness and stability of traveling wave solutions of the buffered bistable equation, which is the simplest possible model of the upstroke of a calcium wave. Taken together, the results show that immobile buffers do not change the existence, uniqueness or stability of the traveling wave, while mobile buffers can eliminate a traveling wave. However, if a wave exists in the latter case, it remains unique and stable.
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.
On the asymptotic stability of linear discrete time-delay systems: The Lyapunov approach
Stojanović Sreten B.
2006-01-01
Full Text Available New conditions for the stability of discrete delay systems of the form x (k+1 = Arjx (k + Aix (k-h are presented in the paper. These new delay-independent conditions were derived using an approach based on the second Lyapunov's method. These results are less conservative than some in the existing literature. A numerical example was worked out to show the applicability of the derived results.
离散时延双神经元网络的渐近稳定性%Asymptotic Stability Criteria for a Two-Neuron Network with Different Time Delays
李绍文; 李绍荣; 廖晓峰
2003-01-01
New sufficient conditions for the asymptotic stability of a two-neuron network with different time delays are derived. These conditions lead to delay-dependent and delay-independent asymptotic stability. Our results are shown to be less conservative and restrictive than those reported in the literature. Some examples are given to illustrate the correctness of our results.
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.
Thermal stability analysis of nonlinearly charged asymptotic AdS black hole solutions
Dehghani, M.; Hamidi, S. F.
2017-08-01
In this paper, the four-dimensional nonlinearly charged black hole solutions have been considered in the presence of the power Maxwell invariant electrodynamics. Two new classes of anti-de Sitter (AdS) black hole solutions have been introduced according to different amounts of the parameters in the nonlinear theory of electrodynamics. The conserved and thermodynamical quantities of either of the black hole classes have been calculated from geometrical and thermodynamical approaches, separately. It has been shown that the first law of black hole thermodynamics is satisfied for either of the AdS black hole solutions we just obtained. Through the canonical and grand canonical ensemble methods, the black hole thermal stability or phase transitions have been analyzed by considering the heat capacities with the fixed black hole charge and fixed electric potential, respectively. It has been found that the new AdS black holes are stable if some simple conditions are satisfied.
Existence and asymptotic stability of a viscoelastic wave equation with a delay
Kirane, Mokhtar
2011-07-07
In this paper, we consider the viscoelastic wave equation with a delay term in internal feedbacks; namely, we investigate the following problem, together with initial conditions and boundary conditions of Dirichlet type. Here (x, t) ∈ Ω × (0, ∞), g is a positive real valued decreasing function and μ1, μ2 are positive constants. Under an hypothesis between the weight of the delay term in the feedback and the weight of the term without delay, using the Faedo-Galerkin approximations together with some energy estimates, we prove the global existence of the solutions. Under the same assumptions, general decay results of the energy are established via suitable Lyapunov functionals. © 2011 Springer Basel AG.
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 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
Markowich, Peter
2010-06-01
We study the system ct + u · ∇c = ∇c -nf(c) nt + u · ∇n = ∇n m - ∇ · (n×(c) ∇c) ut + u·∇u + ∇P - η∇u + n∇φ/ = 0 ∇·u = 0. arising in the modelling of the motion of swimming bacteria under the effect of diffusion, oxygen-taxis and transport through an incompressible fluid. The novelty with respect to previous papers in the literature lies in the presence of nonlinear porous-medium-like diffusion in the equation for the density n of the bacteria, motivated by a finite size effect. We prove that, under the constraint m ε (3/2, 2] for the adiabatic exponent, such system features global in time solutions in two space dimensions for large data. Moreover, in the case m = 2 we prove that solutions converge to constant states in the large-time limit. The proofs rely on standard energy methods and on a basic entropy estimate which cannot be achieved in the case m = 1. The case m = 2 is very special as we can provide a Lyapounov functional. We generalize our results to the three-dimensional case and obtain a smaller range of exponents m ε (m*, 2] with m* > 3/2, due to the use of classical Sobolev inequalities.
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.
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.
STABILITY OF SOLUTIONS TO CERTAIN FOURTH-ORDER DELAY DIFFERENTIAL EQUATIONS
无
2010-01-01
By the Lyapunov functional approach, some better results on the asymptotic stabiBy the Lyapunov functional approach, some better results on the asymptotic stability and global asymptotic stability of zero solution to a certain fourth-order non-linear differential equation with delay are obtained.
Wedin, Håkan; Cherubini, Stefania
2016-12-01
The asymptotic suction boundary layer (ASBL) is used for studying two permeability models, namely the Darcy and the Forchheimer model, the latter being more physically correct according to the literature. The term that defines the two apart is a function of the non-Darcian wall permeability {\\hat{K}}2 and of the wall suction {\\hat{V}}0, whereas the Darcian wall permeability {\\hat{K}}1 is common to the two models. The underlying interest of the study lies in the field of transition to turbulence where focus is put on two-dimensional nonlinear traveling waves (TWs) and their three-dimensional linear stability. Following a previous study by Wedin et al (2015 Phys. Rev. E 92 013022), where only the Darcy model was considered, the present work aims at comparing the two models, assessing where in the parameter space they cease to produce the same results. For low values of {\\hat{K}}1 both models produce almost identical TW solutions. However, when both increasing the suction {\\hat{V}}0 to sufficiently high amplitudes (i.e. lowering the Reynolds number Re, based on the displacement thickness) and using large values of the wall porosity, differences are observed. In terms of the non-dimensional Darcian wall permeability parameter, a, strong differences in the overall shape of the bifurcation curves are observed for a≳ 0.70, with the emergence of a new family of solutions at Re lower than 100. For these large values of a, a Forchheimer number {{Fo}}\\max ≳ 0.5 is found, where Fo expresses the ratio between the kinetic and viscous forces acting on the porous wall. Moreover, the minimum Reynolds number, {{Re}}g, for which the Navier-Stokes equations allow for nonlinear solutions, decreases for increasing values of a. Fixing the streamwise wavenumber to α = 0.154, as used in the study by Wedin et al referenced above, we find that {{Re}}g is lowered from Re ≈ 3000 for zero permeability, to below 50 for a = 0.80 for both permeability models. Finally, the stability of
一类有记忆T-S模糊系统的渐近稳定性%Asymptotic Stability of a Class of T-S Fuzzy System with Memory
王艳华
2014-01-01
For a T-S fuzzy system with uncertain state terms , a memory feedback controller was designed , thus the global asymptotic stability of the system was achieved with Lyapunov stability theory .Firstly, by construc-ting a Lyapunov quadratic function , it was proved that the closed -loop system was asymptotically stable through the application of this memory feedback controller .Secondly , the feedback gain matrix of the controller was found with the linear matrix inequality (LMI) technique in MATLAB.Finally, a simulation example was given to illus-trate the validity of the proposed method .%基于带有状态不确定项的T-S模糊系统，通过设计有记忆反馈控制器，利用Lyapunov稳定性理论实现系统的全局渐近稳定性，首先通过构造Lyapunov 二次函数，证明在此有记忆反馈控制器下，形成的闭环系统是全局渐近稳定的，其次，通过利用matlab中的LMI工具箱求解控制器的反馈增益矩阵，最后通过仿真算例说明文章所用方法的有效性。
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.
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...
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.
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.
Tsyganov, Eugene
2007-09-01
We investigate the asymptotic behavior of the solutions of the compressible Navier Stokes equations with nonmonotonic pressure when the initial data is large and discontinuous. We provide sufficient conditions on the pressure function for different boundary-value problems that guarantee strong convergence of the volume variable as time approaches infinity and show that, typically, fairly arbitrary discontinuous static phase mixtures can be realized as time-asymptotic limits from smooth initial data. It is required in the analysis that we improve known existence theories, which typically have small data or time-dependent bounds.
Global asymptotic stability of a passive juggling strategy: A possible parts-feeding method
Swanson P. J.
1995-01-01
Full Text Available In this paper we demonstrate that a passive vibration strategy can bring a one-degree-of-freedom ball to a specified periodic trajectory from all initial conditions. We draw motivation from the problem of parts feeding in sensorless assembly. We provide simulation results suggesting the relevance of our analysis to the parts feeding problem.
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.
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 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.
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...
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.
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.
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...
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...
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 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.
田慧慧; 苏玉鑫
2012-01-01
针对高度非线性多关节机器人的轨迹跟踪问题,提出一类输出反馈重复学习控制算法,使得在只有位置信息可测以及模型信息不确定的条件下即能获得良好的控制品质.非线性滤波器的引入解决了现实中速度信号较难获得的问题,重复学习控制策略实现了对周期性参考输入的渐近稳定跟踪.应用Lyapunov直接稳定性理论证明了闭环系统的全局渐近稳定性.三自由度机器人系统数值仿真结果表明了所提出的输出反馈重复学习控制的有效性.%An output feedback repetitive control(ORC) method is developed for the trajectory tracking control of robot manipulators with model uncertainty. Despite the fact that only link position is available, the proposed controller obtains favorable performance. A nonlinear filter is utilized in the controller development to remove the requirement of link velocity measurement. The repetitive control strategy ensures that the link position globally asymptotically tracks the desired periodic reference signals. The global asymptotic stability of the resulting closed-loop system is proved by using the Lyapunov's direct method. Simulation results on a three degree-of-freedom robot show the effectiveness of the proposed scheme.
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.
梁保松; 陈振
2004-01-01
J. L Lions and W. A. Stranss [1] have proved the existence of a global solution of the initial boundary value problem for nonlinear generalized Euler-Possion-Darboux equation. In this paper we are going to investigate the asymptotic behavior of the global solution by a difference inequality.
STABILITY ANALYSIS OF HOPFIELD NEURAL NETWORKS WITH TIME DELAY
王林山; 徐道义
2002-01-01
The global asymptotic stability for Hopfield neural networks with time delay was investigated. A theorem and two corollaries were obtained, in which the boundedness and differentiability offjon R in some articles were deleted. Some sufficient conditions for the existence of global asymptotic stable equilibrium of the networks in this paper are better than the sufficient conditions in quoted articles.
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.
STABILITY ANALYSIS OF RUNGE-KUTTA METHODS FOR NONLINEAR SYSTEMS OF PANTOGRAPH EQUATIONS
Yue-xin Yu; Shou-fu Li
2005-01-01
This paper is concerned with numerical stability of nonlinear systems of pantograph equations. Numerical methods based on (k, l)-algebraically stable Runge-Kutta methods are suggested. Global and asymptotic stability conditions for the presented methods are derived.
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 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.
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.
Global stability of Gompertz model of three competing populations
Yu, Yumei; Wang, Wendi; Lu, Zhengyi
2007-10-01
The model of three competitive populations with Gompertz growth is studied. The periodic solutions are ruled out by generalized Dulac criteria. On the basis of the analysis, we obtain conditions that ensure the asymptotic behavior of the model is simple.
Stability Analysis for Stochastic Delayed High-order Neural Networks
无
2006-01-01
In this paper, the global asymptotic stability analysis problem is considered for a class of stochastic high-order neural networks with time-delays. Based on a Lyapunov-Krasovskii functional and the stochastic stability analysis theory, several sufficient conditions are derived in order to guarantee the global asymptotic convergence of the equilibrium point in the mean square. Investigation shows that the addressed stochastic highorder delayed neural networks are globally asymptotically stable in the mean square if there are solutions to some linear matrix inequalities (LMIs). Hence, the global asymptotic stability of the studied stochastic high-order delayed neural networks can be easily checked by the Matlab LMI toolbox. A numerical example is given to demonstrate the usefulness of the proposed global stability criteria.
张长海; 梁久祯; 刘明珠
2000-01-01
This paper deals with the stability analysis of numerical solutionof linear -methods for delay differential equations. We focuson the linear test equation x(t)=ax(t)+bx(［t］), where a,b areconstants and ［t］ is the largest-integer function. Sufficent conditionsare given for the numerical solution to be asymptotic stable
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.
Qin, Yuming
2016-01-01
This book presents recent findings on the global existence, the uniqueness and the large-time behavior of global solutions of thermo(vis)coelastic systems and related models arising in physics, mechanics and materials science such as thermoviscoelastic systems, thermoelastic systems of types II and III, as well as Timoshenko-type systems with past history. Part of the book is based on the research conducted by the authors and their collaborators in recent years. The book will benefit interested beginners in the field and experts alike.
Di Francesco, Marco
2011-04-01
The dependence of tumor on essential nutrients is known to be crucial for its evolution and has become one of the targets for medical therapies. Based on this fact a reaction-diffusion system with chemotaxis term and nutrient-based growth of tumors is presented. The formulation of the model considers also an influence of tumor and pharmacological factors on nutrient concentration. In the paper, convergence of solutions to constant, stationary states in the one-dimensional case for small perturbation of the equilibria is investigated. The nonlinear stability results are obtained by means of the classical symmetrization method and energy Sobolev estimates. © 2010 Elsevier Ltd.
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.
Asymptotic freedom, asymptotic flatness and cosmology
Kiritsis, Elias
2013-01-01
Holographic RG flows in some cases are known to be related to cosmological solutions. In this paper another example of such correspondence is provided. Holographic RG flows giving rise to asymptotically-free $\\beta$-functions have been analyzed in connection with holographic models of QCD. They are shown upon Wick rotation to provide a large class of inflationary models with logarithmically soft inflaton potentials. The scalar spectral index is universal and depends only on the number of e-foldings. The ratio of tensor to scalar power depends on the single extra real parameter that defines this class of models. The Starobinsky inflationary model as well as the recently proposed models of T-inflation are members of this class. The holographic setup gives a completely new (and contrasting) view to the stability and other problems of such inflationary models.
Parshad, Rana
2013-01-01
The purpose of this manuscript is to propose a model for the biological control of invasive species, via introduction of phenotypically modified organisms into a target population. We are inspired by the earlier Trojan Y Chromosome model [J.B. Gutierrez, J.L. Teem, J. Theo. Bio., 241(22), 333-341, 2006]. However, in the current work, we remove the assumption of logisticgrowth rate, and do not consider the addition of sex-reversed supermales. Also the constant birth and death coefficients, considered earlier, are replaced by functionally dependent ones. In this case the nonlinearities present serious difficulties since they change sign, and the components of the solution are not a priori bounded, in some Lp-space for p large, to permit theapplication of the well known regularizing effect principle. Thus functional methods to deducethe global existence in time, for the system in question, are not applicable. Our techniques are based on the Lyapunov functional method. We prove global existence of solutions, as well asexistence of a finite dimensional global attractor, that supports states of extinction. Our analytical finding are in accordance with numerical simulations, which we also present. © 2013 International Press.
Imed Bachar
2014-01-01
Full Text Available We are interested in the following fractional boundary value problem: Dαu(t+atuσ=0, t∈(0,∞, limt→0t2-αu(t=0, limt→∞t1-αu(t=0, where 1<α<2, σ∈(-1,1, Dα is the standard Riemann-Liouville fractional derivative, and a is a nonnegative continuous function on (0,∞ satisfying some appropriate assumptions related to Karamata regular variation theory. Using the Schauder fixed point theorem, we prove the existence and the uniqueness of a positive solution. We also give a global behavior of such solution.
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 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.
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.
WANG; Jinliang
2001-01-01
Surveys, 1993, 7: 305.［16］Shephand, N., Statistical aspects of ARCH and stochastic volatility, in Time Series Models in Econometrics, Finance and Other Fields (eds. Cox, D. R., Hinkley, D. V., Barndorff-Nielsen, O. E.), London: Chapman & Hall, 1996, 1.［17］Pantula, S. G., Estimation of autoregressive models with ARCH errors, Sankhya, Ser. B, 1988, 50: 119.［18］Campbell, J. Y., Lo, A. W., Mackinlay, A. C., The Econometrics of Financial Markets, Princeton: Princeton University Press, 1997, 488.［19］Fan, J., Gijbels, I., Local Polynomial Modeling and Its Applications, London: Chapman & Hall, 1996.［20］Lu, Z. D., A note on geometric ergodicity of autoregressive conditional heteroscedasticity (ARCH) model, Statistics and Probability Letters, 1996, 30: 305.［21］Robinson, P. M., Nonparametric estimators for time series, Journal of Time Series Analysis, 1983, 4: 185.［22］Stone, C. J., Optimal rates of convergence for nonparametric estimators, Annals of Statistics, 1980, 8: 1348.［23］Stone, C. J., Optimal global rates of convergence for nonparametric kernel regression, Annals of Statistics, 1982, 10: 1040.［24］Truong, Y. M., Stone, C. J., Nonparametric function estimation involving time series, Annals of Statistics, 1992, 20: 77.［25］Masry, E., Multivariate polynomial regression for time series; uniform strong consistency and rates, Journal of Time Series Analysis, 1996, 17: 571.［26］Ruppert, D., Wand, M. P., Multivariate locally weighted least squares regression, Annals of Statistics, 1994, 22: 1346.［27］Bollerslev, T., Generalized autoregressive conditional heteroscedasticity, Journal of Econometrics, 1986, 31: 307.［28］Engle, R. F., Granger, C. W. J., Co-integration and error-correction: representation, estimation and testing, Econometrica, 1987, 55: 251.
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 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.
Preheating in an asymptotically safe quantum field theory
Svendsen, Ole; Moghaddam, Hossein Bazrafshan; Brandenberger, Robert
2016-01-01
We consider reheating in a class of asymptotically safe quantum field theories recently studied in [D. F. Litim and F. Sannino, Asymptotic safety guaranteed, J. High Energy Phys. 12 (2014) 178; D. F. Litim, M. Mojaza, and F. Sannino, Vacuum stability of asymptotically safe gauge-Yukawa theories, ...
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.
Control Lyapunov Stabilization of Nonlinear Systems with Structural Uncertainty
CAI Xiu-shan; HAN Zheng-zhi; TANG Hou-jun
2005-01-01
This paper deals with global stabilization problem for the nonlinear systems with structural uncertainty.Based on control Lyapunov function, a sufficient and necessary condition for the globally and asymptotically stabilizing the equailibrium of the closed system is given. Moreovery, an almost smooth state feedback control law is constructed. The simulation shows the effectiveness of the method.
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.
ON THE BOUNDEDNESS AND THE STABILITY OF SOLUTION TO THIRD ORDER NON-LINEAR DIFFERENTIAL EQUATIONS
无
2008-01-01
In this paper we investigate the global asymptotic stability,boundedness as well as the ultimate boundedness of solutions to a general third order nonlinear differential equation,using complete Lyapunov function.
Application of AN Asymptotic Method to Transient Dynamic Problems
Fafard, M.; Henchi, K.; Gendron, G.; Ammar, S.
1997-11-01
A new method to solve linear dynamics problems using an asymptotic method is presented. Asymptotic methods have been efficiently used for many decades to solve non-linear quasistatic structural problems. Generally, structural dynamics problems are solved using finite elements for the discretization of the space domain of the differential equations, and explicit or implicit schemes for the time domain. With the asymptotic method, time schemes are not necessary to solve the discretized (space) equations. Using the analytical solution of a single degree of freedom (DOF) problem, it is demonstrated, that the Dynamic Asymptotic Method (DAM) converges to the exact solution when an infinite series expansion is used. The stability of the method has been studied. DAM is conditionally stable for a finite series expansion and unconditionally stable for an infinite series expansion. This method is similar to the analytical method of undetermined coefficients or to power series method being used to solve ordinary differential equations. For a multi-degree-of-freedom (MDOF) problem with a lumped mass matrix, no factorization or explicit inversion of global matrices is necessary. It is shown that this conditionally stable method is more efficient than other conditionally stable explicit central difference integration techniques. The solution is continuous irrespective of the time segment (step) and the derivatives are continuous up to orderN-1 whereNis the order of the series expansion.
Asymptotically Safe Dark Matter
Sannino, Francesco; Shoemaker, Ian M.
2015-01-01
We introduce a new paradigm for dark matter (DM) interactions in which the interaction strength is asymptotically safe. In models of this type, the coupling strength is small at low energies but increases at higher energies, and asymptotically approaches a finite constant value. The resulting...... searches are the primary ways to constrain or discover asymptotically safe dark matter....
Asymptotically Safe Dark Matter
Sannino, Francesco; Shoemaker, Ian M.
2015-01-01
We introduce a new paradigm for dark matter (DM) interactions in which the interaction strength is asymptotically safe. In models of this type, the coupling strength is small at low energies but increases at higher energies, and asymptotically approaches a finite constant value. The resulting...... searches are the primary ways to constrain or discover asymptotically safe dark matter....
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...
Global Dynamics of a Virus Dynamical Model with Cell-to-Cell Transmission and Cure Rate
Tongqian Zhang
2015-01-01
Full Text Available The cure effect of a virus model with both cell-to-cell transmission and cell-to-virus transmission is studied. By the method of next generation matrix, the basic reproduction number is obtained. The locally asymptotic stability of the virus-free equilibrium and the endemic equilibrium is considered by investigating the characteristic equation of the model. The globally asymptotic stability of the virus-free equilibrium is proved by constructing suitable Lyapunov function, and the sufficient condition for the globally asymptotic stability of the endemic equilibrium is obtained by constructing suitable Lyapunov function and using LaSalle invariance principal.
Stability for a class of semilinear fractional stochastic integral equations
Fiel, Allan; Jorge A. León; Márquez-Carreras, David
2015-01-01
In this paper we study some stability criteria for some semilinear integral equations with a function as initial condition and with additive noise, which is a Young integral that could be a functional of fractional Brownian motion. Namely, we consider stability in the mean, asymptotic stability, stability, global stability and Mittag-Leffler stability. To do so, we use comparison results for fractional equations and an equation (in terms of Mittag-Leffler functions) whose family of solutions ...
Stability of oblique shock front
CHEN; Shuxing(陈恕行)
2002-01-01
The stability of the weak planar oblique shock front with respect to the perturbation of the wall is discussed. By the analysis of the formation and the global construction of shock and its asymptotic behaviour for stationary supersonic flow along a smooth rigid wall we obtain the stability of the solution containing a weak planar shock front. The stability can be used to single out a physically reasonable solution together with the entropy condition.
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.
Universal asymptotic umbrella for hydraulic fracture modeling
Linkov, Aleksandr M
2014-01-01
The paper presents universal asymptotic solution needed for efficient modeling of hydraulic fractures. We show that when neglecting the lag, there is universal asymptotic equation for the near-front opening. It appears that apart from the mechanical properties of fluid and rock, the asymptotic opening depends merely on the local speed of fracture propagation. This implies that, on one hand, the global problem is ill-posed, when trying to solve it as a boundary value problem under a fixed position of the front. On the other hand, when properly used, the universal asymptotics drastically facilitates solving hydraulic fracture problems (both analytically and numerically). We derive simple universal asymptotics and comment on their employment for efficient numerical simulation of hydraulic fractures, in particular, by well-established Level Set and Fast Marching Methods.
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.
樊铁钢
2000-01-01
The vibrational systems of a class of Timoshenko-beams are discussed.The conditions of the asymptotic stability and pole-assignment of the closed-loop systems of Timoshenko-beam are given out,where the theory of semigroups of linear operators and unconditional basis theory and the theory of (D) operators are used.%利用了算子半群理论、无条件基理论和(D)类算子理论讨论了一类Timoshenko梁振动系统,给出了闭环系统渐近稳定与极点配置的条件.
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...
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.
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.
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 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.
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 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.
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 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 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.
New delay-dependent criterion for the stability of recurrent neural networks with time-varying delay
ZHANG HuaGuang; WANG ZhanShan
2009-01-01
This paper is concerned with the global asymptotic stability of a class of recurrent neural networks with interval time-varying delay. By constructing a suitable Lyapunov functional, a new criterion is established to ensure the global asymptotic stability of the concerned neural networks, which can be expressed in the form of linear matrix inequality and independent of the size of derivative of time varying delay. Two numerical examples show the effectiveness of the obtained results.
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
Remarks on asymptotically safe inflation
Tye, S.-H. Henry; Xu, Jiajun
2010-12-01
We comment on Weinberg’s interesting analysis of asymptotically safe inflation [S. Weinberg, Phys. Rev. DPRVDAQ1550-7998 81, 083535 (2010).10.1103/PhysRevD.81.083535]. We find that even if the gravity theory exhibits an ultraviolet fixed point, the energy scale during inflation is way too low to drive the theory close to the fixed point value. We choose the specific renormalization group flow away from the fixed point towards the infrared region that reproduces the Newton’s constant and today’s cosmological constant. We follow this renormalization group flow path to scales below the Planck scale to study the stability of the inflationary scenario. Again, we find that some fine-tuning is necessary to get enough e folds of inflation in the asymptotically safe inflationary scenario.
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.
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.
Stability in a diffusive food chain model with Michaelis-Menten functional response
Lin, Zhigui; Pedersen, Michael
2004-01-01
This paper deals with the behavior of positive solutions to a reaction-diffusion system with homogeneous Neumann boundary conditions describing a three species food chain. A sufficient condition for the local asymptotical stability is given by linearization and also a sufficient condition...... for the global asymptotical stability is given by a Lyapunov function. Our result shows that the equilibrium solution is globally asymptotically stable if the net birth rate of the first species is big enough and the net death rate of the third species is neither too big nor too small. (C) 2004 Elsevier Ltd. All...
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 ...
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.
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.
Asymptotics of Random Contractions
Hashorva, Enkelejd; Tang, Qihe
2010-01-01
In this paper we discuss the asymptotic behaviour of random contractions $X=RS$, where $R$, with distribution function $F$, is a positive random variable independent of $S\\in (0,1)$. Random contractions appear naturally in insurance and finance. Our principal contribution is the derivation of the tail asymptotics of $X$ assuming that $F$ is in the max-domain of attraction of an extreme value distribution and the distribution function of $S$ satisfies a regular variation property. We apply our result to derive the asymptotics of the probability of ruin for a particular discrete-time risk model. Further we quantify in our asymptotic setting the effect of the random scaling on the Conditional Tail Expectations, risk aggregation, and derive the joint asymptotic distribution of linear combinations of random contractions.
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.
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.
ASYMPTOTIC QUANTIZATION OF PROBABILITY DISTRIBUTIONS
Klaus P(o)tzelberger
2003-01-01
We give a brief introduction to results on the asymptotics of quantization errors.The topics discussed include the quantization dimension,asymptotic distributions of sets of prototypes,asymptotically optimal quantizations,approximations and random quantizations.
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...
Weakly asymptotically hyperbolic manifolds
Allen, Paul T; Lee, John M; Allen, Iva Stavrov
2015-01-01
We introduce a class of "weakly asymptotically hyperbolic" geometries whose sectional curvatures tend to $-1$ and are $C^0$, but are not necessarily $C^1$, conformally compact. We subsequently investigate the rate at which curvature invariants decay at infinity, identifying a conformally invariant tensor which serves as an obstruction to "higher order decay" of the Riemann curvature operator. Finally, we establish Fredholm results for geometric elliptic operators, extending the work of Rafe Mazzeo and John M. Lee to this setting. As an application, we show that any weakly asymptotically hyperbolic metric is conformally related to a weakly asymptotically hyperbolic metric of constant negative curvature.
Liapunov structure and asymptotic expressions of linear differential systems
高维新
1996-01-01
With a view to the researches on asymptotic properties for linear differential systems,the characteristic number is transformed into functional dass which can indicate the change trend of the norm for solution,so the invariant structure is given under Liapunov changes and feasible computational method of asymptotic expressions for linear differential systems with variant coefficients,and various asymptotic conclusions induding the necessary and sufllcient conditions of stability are got.
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 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 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.
Nonstandard asymptotic analysis
Berg, Imme
1987-01-01
This research monograph considers the subject of asymptotics from a nonstandard view point. It is intended both for classical asymptoticists - they will discover a new approach to problems very familiar to them - and for nonstandard analysts but includes topics of general interest, like the remarkable behaviour of Taylor polynomials of elementary functions. Noting that within nonstandard analysis, "small", "large", and "domain of validity of asymptotic behaviour" have a precise meaning, a nonstandard alternative to classical asymptotics is developed. Special emphasis is given to applications in numerical approximation by convergent and divergent expansions: in the latter case a clear asymptotic answer is given to the problem of optimal approximation, which is valid for a large class of functions including many special functions. The author's approach is didactical. The book opens with a large introductory chapter which can be read without much knowledge of nonstandard analysis. Here the main features of the t...
ANALYSIS ON STABILITY OF AN AUTONOMOUS DYNAMICS SYSTEM FOR SARS EPIDEMIC
ZHANG Shuang-de; HAO Hai
2005-01-01
An extended dynamic model for SARS epidemic was deduced on the basis of the K-M infection model with taking the density constraint of susceptible population and the cure and death rates of patients into consideration. It is shown that the infectionfree equilibrium is the global asymptotic stability under given conditions, and endemic equilibrium is not the asymptotic stability. It comes to the conclusion that the epidemic system is the permanent persistence existence under appropriate conditions.
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
Zumbrun, Kevin
2010-01-01
We establish one-dimensional spectral, or "normal modes", stability of ZND detonations in the small heat release limit and the related high overdrive limit with heat release and activation energy held fixed, verifying numerical observations of Erpenbeck in the 1960s. The key technical points are a strategic rescaling of parameters converting the infinite overdrive limit to a finite, regular perturbation problem, and a careful high-frequency analysis depending uniformly on model parameters. The latter recovers the important result of high-frequency stability established by Erpenbeck by somewhat different techniques. Notably, the techniques used here yield quantitative estimates well suited for numerical stability investigation.
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.
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.
赵聪; 李耀华; 李子欣; 王平; 楚遵方
2016-01-01
The circulating current of modular multilevel converter ( MMC) makes arm current distorted. It increa⁃ses converter losses and also threatens safe operating of power devices. This paper analyzes the open⁃loop circulat⁃ing current suppression method based on arm energy from two aspects. Firstly, the fundamental of the open⁃loop circulating current suppression algorithm is proved. This paper also proposes general principle of open⁃loop circulat⁃ing current suppression which provides theoretical basis for system design of MMC. Secondly, compared with the actual value modulation algorithm which is easier to implement, the method based on arm energy in this paper has module capacitor voltage self⁃balancing features without additional control. This paper also proves that the open⁃loop circulating current suppression based on arm energy has module voltage self⁃balancing features theoretically. Hence, the global asymptotic stability of the open⁃loop circulating current suppression is proved. Finally, the meth⁃od and its module capacitor voltage self⁃balancing are verified by simulation.%模块化多电平变流器相间环流的存在使得桥臂电流产生畸变，一方面增加了变流器的损耗，另一方面对功率器件的安全工作范围也提出了更高的要求。本文从两个方面分析了开环环流抑制策略的渐进稳定性。首先证明了开环环流抑制策略的基本原理，并在此基础上提出开环环流抑制的一般原理，为模块化多电平变流器开环环流抑制的系统设计提供了理论依据。其次，相比实现起来更为简单的实际值调制环流抑制方法，本文的基于桥臂能量的开环环流抑制策略具有模块电容电压自平衡的特性，无需施加额外的控制；同时，从理论上证明了该开环环流抑制策略具备在不平衡条件下电容电压自平衡的特性，从而证明了该方法的渐近稳定性。最后，通过仿真验证了
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.
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.
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.
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.
Asymptotic symmetry algebra of conformal gravity
Irakleidou, M
2016-01-01
We compute asymptotic symmetry algebras of conformal gravity. Due to more general boundary conditions allowed in conformal gravity in comparison to those in Einstein gravity, we can classify the corresponding algebras. The highest algebra for non-trivial boundary conditions is five dimensional and it leads to global geon solution with non-vanishing charges.
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.
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.
Optimization of Parameters of Asymptotically Stable Systems
Anna Guerman
2011-01-01
Full Text Available This work deals with numerical methods of parameter optimization for asymptotically stable systems. We formulate a special mathematical programming problem that allows us to determine optimal parameters of a stabilizer. This problem involves solutions to a differential equation. We show how to chose the mesh in order to obtain discrete problem guaranteeing the necessary accuracy. The developed methodology is illustrated by an example concerning optimization of parameters for a satellite stabilization system.
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.
Singh, S. N.
1982-03-01
Using the invariance principle of LaSalle (1962) sufficient conditions for the existence of linear and nonlinear control laws for local and global asymptotic stability of nonlinear Hamiltonian systems are derived. An instability theorem is also presented which identifies the control laws from the given class which cannot achieve asymptotic stability. Some of the stability results are based on certain results for the univalence of nonlinear maps. A similar approach for the stabilization of bilinear systems which include nonconservative systems in elasticity is used and a necessary and sufficient condition for stabilization is obtained. An application to attitude control of a gyrostat Satellite is presented.
Wu, Guochun
2017-01-01
In this paper, we investigate the global existence and uniqueness of strong solutions to the initial boundary value problem for the 3D compressible Navier-Stokes equations without heat conductivity in a bounded domain with slip boundary. The global existence and uniqueness of strong solutions are obtained when the initial data is near its equilibrium in H2 (Ω). Furthermore, the exponential convergence rates of the pressure and velocity are also proved by delicate energy methods.
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...
Asymptotics of a horizontal liquid bridge
Haynes, M.; O'Brien, S. B. G.; Benilov, E. S.
2016-04-01
This paper uses asymptotic techniques to find the shape of a two dimensional liquid bridge suspended between two vertical walls. We model the equilibrium bridge shape using the Laplace-Young equation. We use the Bond number as a small parameter to deduce an asymptotic solution which is then compared with numerical solutions. The perturbation approach demonstrates that equilibrium is only possible if the contact angle lies within a hysteresis interval and the analysis relates the width of this interval to the Bond number. This result is verified by comparison with a global force balance. In addition, we examine the quasi-static evolution of such a two dimensional bridge.
Ramnath, Rudrapatna V
2012-01-01
This book addresses the task of computation from the standpoint of asymptotic analysis and multiple scales that may be inherent in the system dynamics being studied. This is in contrast to the usual methods of numerical analysis and computation. The technical literature is replete with numerical methods such as Runge-Kutta approach and its variations, finite element methods, and so on. However, not much attention has been given to asymptotic methods for computation, although such approaches have been widely applied with great success in the analysis of dynamic systems. The presence of differen
M Turkyilmazoglu
2009-12-01
In this paper the linear stability properties of the magnetohydro-dynamic ﬂow of an incompressible, viscous and electrically conducting ﬂuid are investigated for the boundary-layer due to an inﬁnite permeable rotating-disk. The ﬂuid is subjected to an external magnetic ﬁeld perpendicular to the disk. The interest lies also in ﬁnding out the effects of uniform suction or injection. In place of the traditional linear stability method, a theoretical approach is adopted here based on the high-Reynolds-number triple-deck theory. It is demonstrated that the nonstationary perturbations evolve in accordance with an eigenrelation analytically obtained.
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.
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.
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 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.
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 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.
Ma Xuan; Yin Hui; Jing Jin
2009-01-01
This article is concerned with the global existence and large time behavior of solutions to the Cauchy problem for a parabolic-elliptic system related to the Camassa-Holm shallow water equation with the initial data u(0,x) = u0(x)→±, as x→±∞. (Ⅰ) Here, u- 0 for all u under consideration. Main aim of this article is to study the relation between solutions to the above Cauchy problem and those to the Riemann problem of the following nonlinear conservation law It is well known that if u- (x) - U(0,x) ∈H1(R) and u- < u+, the above Cauchy problem (E) and (I) admits a unique global classical solution u(t, x) which tends to the rarefaction wave uR(x/t) as t→+∞ in the maximum norm. The proof is given by an elementary energy method.
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.
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.
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 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.
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.
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.
Global dynamics of a dengue epidemic mathematical model
Cai Liming [Department of Mathematics, Xinyang Normal University, Xinyang 464000 (China); Academy of Mathematics and Systems Science, Academia Sinica, Beijing 100080 (China)], E-mail: lmcai06@yahoo.com.cn; Guo Shumin [Beijing Institute of Information Control, Beijing 100037 (China); Li, XueZhi [Department of Mathematics, Xinyang Normal University, Xinyang 464000 (China); Ghosh, Mini [School of Mathematics and Computer Application, Thapar University, Patiala 147004 (India)
2009-11-30
The paper investigates the global stability of a dengue epidemic model with saturation and bilinear incidence. The constant human recruitment rate and exponential natural death, as well as vector population with asymptotically constant population, are incorporated into the model. The model exhibits two equilibria, namely, the disease-free equilibrium and the endemic equilibrium. The stability of these two equilibria is controlled by the threshold number R{sub 0}. It is shown that if R{sub 0} is less than one, the disease-free equilibrium is globally asymptotically stable and in such a case the endemic equilibrium does not exist; if R{sub 0} is greater than one, then the disease persists and the unique endemic equilibrium is globally asymptotically stable.
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.
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...
Sufficient Conditions for Dynamical Output Feedback Stabilization Via the Circle Criterion
2003-01-01
This paper suggests sufficient conditions for asymptotically stable dynamical output feedback controller design based on the circle criterion. It is shown that a dynamic output feedback stabilization problem with impending problems of finite escape time, previously attacked by observer-based design, can be successfully solved using circle criterion design. Stability of the closed-loop system is global and robust to parameter uncertainty.
Asymptotically hyperbolic connections
Fine, Joel; Krasnov, Kirill; Scarinci, Carlos
2015-01-01
General Relativity in 4 dimensions can be equivalently described as a dynamical theory of SO(3)-connections rather than metrics. We introduce the notion of asymptotically hyperbolic connections, and work out an analog of the Fefferman-Graham expansion in the language of connections. As in the metric setup, one can solve the arising "evolution" equations order by order in the expansion in powers of the radial coordinate. The solution in the connection setting is arguably simpler, and very straightforward algebraic manipulations allow one to see how the obstruction appears at third order in the expansion. Another interesting feature of the connection formulation is that the "counter terms" required in the computation of the renormalised volume all combine into the Chern-Simons functional of the restriction of the connection to the boundary. As the Chern-Simons invariant is only defined modulo large gauge transformations, the requirement that the path integral over asymptotically hyperbolic connections is well-d...
Litim, Daniel F.; Sannino, Francesco
2014-01-01
We study the ultraviolet behaviour of four-dimensional quantum field theories involving non-abelian gauge fields, fermions and scalars in the Veneziano limit. In a regime where asymptotic freedom is lost, we explain how the three types of fields cooperate to develop fully interacting ultraviolet ...... fixed points, strictly controlled by perturbation theory. Extensions towards strong coupling and beyond the large-N limit are discussed.......We study the ultraviolet behaviour of four-dimensional quantum field theories involving non-abelian gauge fields, fermions and scalars in the Veneziano limit. In a regime where asymptotic freedom is lost, we explain how the three types of fields cooperate to develop fully interacting ultraviolet...
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
Litim, Daniel F
2014-01-01
We study the ultraviolet behaviour of four-dimensional quantum field theories involving non-abelian gauge fields, fermions and scalars in the Veneziano limit. In a regime where asymptotic freedom is lost, we explain how the three types of fields cooperate to develop fully interacting ultraviolet fixed points, strictly controlled by perturbation theory. Extensions towards strong coupling and beyond the large-N limit are discussed.
Cross-Diffusion Systems with Excluded-Volume Effects and Asymptotic Gradient Flow Structures
Bruna, Maria; Burger, Martin; Ranetbauer, Helene; Wolfram, Marie-Therese
2017-04-01
In this paper, we discuss the analysis of a cross-diffusion PDE system for a mixture of hard spheres, which was derived in Bruna and Chapman (J Chem Phys 137:204116-1-204116-16, 2012a) from a stochastic system of interacting Brownian particles using the method of matched asymptotic expansions. The resulting cross-diffusion system is valid in the limit of small volume fraction of particles. While the system has a gradient flow structure in the symmetric case of all particles having the same size and diffusivity, this is not valid in general. We discuss local stability and global existence for the symmetric case using the gradient flow structure and entropy variable techniques. For the general case, we introduce the concept of an asymptotic gradient flow structure and show how it can be used to study the behavior close to equilibrium. Finally, we illustrate the behavior of the model with various numerical simulations.
Asymptotically hyperbolic connections
Fine, Joel; Herfray, Yannick; Krasnov, Kirill; Scarinci, Carlos
2016-09-01
General relativity in four-dimensions can be equivalently described as a dynamical theory of {SO}(3)˜ {SU}(2)-connections rather than metrics. We introduce the notion of asymptotically hyperbolic connections, and work out an analogue of the Fefferman-Graham expansion in the language of connections. As in the metric setup, one can solve the arising ‘evolution’ equations order by order in the expansion in powers of the radial coordinate. The solution in the connection setting is arguably simpler, and very straightforward algebraic manipulations allow one to see how the unconstrained by Einstein equations ‘stress-energy tensor’ appears at third order in the expansion. Another interesting feature of the connection formulation is that the ‘counter terms’ required in the computation of the renormalised volume all combine into the Chern-Simons functional of the restriction of the connection to the boundary. As the Chern-Simons invariant is only defined modulo large gauge transformations, the requirement that the path integral over asymptotically hyperbolic connections is well-defined requires the cosmological constant to be quantised. Finally, in the connection setting one can deform the 4D Einstein condition in an interesting way, and we show that asymptotically hyperbolic connection expansion is universal and valid for any of the deformed theories.
Composite asymptotic expansions
Fruchard, Augustin
2013-01-01
The purpose of these lecture notes is to develop a theory of asymptotic expansions for functions involving two variables, while at the same time using functions involving one variable and functions of the quotient of these two variables. Such composite asymptotic expansions (CAsEs) are particularly well-suited to describing solutions of singularly perturbed ordinary differential equations near turning points. CAsEs imply inner and outer expansions near turning points. Thus our approach is closely related to the method of matched asymptotic expansions. CAsEs offer two unique advantages, however. First, they provide uniform expansions near a turning point and away from it. Second, a Gevrey version of CAsEs is available and detailed in the lecture notes. Three problems are presented in which CAsEs are useful. The first application concerns canard solutions near a multiple turning point. The second application concerns so-called non-smooth or angular canard solutions. Finally an Ackerberg-O’Malley resonance pro...
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.
Collet, P; Collet, P; Xin, J
1994-01-01
We consider the initial value problem for the thermal-diffusive combustion systems of the form: u_{1,t}= Delta_{x}u_1 - u_1 u_2^m, u_{2,t}= d Delta_{x} u_2 + u_1 u_2^m, x in R^{n}, n geq 1, m geq 1, d > 1, with bounded uniformly continuous nonnegative initial data. For such initial data, solutions can be simple traveling fronts or complicated domain walls. Due to the well-known thermal-diffusive instabilities when d, the Lewis number, is sufficiently away from one, front solutions are potentially chaotic. It is known in the literature that solutions are uniformly bounded in time in case d leq 1 by a simple comparison argument. In case d >1, no comparison principle seems to apply. Nevertheless, we prove the existence of global classical solutions and show that the L^{infty} norm of u_2 can not grow faster than O(log log t) for any space dimension. Our main tools are local L^{p} a-priori estimates and time dependent spatially decaying test functions. Our results also hold for the Arrhenius type reactions.
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
NONLINEAR STABILITY OF NATURAL RUNGE-KUTTA METHODS FOR NEUTRAL DELAY DIFFERENTIAL EQUATIONS
Cheng-jian Zhang
2002-01-01
This paper first presents the stability analysis of theoretical solutions for a class of nonlinear neutral delay-differential equations (NDDEs). Then the numerical analogous results, of the natural Runge-Kutta (NRK) methods for the same class of nonlinear NDDEs,are given. In particular, it is shown that the (k, l)-algebraic stability of a RK method for ODEs implies the generalized asymptotic stability and the global stability of the induced NRK method.
Stability of switched nonlinear systems via extensions of LaSalle's invariance principle
WANG JinHuan; CHENG DaiZhan
2009-01-01
This paper studies the extension of LaSalle's invariance principle for switched nonlinear systems. Unlike most existing results in which each switching mode in the system needs to be asymptotically stable, this paper allows the switching modes to be only stable. Under certain ergodicity assumptions of the switching signals, two extensions of LaSalle's invariance principle for global asymptotic stability of switched nonlinear systems are obtained using the method of common joint Lyapunov function.
Asymptotic stabilisation for a class of feedforward input-delay systems with ratios of odd integers
Wu, Jian; Chen, Weisheng; Miao, Qiguang
2013-11-01
This article addresses the stabilisation problem by state-feedback for a class of feedforward input-delay nonlinear systems with ratios of odd integer powers. The designed controller achieves the global asymptotic stability. Based on the appropriate state transformation of time-delay systems and the Lyapunov method, the problem of controller design can be converted into the problem of finding a parameter which can be obtained by appraising the nonlinear terms of the systems. Finally, three simulation examples are given to illustrate the effectiveness of the control algorithm proposed in this article.
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.
CHEN Lei; YANG Geng; XU Bi-huan
2011-01-01
Asymptotical stability is an important property of the associative memory neural networks. In this comment, we demonstrate that the asymptotical stability analyses of the MV-ECAM and MV-eBAM in the asynchronous update mode by Wang et al are not rigorous, and then we modify the errors and further prove that the two models are all asymptotically stable in both synchronous and asynchronous update modes.
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.
Ho, Pei-Ming
2017-04-01
Following earlier works on the KMY model of black-hole formation and evaporation, we construct the metric for a matter sphere in gravitational collapse, with the back-reaction of pre-Hawking radiation taken into consideration. The mass distribution and collapsing velocity of the matter sphere are allowed to have an arbitrary radial dependence. We find that a generic gravitational collapse asymptote to a universal configuration which resembles a black hole but without horizon. This approach clarifies several misunderstandings about black-hole formation and evaporation, and provides a new model for black-hole-like objects in the universe.
Ho, Pei-Ming
2016-01-01
Following earlier works on the KMY model of black-hole formation and evaporation, we construct the metric for a matter sphere in gravitational collapse, with the back-reaction of pre-Hawking radiation taken into consideration. The mass distribution and collapsing velocity of the matter sphere are allowed to have an arbitrary radial dependence. We find that a generic gravitational collapse asymptote to a universal configuration which resembles a black hole but without horizon. This approach clarifies several misunderstandings about black-hole formation and evaporation, and provides a new model for black-hole-like objects in the universe.
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
Stability and synchronization of memristor-based fractional-order delayed neural networks.
Chen, Liping; Wu, Ranchao; Cao, Jinde; Liu, Jia-Bao
2015-11-01
Global asymptotic stability and synchronization of a class of fractional-order memristor-based delayed neural networks are investigated. For such problems in integer-order systems, Lyapunov-Krasovskii functional is usually constructed, whereas similar method has not been well developed for fractional-order nonlinear delayed systems. By employing a comparison theorem for a class of fractional-order linear systems with time delay, sufficient condition for global asymptotic stability of fractional memristor-based delayed neural networks is derived. Then, based on linear error feedback control, the synchronization criterion for such neural networks is also presented. Numerical simulations are given to demonstrate the effectiveness of the theoretical results.
Confinement versus asymptotic freedom
Dubin, A Yu
2002-01-01
I put forward the low-energy confining asymptote of the solution $$ (valid for large macroscopic contours C of the size $>>1/\\Lambda_{QCD}$) to the large N Loop equation in the D=4 U(N) Yang-Mills theory with the asymptotic freedom in the ultraviolet domain. Adapting the multiscale decomposition characteristic of the Wilsonean renormgroup, the proposed Ansatz for the loop-average is composed in order to sew, along the lines of the bootstrap approach, the large N weak-coupling series for high-momentum modes with the $N\\to{\\infty}$ limit of the recently suggested stringy representation of the 1/N strong-coupling expansion Dub4 applied to low-momentum excitations. The resulting low-energy stringy theory can be described through such superrenormalizable deformation of the noncritical Liouville string that, being devoid of ultraviolet divergences, does not possess propagating degrees of freedom at short-distance scales $<<1/{\\sqrt{\\sigma_{ph}}}$, where $\\sigma_{ph}\\sim{(\\Lambda_{QCD})^{2}}$ is the physical s...
Asymptotic Symmetries from finite boxes
Andrade, Tomas
2015-01-01
It is natural to regulate an infinite-sized system by imposing a boundary condition at finite distance, placing the system in a "box." This breaks symmetries, though the breaking is small when the box is large. One should thus be able to obtain the asymptotic symmetries of the infinite system by studying regulated systems. We provide concrete examples in the context of Einstein-Hilbert gravity (with negative or zero cosmological constant) by showing in 4 or more dimensions how the Anti-de Sitter and Poincar\\'e asymptotic symmetries can be extracted from gravity in a spherical box with Dirichlet boundary conditions. In 2+1 dimensions we obtain the full double-Virasoro algebra of asymptotic symmetries for AdS$_3$ and, correspondingly, the full Bondi-Metzner-Sachs (BMS) algebra for asymptotically flat space. In higher dimensions, a related approach may continue to be useful for constructing a good asymptotically flat phase space with BMS asymptotic symmetries.
M. Syed, Ali
2014-06-01
In this paper, the global asymptotic stability problem of Markovian jumping stochastic Cohen—Grossberg neural networks with discrete and distributed time-varying delays (MJSCGNNs) is considered. A novel LMI-based stability criterion is obtained by constructing a new Lyapunov functional to guarantee the asymptotic stability of MJSCGNNs. Our results can be easily verified and they are also less restrictive than previously known criteria and can be applied to Cohen—Grossberg neural networks, recurrent neural networks, and cellular neural networks. Finally, the proposed stability conditions are demonstrated with numerical examples.
Thermodynamics of Asymptotically Conical Geometries.
Cvetič, Mirjam; Gibbons, Gary W; Saleem, Zain H
2015-06-12
We study the thermodynamical properties of a class of asymptotically conical geometries known as "subtracted geometries." We derive the mass and angular momentum from the regulated Komar integral and the Hawking-Horowitz prescription and show that they are equivalent. By deriving the asymptotic charges, we show that the Smarr formula and the first law of thermodynamics hold. We also propose an analog of Christodulou-Ruffini inequality. The analysis can be generalized to other asymptotically conical geometries.
Probabilistic and asymptotic methods with the Perron Frobenius's operator
Cirier, Guy
2012-01-01
We give a new global presentation of our results on the asymptotic behavior of an iteration. This paper brings many improvements and corrections to our previous preprints on the subject.Among the applications, we use new methods to compute asymptotic results of PDE like Lorenz or Navier-Stokes equations. New questions as the resonance are studied.Perron-Frobenius;resolving deviation;Julia's sets;Plancherel-Rotach'function;Lorenz andNavier-Sto kes equations;resonance;
Asymptotic behaviour for a diffusion equation governed by nonlocal interactions
Ovono, Armel Andami
2010-01-01
In this paper we study the asymptotic behaviour of a nonlocal nonlinear parabolic equation governed by a parameter. After giving the existence of unique branch of solutions composed by stable solutions in stationary case, we gives for the parabolic problem $L^\\infty $ estimates of solution based on using the Moser iterations and existence of global attractor. We finish our study by the issue of asymptotic behaviour in some cases when $t\\to \\infty$.
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.
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.
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.
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.
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.
一类带有复发的海洛因传染病模型的全局稳定性%Global Stability of a Heroin Epidemic Model with Relapse
方彬; 郭淑利; 李学志; 张凯丽
2016-01-01
建立并研究了一类带有复发的海洛因传染病ODE模型，给出了海洛因传染病模型的基本再生数，讨论了模型平衡点存在性，证明了模型平衡点的局部渐近稳定性和全局渐近稳定性。%In this paper,an ODE model of the heroin epidemic with relapse is formulated and studied.First, the basic reproduction number of the heroin spread is also identified.Next,we discuss the existence of equilibria and prove their locally and globally asymptotical stability of equilibria.
Asymptotically safe grand unification
Bajc, Borut; Sannino, Francesco
2016-12-01
Phenomenologically appealing supersymmetric grand unified theories have large gauge representations and thus are not asymptotically free. Their ultraviolet validity is limited by the appearance of a Landau pole well before the Planck scale. One could hope that these theories save themselves, before the inclusion of gravity, by generating an interacting ultraviolet fixed point, similar to the one recently discovered in non-supersymmetric gauge-Yukawa theories. Employing a-maximization, a-theorem, unitarity bounds, as well as positivity of other central charges we nonperturbatively rule out this possibility for a broad class of prime candidates of phenomenologically relevant supersymmetric grand unified theories. We also uncover candidates passing these tests, which have either exotic matter or contain one field decoupled from the superpotential. The latter class of theories contains a model with the minimal matter content required by phenomenology.
Asymptotically Safe Grand Unification
Bajc, Borut
2016-01-01
Phenomenologically appealing supersymmetric grand unified theories have large gauge representations and thus are not asymptotically free. Their ultraviolet validity is limited by the appearance of a Landau pole well before the Planck scale. One could hope that these theories save themselves, before the inclusion of gravity, by generating an interacting ultraviolet fixed point, similar to the one recently discovered in non-supersymmetric gauge-Yukawa theories. Employing a-maximization, a-theorem, unitarity bounds, as well as positivity of other central charges we nonperturbatively rule out this possibility for a broad class of prime candidates of phenomenologically relevant supersymmetric grand unified theories. We also uncover candidates passing these tests, which have either exotic matter or contain one field decoupled from the superpotential. The latter class of theories contains a model with the minimal matter content required by phenomenology.
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
STABILITY ANALYSIS OF A COMPUTER VIRUS PROPAGATION MODEL WITH ANTIDOTE IN VULNERABLE SYSTEM
Nguyen Huu KHANH; Nguyen Bich HUY
2016-01-01
We study a proposed model describing the propagation of computer virus in the network with antidote in vulnerable system. Mathematical analysis shows that dynamics of the spread of computer viruses is determined by the threshold R0. If R0 ≤ 1, the virus-free equilibrium is globally asymptotically stable, and if R0 >1, the endemic equilibrium is globally asymptotically stable. Lyapunov functional method as well as geometric approach are used for proving the global stability of equilibria. A numerical investigation is carried out to confirm the analytical results. Through parameter analysis, some effective strategies for eliminating viruses are suggested.
Superradiant instabilities of asymptotically anti-de Sitter black holes
Green, Stephen R.; Hollands, Stefan; Ishibashi, Akihiro; Wald, Robert M.
2016-06-01
We study the linear stability of asymptotically anti-de Sitter black holes in general relativity in spacetime dimension d≥slant 4. Our approach is an adaptation of the general framework of Hollands and Wald, which gives a stability criterion in terms of the sign of the canonical energy, { E }. The general framework was originally formulated for static or stationary and axisymmetric black holes in the asymptotically flat case, and the stability analysis for that case applies only to axisymmetric perturbations. However, in the asymptotically anti-de Sitter case, the stability analysis requires only that the black hole have a single Killing field normal to the horizon and there are no restrictions on the perturbations (apart from smoothness and appropriate behavior at infinity). For an asymptotically anti-de Sitter black hole, we define an ergoregion to be a region where the horizon Killing field is spacelike; such a region, if present, would normally occur near infinity. We show that for black holes with ergoregions, initial data can be constructed such that { E }\\lt 0, so all such black holes are unstable. To obtain such initial data, we first construct an approximate solution to the constraint equations using the WKB method, and then we use the Corvino-Schoen technique to obtain an exact solution. We also discuss the case of charged asymptotically anti-de Sitter black holes with generalized ergoregions.
Global Observer-Based Attitude Controller Using Direct Inertial Measurements
Saâdi Bouhired
2014-04-01
Full Text Available In this work, we address the problem of global attitude control using direct inertial measurements. When using direct inertial measurement to observe the rigid body attitude, it is shown that due to a geometrical obstruction, it is impossible to achieve global asymptotic stability. In fact, for a particular initial condition the tracking error quaternion converges to a pure imaginary quaternion formed by an eigenvector of a characteristic matrix related to the inertial constant and known vectors. Our proposition consists of adding a dynamic signal to force the rigid body to escape from such a situation. The proposed observer-based controller is synthesized based on a single Lyapunov function and a stability analysis shows that the controller stabilizes globally and asymptotically the rigid body attitude at the desired one. The effectiveness of the proposed observer-based controller is confirmed by simulation results.
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.
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.
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.
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.
Stabilization of discrete nonlinear systems based on control Lyapunov functions
无
2008-01-01
The stabilization of discrete nonlinear systems is studied.Based on control Lyapunov functions,asufficient and necessary condition for a quadratic function to be a control Lyapunov function is given.From this condition,a continuous state feedback law is constructed explicitly.It can globally asymptotically stabilize the equilibrium of the closed-loop system.A simulation example shows the effectiveness of the proposed method.
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.
Stability analysis of extended discrete-time BAM neural networks based on LMI approach
无
2005-01-01
We propose a new approach for analyzing the global asymptotic stability of the extended discrete-time bidirectional associative memory (BAM) neural networks. By using the Euler rule, we discretize the continuous-time BAM neural networks as the extended discrete-time BAM neural networks with non-threshold activation functions. Here we present some conditions under which the neural networks have unique equilibrium points. To judge the global asymptotic stability of the equilibrium points, we introduce a new neural network model - standard neural network model (SNNM).For the SNNMs, we derive the sufficient conditions for the global asymptotic stability of the equilibrium points, which are formulated as some linear matrix inequalities (LMIs). We transform the discrete-time BAM into the SNNM and apply the general result about the SNNM to the determination of global asymptotic stability of the discrete-time BAM. The approach proposed extends the known stability results, has lower conservativeness, can be verified easily, and can also be applied to other forms of recurrent neural networks.
Huaiqin Wu
2012-01-01
Full Text Available By combing the theories of the switched systems and the interval neural networks, the mathematics model of the switched interval neural networks with discrete and distributed time-varying delays of neural type is presented. A set of the interval parameter uncertainty neural networks with discrete and distributed time-varying delays of neural type are used as the individual subsystem, and an arbitrary switching rule is assumed to coordinate the switching between these networks. By applying the augmented Lyapunov-Krasovskii functional approach and linear matrix inequality (LMI techniques, a delay-dependent criterion is achieved to ensure to such switched interval neural networks to be globally asymptotically robustly stable in terms of LMIs. The unknown gain matrix is determined by solving this delay-dependent LMIs. Finally, an illustrative example is given to demonstrate the validity of the theoretical results.
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...
On the Stabilization of the Inverted-Cart Pendulum Using the Saturation Function Approach
Carlos Aguilar-Ibañez
2011-01-01
of a well-characterized small vicinity, whereas the second control action asymptotically brings the whole state of the system to the origin. The corresponding closed-loop stability analysis uses standard linear stability arguments as well as the traditional Lyapunov method and the LaSalle's theorem. Our proposed control law ensures global stability of the system in the upper half plane. We illustrate the effectiveness of the proposed control strategy via numerical simulations.
Wong, Willie Wai-Yeung
2014-01-01
We study constant mean curvature Lorentzian hypersurfaces of $\\mathbb{R}^{1,d+1}$ from the point of view of its Cauchy problem. We completely classify the spherically symmetric solutions, which include among them a manifold isometric to the de Sitter space of general relativity. We show that the spherically symmetric solutions exhibit one of three (future) asymptotic behaviours: (i) finite time collapse (ii) convergence to a time-like cylinder isometric to some $\\mathbb{R}\\times\\mathbb{S}^d$ and (iii) infinite expansion to the future converging asymptotically to a time translation of the de Sitter solution. For class (iii) we examine the future stability properties of the solutions under arbitrary (not necessarily spherically symmetric) perturbations. We show that the usual notions of asymptotic stability and modulational stability cannot apply, and connect this to the presence of cosmological horizons in these class (iii) solutions. We can nevertheless show the global existence and future stability for small...
Stability of a liquid bridge under vibration
Benilov, E. S.
2016-06-01
We examine the stability of a vertical liquid bridge between two vertically vibrating, coaxial disks. Assuming that the vibration amplitude and period are much smaller than the mean distance between the disks and the global timescale, respectively, we employ the method of multiple scales to derive a set of asymptotic equations. The set is then used to examine the stability of a bridge of an almost cylindrical shape. It is shown that, if acting alone, gravity is a destabilizing influence, whereas vibration can weaken it or even eliminate altogether. Thus, counter-intuitively, vibration can stabilize an otherwise unstable capillary structure.
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.
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 chaos synchronization of coupled parametrically excited pendula
O I Olusola; U E Vincent; A N Njah
2009-12-01
In this paper, we study the synchronization behaviour of two linearly coupled parametrically excited chaotic pendula. The stability of the synchronized state is examined using Lyapunov stability theory and linear matrix inequality (LMI); and some sufficient criteria for global asymptotic synchronization are derived from which an estimated critical coupling is determined. Numerical solutions are presented to verify the theoretical analysis. We also examined the transition to stable synchronous state and show that this corresponds to a boundary crisis of the chaotic attractor.
On stability of randomly switched nonlinear systems
Chatterjee, Debasish
2007-01-01
This article is concerned with stability analysis and stabilization of randomly switched nonlinear systems. These systems may be regarded as piecewise deterministic stochastic systems: the discrete switches are triggered by a stochastic process which is independent of the state of the system, and between two consecutive switching instants the dynamics are deterministic. Our results provide sufficient conditions for almost sure global asymptotic stability using Lyapunov-based methods when individual subsystems are stable and a certain ``slow switching'' condition holds. This slow switching condition takes the form of an asymptotic upper bound on the probability mass function of the number of switches that occur between the initial and current time instants. This condition is shown to hold for switching signals coming from the states of finite-dimensional continuous-time Markov chains; our results therefore hold for Markov jump systems in particular. For systems with control inputs we provide explicit control s...
Burns, Daniel; Wang, Zuoqin
2008-01-01
In this article we discuss the role of stability functions in geometric invariant theory and apply stability function techniques to problems in toric geometry. In particular we show how one can use these techniques to recover results of Burns-Guillemin-Uribe and Shiffman-Tate-Zelditch on asymptotic properties of sections of holomorphic line bundles over toric varieties.
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.
A Note on Asymptotic Contractions
Marina Arav
2006-12-01
Full Text Available We provide sufficient conditions for the iterates of an asymptotic contraction on a complete metric space X to converge to its unique fixed point, uniformly on each bounded subset of X.
A Note on Asymptotic Contractions
Castillo Santos Francisco Eduardo
2007-01-01
Full Text Available We provide sufficient conditions for the iterates of an asymptotic contraction on a complete metric space to converge to its unique fixed point, uniformly on each bounded subset of .
Asymptotic Dynamics of Monopole Walls
Cross, R
2015-01-01
We determine the asymptotic dynamics of the U(N) doubly periodic BPS monopole in Yang-Mills-Higgs theory, called a monopole wall, by exploring its Higgs curve using the Newton polytope and amoeba. In particular, we show that the monopole wall splits into subwalls when any of its moduli become large. The long-distance gauge and Higgs field interactions of these subwalls are abelian, allowing us to derive an asymptotic metric for the monopole wall moduli space.
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.
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.
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
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.
The Asymptotic Behavior for Numerical Solution of a Volterra Equation
Da Xu
2003-01-01
Long-time asymptotic stability and convergence properties for the numerical solution of a Volterra equation of parabolic type are studied. The methods are based on the first-second order backward difference methods. The memory term is approximated by the convolution quadrature and the interpolant quadrature. Discretization of the spatial partial differential operators by the finite element method is also considered.
Superradiant instabilities of asymptotically anti-de Sitter black holes
Green, Stephen R; Ishibashi, Akihiro; Wald, Robert M
2015-01-01
We study the linear stability of asymptotically anti-de Sitter black holes in general relativity in spacetime dimension $d\\ge4$. Our approach is an adaptation of the general framework of Hollands and Wald, which gives a stability criterion in terms of the sign of the canonical energy, $\\mathcal{E}$. The general framework was originally formulated for static or stationary and axisymmetric black holes in the asymptotically flat case, and the stability analysis for that case applies only to axisymmetric perturbations. However, in the asymptotically anti-de Sitter case, the stability analysis requires only that the black hole have a single Killing field normal to the horizon and there are no restrictions on the perturbations (apart from smoothness and appropriate behavior at infinity). For an asymptotically anti-de Sitter black hole, we define an ergoregion to be a region where the horizon Killing field is spacelike; such a region, if present, would normally occur near infinity. We show that for black holes with ...
Stabilization of nonlinear systems based on robust control Lyapunov function
CAI Xiu-shan; HAN Zheng-zhi; LU Gan-yun
2007-01-01
This paper deals with the robust stabilization problem for a class of nonlinear systems with structural uncertainty. Based on robust control Lyapunov function, a sufficient and necessary condition for a function to be a robust control Lyapunov function is given. From this condition, simply sufficient condition for the robust stabilization (robust practical stabilization) is deduced. Moreover, if the equilibrium of the closed-loop system is unique, the existence of such a robust control Lyapunov function will also imply robustly globally asymptotical stabilization. Then a continuous state feedback law can be constructed explicitly. The simulation shows the effectiveness of the method.
Polynomial Asymptotes of the Second Kind
Dobbs, David E.
2011-01-01
This note uses the analytic notion of asymptotic functions to study when a function is asymptotic to a polynomial function. Along with associated existence and uniqueness results, this kind of asymptotic behaviour is related to the type of asymptote that was recently defined in a more geometric way. Applications are given to rational functions and…
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...
Preheating in an asymptotically safe quantum field theory
Svendsen, Ole; Moghaddam, Hossein Bazrafshan; Brandenberger, Robert
2016-10-01
We consider reheating in a class of asymptotically safe quantum field theories recently studied in [D. F. Litim and F. Sannino, Asymptotic safety guaranteed, J. High Energy Phys. 12 (2014) 178; D. F. Litim, M. Mojaza, and F. Sannino, Vacuum stability of asymptotically safe gauge-Yukawa theories, J. High Energy Phys. 01 (2016) 081]. These theories allow for an inflationary phase in the very early universe. Inflation ends with a period of reheating. Since the models contain many scalar fields which are intrinsically coupled to the inflaton there is the possibility of parametric resonance instability in the production of these fields, and the danger that the induced curvature fluctuations will become too large. Here we show that the parametric instability indeed arises, and that hence the energy transfer from the inflaton condensate to fluctuating fields is rapid. Demanding that the curvature fluctuations induced by the parametrically amplified entropy modes do not exceed the upper observational bounds puts a lower bound on the number of fields which the model followed in [D. F. Litim and F. Sannino, Asymptotic safety guaranteed, J. High Energy Phys. 12 (2014) 178; D. F. Litim, M. Mojaza, and F. Sannino, Vacuum stability of asymptotically safe gauge-Yukawa theories, J. High Energy Phys. 01 (2016) 081] must contain. This bound also depends on the total number of e -foldings of the inflationary phase.
Stability Analysis of an HIV/AIDS Dynamics Model with Drug Resistance
Qianqian Li
2012-01-01
Full Text Available A mathematical model of HIV/AIDS transmission incorporating treatment and drug resistance was built in this study. We firstly calculated the threshold value of the basic reproductive number (R0 by the next generation matrix and then analyzed stability of two equilibriums by constructing Lyapunov function. When R0<1, the system was globally asymptotically stable and converged to the disease-free equilibrium. Otherwise, the system had a unique endemic equilibrium which was also globally asymptotically stable. While an antiretroviral drug tried to reduce the infection rate and prolong the patients’ survival, drug resistance was neutralizing the effects of treatment in fact.
DISSIPATION AND DISPERSION APPROXIMATION TO HYDRODYNAMICAL EQUATIONS AND ASYMPTOTIC LIMIT
Hsiao Ling; Li Hailiang
2008-01-01
The compressible Euler equations with dissipation and/or dispersion correction are widely used in the area of applied sciences, for instance, plasma physics,charge transport in semiconductor devices, astrophysics, geophysics, etc. We consider the compressible Euler equation with density-dependent (degenerate) viscosities and capillarity, and investigate the global existence of weak solutions and asymptotic limit.
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.
Asymptotic Bifurcation Solutions for Perturbed Kuramoto-Sivashinsky Equation
HUANG Qiong-Wei; TANG Jia-Shi
2011-01-01
Stability and dynamic bifurcation in the perturbed Kuramoto-Sivashinsky (KS) equation with Dirichlet boundary condition are investigated by using central manifold reduction procedure.The result shows, as the bifurcation parameter crosses a critical value, the system undergoes a pitchfork bifurcation to produce two asymptotically stable solutions.Furthermore, when the distance from bifurcation is of comparable order ∈2 (｜∈｜ (≤) 1), the first two terms in e-expansions for the new asymptotic bifurcation solutions are derived by multiscale expansion method.Such information is useful to the bifurcation control.
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.
Asymptotics of trimmed CUSUM statistics
Berkes, István; Schauer, Johannes; 10.3150/10-BEJ318
2012-01-01
There is a wide literature on change point tests, but the case of variables with infinite variances is essentially unexplored. In this paper we address this problem by studying the asymptotic behavior of trimmed CUSUM statistics. We show that in a location model with i.i.d. errors in the domain of attraction of a stable law of parameter $0<\\alpha <2$, the appropriately trimmed CUSUM process converges weakly to a Brownian bridge. Thus, after moderate trimming, the classical method for detecting change points remains valid also for populations with infinite variance. We note that according to the classical theory, the partial sums of trimmed variables are generally not asymptotically normal and using random centering in the test statistics is crucial in the infinite variance case. We also show that the partial sums of truncated and trimmed random variables have different asymptotic behavior. Finally, we discuss resampling procedures which enable one to determine critical values in the case of small and mo...
Asymptotic aspects of Cayley graphs
Dejter, Italo J
2011-01-01
Arising from complete Cayley graphs $\\Gamma_n$ of odd cyclic groups $\\Z_n$, an asymptotic approach is presented on connected labeled graphs whose vertices are labeled via equally-multicolored copies of $K_4$ in $\\Gamma_n$ with adjacency of any two such vertices whenever they are represented by copies of $K_4$ in $\\Gamma_n$ sharing two equally-multicolored triangles. In fact, these connected labeled graphs are shown to form a family of graphs of largest degree 6 and diameter asymptotically of order $|V|^{1/3}$, properties shared by the initial member of a collection of families of Cayley graphs of degree $2m\\geq 6$ with diameter asymptotically of order $|V|^{1/m}$, where $3\\leq m\\in\\Z$.
Asymptotic analysis and boundary layers
Cousteix, Jean
2007-01-01
This book presents a new method of asymptotic analysis of boundary-layer problems, the Successive Complementary Expansion Method (SCEM). The first part is devoted to a general comprehensive presentation of the tools of asymptotic analysis. It gives the keys to understand a boundary-layer problem and explains the methods to construct an approximation. The second part is devoted to SCEM and its applications in fluid mechanics, including external and internal flows. The advantages of SCEM are discussed in comparison with the standard Method of Matched Asymptotic Expansions. In particular, for the first time, the theory of Interactive Boundary Layer is fully justified. With its chapter summaries, detailed derivations of results, discussed examples and fully worked out problems and solutions, the book is self-contained. It is written on a mathematical level accessible to graduate and post-graduate students of engineering and physics with a good knowledge in fluid mechanics. Researchers and practitioners will estee...
An improved robust stability result for uncertain neural networks with multiple time delays.
Arik, Sabri
2014-06-01
This paper proposes a new alternative sufficient condition for the existence, uniqueness and global asymptotic stability of the equilibrium point for the class of delayed neural networks under the parameter uncertainties of the neural system. The existence and uniqueness of the equilibrium point is proved by using the Homomorphic mapping theorem. The asymptotic stability of the equilibrium point is established by employing the Lyapunov stability theorems. The obtained robust stability condition establishes a new relationship between the network parameters of the system. We compare our stability result with the previous corresponding robust stability results derived in the past literature. Some comparative numerical examples together with some simulation results are also given to show the applicability and advantages of our result.
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.
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.
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.
Input-to-state stabilization of the perturbed systems in the generalized triangular form
Dashkovskiy, Sergey
2010-01-01
We consider nonlinear control systems of the so-called generalized triangular form (GTF) with time-varying and periodic dynamics which linearly depends on some external disturbances. Our purpose is to construct a feedback controller which provides the global input-to-state stability of the corresponding closed-loop w.r.t. the disturbances. To do this, we combine the method proposed in the earlier work \\cite{pavlichkov_ge_2009} devoted the the global asymptotic stabilization of the GTF systems without disturbances with the ISS theory for time-varying systems proposed in \\cite{wang}. Following this pattern we construct a feedback which provides the properties of uniform global stability and asymptotic gain w.r.t the disturbances. Then we obtain the semi-uniform ISS of the closed-loop system.
Expansions and Asymptotics for Statistics
Small, Christopher G
2010-01-01
Providing a broad toolkit of analytical methods, this book shows how asymptotics, when coupled with numerical methods, becomes a powerful way to acquire a deeper understanding of the techniques used in probability and statistics. It describes core ideas in statistical asymptotics; covers Laplace approximation, the saddle-point method, and summation of series; and, includes vignettes of various people from statistics and mathematics whose ideas have been instrumental in the development of the subject. The author also supplements some topics with relevant Maplea commands and provides a list of c
Asymptotic Rayleigh instantaneous unit hydrograph
Troutman, B.M.; Karlinger, M.R.
1988-01-01
The instantaneous unit hydrograph for a channel network under general linear routing and conditioned on the network magnitude, N, tends asymptotically, as N grows large, to a Rayleigh probability density function. This behavior is identical to that of the width function of the network, and is proven under the assumption that the network link configuration is topologically random and the link hydraulic and geometric properties are independent and identically distributed random variables. The asymptotic distribution depends only on a scale factor, {Mathematical expression}, where ?? is a mean link wave travel time. ?? 1988 Springer-Verlag.
Asymptotics for dissipative nonlinear equations
Hayashi, Nakao; Kaikina, Elena I; Shishmarev, Ilya A
2006-01-01
Many of problems of the natural sciences lead to nonlinear partial differential equations. However, only a few of them have succeeded in being solved explicitly. Therefore different methods of qualitative analysis such as the asymptotic methods play a very important role. This is the first book in the world literature giving a systematic development of a general asymptotic theory for nonlinear partial differential equations with dissipation. Many typical well-known equations are considered as examples, such as: nonlinear heat equation, KdVB equation, nonlinear damped wave equation, Landau-Ginzburg equation, Sobolev type equations, systems of equations of Boussinesq, Navier-Stokes and others.
Higher dimensional nonclassical eigenvalue asymptotics
Camus, Brice; Rautenberg, Nils
2015-02-01
In this article, we extend Simon's construction and results [B. Simon, J. Funct. Anal. 53(1), 84-98 (1983)] for leading order eigenvalue asymptotics to n-dimensional Schrödinger operators with non-confining potentials given by Hn α = - Δ + ∏ i = 1 n |x i| α i on ℝn (n > 2), α ≔ ( α 1 , … , α n ) ∈ ( R+ ∗ ) n . We apply the results to also derive the leading order spectral asymptotics in the case of the Dirichlet Laplacian -ΔD on domains Ωn α = { x ∈ R n : ∏ j = 1 n }x j| /α j α n < 1 } .
Asymptotic Normality of Quadratic Estimators.
Robins, James; Li, Lingling; Tchetgen, Eric; van der Vaart, Aad
2016-12-01
We prove conditional asymptotic normality of a class of quadratic U-statistics that are dominated by their degenerate second order part and have kernels that change with the number of observations. These statistics arise in the construction of estimators in high-dimensional semi- and non-parametric models, and in the construction of nonparametric confidence sets. This is illustrated by estimation of the integral of a square of a density or regression function, and estimation of the mean response with missing data. We show that estimators are asymptotically normal even in the case that the rate is slower than the square root of the observations.
Asymptotic geometric analysis, part I
Artstein-Avidan, Shiri
2015-01-01
The authors present the theory of asymptotic geometric analysis, a field which lies on the border between geometry and functional analysis. In this field, isometric problems that are typical for geometry in low dimensions are substituted by an "isomorphic" point of view, and an asymptotic approach (as dimension tends to infinity) is introduced. Geometry and analysis meet here in a non-trivial way. Basic examples of geometric inequalities in isomorphic form which are encountered in the book are the "isomorphic isoperimetric inequalities" which led to the discovery of the "concentration phenomen
Aid, R.
1998-01-07
This work comes from an industrial problem of validating numerical solutions of ordinary differential equations modeling power systems. This problem is solved using asymptotic estimators of the global error. Four techniques are studied: Richardson estimator (RS), Zadunaisky's techniques (ZD), integration of the variational equation (EV), and Solving for the correction (SC). We give some precisions on the relative order of SC w.r.t. the order of the numerical method. A new variant of ZD is proposed that uses the Modified Equation. In the case of variable step-size, it is shown that under suitable restriction, on the hypothesis of the step-size selection, ZD and SC are still valid. Moreover, some Runge-Kutta methods are shown to need less hypothesis on the step-sizes to exhibit a valid order of convergence for ZD and SC. Numerical tests conclude this analysis. Industrial cases are given. Finally, an algorithm to avoid the a priori specification of the integration path for complex time differential equations is proposed. (author)
Asymptotic analysis of a vibrating cantilever with a nonlinear boundary
C.; W.; LIM
2009-01-01
Nonlinear vibration of a cantilever in a contact atomic force microscope is analyzed via an asymptotic approach. The asymptotic solution is sought for a beam equation with a nonlinear boundary condition. The steady-state responses are determined in primary resonance and subharmonic resonance. The relations between the response amplitudes and the excitation frequencies and amplitudes are derived from the solvability condition. Multivaluedness occurs in the relations as a consequence of the nonlinearity. The stability of steady-state responses is analyzed by use of the Lyapunov linearized stability theory. The stability analysis predicts the jumping phenomenon for certain parameters. The curves of the response amplitudes changing with the excitation frequencies are numerically compared with those obtained via the method of multiple scales. The calculation results demonstrate that the two methods predict the same varying tendencies while there are small quantitative differences.
Asymptotic analysis of a vibrating cantilever with a nonlinear boundary
CHEN LiQun; C.W.LIM; HU QingQuan; DING Hu
2009-01-01
Nonlinear vibration of a cantilever in a contact atomic force microscope is analyzed via an asymptotic approach.The asymptotic solution is sought for a beam equation with a nonlinear boundary condition.The steady-state responses are determined in primary resonance and subharmonic resonance.The relations between the response amplitudes and the excitation frequencies and amplitudes are derived from the solvability condition.Multivaluedness occurs in the relations as a consequence of the nonlinearity.The stability of steady-state responses is analyzed by use of the Lyapunov linearized sta-bility theory.The stability analysis predicts the jumping phenomenon for certain parameters.The curves of the response amplitudes changing with the excitation frequencies are numerically compared with those obtained via the method of multiple scales.The calculation results demonstrate that the two methods predict the same varying tendencies while there are small quantitative differences.
Asymptotic analysis of a vibrating cantilever with a nonlinear boundary
Chen, Liqun; Lim, C. W.; Hu, Qingquan; Ding, Hu
2009-09-01
Nonlinear vibration of a cantilever in a contact atomic force microscope is analyzed via an asymptotic approach. The asymptotic solution is sought for a beam equation with a nonlinear boundary condition. The steady-state responses are determined in primary resonance and subharmonic resonance. The relations between the response amplitudes and the excitation frequencies and amplitudes are derived from the solvability condition. Multivaluedness occurs in the relations as a consequence of the nonlinearity. The stability of steady-state responses is analyzed by use of the Lyapunov linearized stability theory. The stability analysis predicts the jumping phenomenon for certain parameters. The curves of the response amplitudes changing with the excitation frequencies are numerically compared with those obtained via the method of multiple scales. The calculation results demonstrate that the two methods predict the same varying tendencies while there are small quantitative differences.
Nonabelian Higgs models: paving the way for asymptotic freedom
Gies, Holger
2016-01-01
Asymptotically free renormalization group trajectories can be constructed in nonabelian Higgs models with the aid of generalized boundary conditions imposed on the renormalized action. We detail this construction within the languages of simple low-order perturbation theory, effective field theory, as well as modern functional renormalization group equations. We construct a family of explicit scaling solutions using a controlled weak-coupling expansion in the ultraviolet, and obtain a standard Wilsonian RG relevance classification of perturbations about scaling solutions. We obtain global information about the quasi-fixed function for the scalar potential by means of analytic asymptotic expansions and numerical shooting methods. Further analytical evidence for such asymptotically free theories is provided in the large-N limit. We estimate the long-range properties of these theories, and identify initial/boundary conditions giving rise to a conventional Higgs phase.
Asymptotic orbits in the ( N+1)-body ring problem
Papadakis, K. E.
2009-10-01
In this paper we study the asymptotic solutions of the ( N+1)-body ring planar problem, N of which are finite and ν= N-1 are moving in circular orbits around their center of masses, while the Nth+1 body is infinitesimal. ν of the primaries have equal masses m and the Nth most-massive primary, with m 0= β m, is located at the origin of the system. We found the invariant unstable and stable manifolds around hyperbolic Lyapunov periodic orbits, which emanate from the collinear equilibrium points L 1 and L 2. We construct numerically, from the intersection points of the appropriate Poincaré cuts, homoclinic symmetric asymptotic orbits around these Lyapunov periodic orbits. There are families of symmetric simple-periodic orbits which contain as terminal points asymptotic orbits which intersect the x-axis perpendicularly and tend asymptotically to equilibrium points of the problem spiraling into (and out of) these points. All these families, for a fixed value of the mass parameter β=2, are found and presented. The eighteen (more geometrically simple) families and the corresponding eighteen terminating homo- and heteroclinic symmetric asymptotic orbits are illustrated. The stability of these families is computed and also presented.
Asymptotic orbits in the restricted four-body problem
Papadakis, K. E.
2007-07-01
This paper studies the asymptotic solutions of the restricted planar problem of four bodies, three of which are finite, moving in circular orbits around their center of masses, while the fourth is infinitesimal. Two of the primaries have equal mass and the most-massive primary is located at the origin of the system. We found the invariant unstable and stable manifolds around the hyperbolic Lyapunov periodic orbits which emanate from the collinear equilibrium points Li,i=1,…,4, as well as the invariant manifolds from the Lagrangian critical points L5 and L6. We construct numerically, applying forward and backward integration from the intersection points of the appropriate Poincaré cuts, homo- and hetero-clinic, symmetric and non-symmetric asymptotic orbits. We present the characteristic curves of the 24 families which consist of symmetric simple-periodic orbits of the problem for a fixed value of the mass parameter b. The stability of the families is computed and also presented. Sixteen families contain as terminal points asymptotic periodic orbits which intersect the x-axis perpendicularly and tend asymptotically to L5 for t→+∞ and to L6 for t→-∞, spiralling into (and out of) these points. The corresponding 16 terminating heteroclinic asymptotic orbits, for b=2, are illustrated.
Ruin problems and tail asymptotics
Rønn-Nielsen, Anders
The thesis Ruin Problems and Tail Asymptotics provides results on ruin problems for several classes of Markov processes. For a class of diffusion processes with jumps an explicit expression for the joint Laplace transform of the first passage time and the corresponding undershoot is derived...
Inaccurate usage of asymptotic formulas
Maj, R; Maj, Radoslaw; Mrowczynski, Stanislaw
2004-01-01
The asymptotic form of the plane-wave decomposition into spherical waves, which is often used, in particular, to express the scattering amplitude through the phase shifts, is incorrect. We precisely explain why it is incorrect and show how to circumvent mathematical inconsistency.
Thermodynamics of asymptotically safe theories
Rischke, Dirk H.; Sannino, Francesco
2015-01-01
We investigate the thermodynamic properties of a novel class of gauge-Yukawa theories that have recently been shown to be completely asymptotically safe, because their short-distance behaviour is determined by the presence of an interacting fixed point. Not only do all the coupling constants freeze...
Stability of differential susceptibility and infectivity epidemic models
Bonzi, B.; Fall, A. A.; Iggidr, Abderrahman; Sallet, Gauthier
2011-01-01
We introduce classes of differential susceptibility and infectivity epidemic models. These models address the problem of flows between the different susceptible, infectious and infected compartments and differential death rates as well. We prove the global stability of the disease free equilibrium when the basic reproduction ratio ≤ 1 and the existence and uniqueness of an endemic equilibrium when > 1. We also prove the global asymptotic stability of the endemic equilibrium for a differential susceptibility and staged progression infectivity model, when > 1. Our results encompass and generalize those of [18, 22]. AMS Subject Classification : 34A34,34D23,34D40,92D30 PMID:20148330
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.
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.
Stability analysis of BAM neural networks with time-varying delays
ZHANG Huaguang; WANG Zhanshan
2007-01-01
Some new criteria for the global asymptotic stability of the equilibrium point for the bi-directional associative memory neural networks with time varying delays are presented. The obtained results present the structure of linear matrix inequality which can be solved efficiently. The comparison with some previously reported results in the literature demonstrates that the results in this paper provide one more set of criteria for determining the stability of the bi-directional associative memory neural networks with delays.
STABILIZATION OF A KIND OF PREY-PREDATOR MODEL WITH HOLLING FUNCTIONAL RESPONSE
Xi LIU; Qingling ZHANG; Lichun ZHAO
2006-01-01
The stabilization problem of a kind of prey-predator model with Holling functional response is investigated. By approximate linearization approach, a feedback control law stabilizing the closedloop system is obtained. On the other hand, by exact linearization approach, a suitable change of coordinates in the state space and a feedback control law render the complex nonlinear system to be a linear controllable one such that the positive equilibrium point of the closed-loop system is globally asymptotically stable.
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.
胡薇薇
2006-01-01
This paper presents the asymptotic stability of a two identical unit parallel system with a warm standby subject to common-cause failures. First, we obtain the existence and uniqueness of the nonnegative time-dependent solution of the system by using the Volterra operator equation in Banach space. Second, we use the C0-semigroup theory of linear operators to prove the existence and uniqueness of the positive time-dependent solution of the model, which is a mild solution for the initial value is not in the domain. However, it equals to the classical solution whent ＞ 0. As a result of the stability of C0-semigroup theory of linear operators, we get the time-dependent solution converging to its static solution in the sense of the norm, thus obtain the asymptotic stability of the solution of this system.%讨论了具有热储备和两个独立相同部件的平行系统在由常规错误引起失效下的渐进稳定性.首先,利用Banach空间的Volttera算子方程得到了非负动态解的存在唯一性;然后,利用强连续线性算子半群理论证明了系统正的动态解的存在唯一性,而由于初始值不在定义域内,故得到的是mild解.但在t＞0时系统古典解存在唯一,所以此时mild解即为古典解.最后,利用线性算子半群稳定性的结果,证明了该动态解在范数意义下收敛到稳态解,进而得到了系统的渐进稳定性.
Asymptotic charged BTZ black hole solutions
Hendi, S. H.
2012-03-01
The well-known (2 + 1)-dimensional Reissner-Nordström (BTZ) black hole can be generalized to three dimensional Einstein-nonlinear electromagnetic field, motivated from obtaining a finite value for the self-energy of a pointlike charge. Considering three types of nonlinear electromagnetic fields coupled with Einstein gravity, we derive three kinds of black hole solutions which their asymptotic properties are the same as charged BTZ solution. In addition, we calculate conserved and thermodynamic quantities of the solutions and show that they satisfy the first law of thermodynamics. Finally, we perform a stability analysis in the canonical ensemble and show that the black holes are stable in the whole phase space.
Asymptotic methods in mechanics of solids
Bauer, Svetlana M; Smirnov, Andrei L; Tovstik, Petr E; Vaillancourt, Rémi
2015-01-01
The construction of solutions of singularly perturbed systems of equations and boundary value problems that are characteristic for the mechanics of thin-walled structures are the main focus of the book. The theoretical results are supplemented by the analysis of problems and exercises. Some of the topics are rarely discussed in the textbooks, for example, the Newton polyhedron, which is a generalization of the Newton polygon for equations with two or more parameters. After introducing the important concept of the index of variation for functions special attention is devoted to eigenvalue problems containing a small parameter. The main part of the book deals with methods of asymptotic solutions of linear singularly perturbed boundary and boundary value problems without or with turning points, respectively. As examples, one-dimensional equilibrium, dynamics and stability problems for rigid bodies and solids are presented in detail. Numerous exercises and examples as well as vast references to the relevant Russi...
On transfinite extension of asymptotic dimension
Radul, Taras
2006-01-01
We prove that a transfinite extension of asymptotic dimension asind is trivial. We introduce a transfinite extension of asymptotic dimension asdim and give an example of metric proper space which has transfinite infinite dimension.
On L3,∞-stability of the Navier-Stokes system in exterior domains
Koba, Hajime
2017-02-01
This paper studies the stability of a stationary solution of the Navier-Stokes system with a constant velocity at infinity in an exterior domain. More precisely, this paper considers the stability of the Navier-Stokes system governing the stationary solution which belongs to the weak L3-space L 3 , ∞. Under the condition that the initial datum belongs to a solenoidal L 3 , ∞-space, we prove that if both the L 3 , ∞-norm of the initial datum and the L 3 , ∞-norm of the stationary solution are sufficiently small then the system admits a unique global-in-time strong L 3 , ∞-solution satisfying both L 3 , ∞-asymptotic stability and L∞-asymptotic stability. Moreover, we investigate L 3 , r-asymptotic stability of the global-in-time solution. Using Lp-Lq type estimates for the Oseen semigroup and applying an equivalent norm on the Lorentz space are key ideas to establish both the existence of a unique global-in-time strong (or mild) solution of our system and the stability of our solution.
Asymptotic properties of restricted naming games
Bhattacherjee, Biplab; Datta, Amitava; Manna, S. S.
2017-07-01
Asymptotic properties of the symmetric and asymmetric naming games have been studied under some restrictions in a community of agents. In one version, the vocabulary sizes of the agents are restricted to finite capacities. In this case, compared to the original naming games, the dynamics takes much longer time for achieving the consensus. In the second version, the symmetric game starts with a limited number of distinct names distributed among the agents. Three different quantities are measured for a quantitative comparison, namely, the maximum value of the total number of names in the community, the time at which the community attains the maximal number of names, and the global convergence time. Using an extensive numerical study, the entire set of three power law exponents characterizing these quantities are estimated for both the versions which are observed to be distinctly different from their counter parts of the original naming games.
Global analysis of a class of HIV models with immune response and antigenic variation
Souza, Max O
2008-01-01
We study the global stability of two models for the HIV virus dynamics, that take into account the CTL immune response and antigenic variation. We show that both models are globally asymptotically stable, by using appropriate Lyapunov functions. For both models, we characterise the stable equilibrium points for the entire biologically relevant parameter range. In the model with antigenic variation, which can have a large number of equilibrium points, this allows us to determine what is the diversity of the persistent strains.
Stability of gyro with harmonic nonlinearity in spinning vehicle
Singh, S. N.
1983-03-01
The stability analysis of a rate gyro mounted in a vehicle which is spinning with uncertain angular velocity about the spin axis of the gyro is presented. The complete nonlinear equation of the motion of the gimbal is considered, retaining the fundamental and second harmonic nonlinear terms which are functions of the angular velocity of the vehicle about the spin axis of the gyro. Using the circle criterion for the case of time-varying angular momentum and the Lyapunov approach for the case of uncertain constant angular velocity, conditions for asymptotic stability and global asymptotic stability are obtained. Stable regions in parameter space of the gyro and state space are obtained, and analytical relations for the selection of gyro parameters are derived.
Composite Operators in Asymptotic Safety
Pagani, Carlo
2016-01-01
We study the role of composite operators in the Asymptotic Safety program for quantum gravity. By including in the effective average action an explicit dependence on new sources we are able to keep track of operators which do not belong to the exact theory space and/or are normally discarded in a truncation. Typical examples are geometric operators such as volumes, lengths, or geodesic distances. We show that this set-up allows to investigate the scaling properties of various interesting operators via a suitable exact renormalization group equation. We test our framework in several settings, including Quantum Einstein Gravity, the conformally reduced Einstein-Hilbert truncation, and two dimensional quantum gravity. Finally, we briefly argue that our construction paves the way to approach observables in the Asymptotic Safety program.
Asymptotic safety goes on shell
Benedetti, Dario
2012-01-01
It is well known in quantum field theory that the off-shell effective action depends on the gauge choice and field parametrization used in calculating it. Nevertheless, the typical scheme in which the scenario of asymptotically safe gravity is investigated is an off-shell version of the functional renormalization group equation. Working with the Einstein-Hilbert truncation as a test bed, we develop a new scheme for the analysis of asymptotically safe gravity in which the on-shell part of the effective action is singled out and we show that the beta function for the essential coupling has no explicit gauge dependence. In order to reach our goal, we introduce several technical novelties, including a different decomposition of the metric fluctuations, a new implementation of the ghost sector and a new cut-off scheme. We find a nontrivial fixed point, with a value of the cosmological constant that is independent of the gauge-fixing parameters.
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. ...
Asymptotic Excisions of Metric Spaces and Ideals of Asymptotic Coarse Roe Algebras
LI Jin-xiu; WANG Qin
2006-01-01
We introduce in this note the notions of asymptotic excision of proper metric spaces and asymptotic equivalence relation for subspaces of metric spaces, which are relevant in characterizing spatial ideals of the asymptotic coarse Roe algebras. We show that the lattice of the asymptotic equivalence classes of the subspaces of a proper metric space is isomorphic to the lattice of the spatial ideals of the asymptotic Roe algebra. For asymptotic excisions of the metric space, we also establish a Mayer-Vietoris sequence in K-theory of the asymptotic coarse Roe algebras.
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.
Global synchronization of two parametrically excited systems using active control
Lei Youming [Department of Applied Mathematics, Northwestern Polytechnical University, Xi' an 710072 (China)] e-mail: leiyouming@nwpu.edu.cn; Xu Wei [Department of Applied Mathematics, Northwestern Polytechnical University, Xi' an 710072 (China)] e-mail: weixu@nwpu.edu.cn; Shen Jianwei [Department of Applied Mathematics, Northwestern Polytechnical University, Xi' an 710072 (China); Fang Tong [Department of Engineering Mechanics, Northwestern Polytechnical University, Xi' an 710072 (China)
2006-04-01
In this paper, we apply an active control technique to synchronize a kind of two parametrically excited chaotic systems. Based on Lyapunov stability theory and Routh-Hurwitz criteria, some generic sufficient conditions for global asymptotic synchronization are obtained. Illustrative examples on synchronization of two Duffing systems subject to a harmonic parametric excitation and that of two parametrically excited chaotic pendulums are considered here. Numerical simulations show the validity and feasibility of the proposed method.
Supersymmetric asymptotic safety is not guaranteed
Intriligator, Kenneth
2015-01-01
It was recently shown that certain perturbatively accessible, non-supersymmetric gauge-Yukawa theories have UV asymptotic safety, without asymptotic freedom: the UV theory is an interacting RG fixed point, and the IR theory is free. We here investigate the possibility of asymptotic safety in supersymmetric theories, and use unitarity bounds, and the a-theorem, to rule it out in broad classes of theories. The arguments apply without assuming perturbation theory. Therefore, the UV completion of a non-asymptotically free susy theory must have additional, non-obvious degrees of freedom, such as those of an asymptotically free (perhaps magnetic dual) extension.
Asymptotic Stabilizability of a Class of Stochastic Nonlinear Hybrid Systems
Ewelina Seroka
2015-01-01
Full Text Available The problem of the asymptotic stabilizability in probability of a class of stochastic nonlinear control hybrid systems (with a linear dependence of the control with state dependent, Markovian, and any switching rule is considered in the paper. To solve the issue, the Lyapunov technique, including a common, single, and multiple Lyapunov function, the hybrid control theory, and some results for stochastic nonhybrid systems are used. Sufficient conditions for the asymptotic stabilizability in probability for a considered class of hybrid systems are formulated. Also the stabilizing control in a feedback form is considered. Furthermore, in the case of hybrid systems with the state dependent switching rule, a method for a construction of stabilizing switching rules is proposed. Obtained results are illustrated by examples and numerical simulations.
Analysis and Synthesis of Global Nonlinear H∞ Controller for Robot Manipulators
Carlos Alberto Chavez Guzmán
2015-01-01
Full Text Available The H∞ regulation problem for robot manipulators using gravitational force compensation or precompensation has been solved locally while global asymptotical stability (or global stability has been demonstrated using other methodologies. A solution to the global nonlinear H∞ regulation problem for l-degrees-of-freedom (l-DOF robot manipulators, affected by external disturbances, is presented. We showed that the Hamilton-Jacobi-Isaacs (HJI inequality, inherited in the solution of the H∞ control problem, is satisfied by defining a strict Lyapunov function. The performance issues of the nonlinear H∞ regulator are illustrated in experimental and simulation studies made for a 3-DOF rigid links robot manipulator.
Asymptotic integration of differential and difference equations
Bodine, Sigrun
2015-01-01
This book presents the theory of asymptotic integration for both linear differential and difference equations. This type of asymptotic analysis is based on some fundamental principles by Norman Levinson. While he applied them to a special class of differential equations, subsequent work has shown that the same principles lead to asymptotic results for much wider classes of differential and also difference equations. After discussing asymptotic integration in a unified approach, this book studies how the application of these methods provides several new insights and frequent improvements to results found in earlier literature. It then continues with a brief introduction to the relatively new field of asymptotic integration for dynamic equations on time scales. Asymptotic Integration of Differential and Difference Equations is a self-contained and clearly structured presentation of some of the most important results in asymptotic integration and the techniques used in this field. It will appeal to researchers i...
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.
M.Syed Ali
2011-01-01
In this paper,the global stability of Takagi-Sugeno(TS)uncertain stochastic fuzzy recurrent neural networks with discrete and distributed time-varying delays(TSUSFRNNs)is considered.A novel LMI-based stability criterion is obtained by using Lyapunov functional theory to guarantee the asymptotic stability of TSUSFRNNs.The proposed stability conditions are demonstrated through numerical examples.Furthermore,the supplementary requirement that the time derivative of time-varying delays must be smaller than one is removed.Comparison results are demonstrated to show that the proposed method is more able to guarantee the widest stability region than the other methods available in the existing literature.
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]).
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.
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.
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 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.
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.
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
UNIFORM BOUNDEDNESS AND STABILITY OF SOLUTIONS TO A CUBIC PREDATOR-PREY SYSTEM WITH CROSS-DIFFUSION
Huaihuo Cao; Shengmao Fu
2009-01-01
Using the energy estimate and Gagliardo-Nirenberg-typo inequalities,the exi-tence and uniform boundedness of the global solutions to a strongly coupled reaction-zdiffusion system are proved. This system is a generalization of the two-species Lotka-Volterra predator-prey model with serf and cross-diffusion. Sufficient condition for the global asymptotic stability of the positive equilibrium point of the model is given by constructing Lyapunov function.
UNIFORM BOUNDEDNESS AND STABILITY OF SOLUTIONS TO A CUBIC PREDATOR-PREY SYSTEM WITH CROSS-DIFFUSION
无
2009-01-01
Using the energy estimate and Gagliardo-Nirenberg-type inequalities,the existence and uniform boundedness of the global solutions to a strongly coupled reaction-diffusion system are proved. This system is a generalization of the two-species Lotka-Volterra predator-prey model with self and cross-diffusion. Suffcient condition for the global asymptotic stability of the positive equilibrium point of the model is given by constructing Lyapunov function.
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,
Asymptotics for Associated Random Variables
Oliveira, Paulo Eduardo
2012-01-01
The book concerns the notion of association in probability and statistics. Association and some other positive dependence notions were introduced in 1966 and 1967 but received little attention from the probabilistic and statistics community. The interest in these dependence notions increased in the last 15 to 20 years, and many asymptotic results were proved and improved. Despite this increased interest, characterizations and results remained essentially scattered in the literature published in different journals. The goal of this book is to bring together the bulk of these results, presenting
Asymptotics of robust utility maximization
Knispel, Thomas
2012-01-01
For a stochastic factor model we maximize the long-term growth rate of robust expected power utility with parameter $\\lambda\\in(0,1)$. Using duality methods the problem is reformulated as an infinite time horizon, risk-sensitive control problem. Our results characterize the optimal growth rate, an optimal long-term trading strategy and an asymptotic worst-case model in terms of an ergodic Bellman equation. With these results we propose a duality approach to a "robust large deviations" criterion for optimal long-term investment.
Asymptotics of Lagged Fibonacci Sequences
Mertens, Stephan
2009-01-01
Consider "lagged" Fibonacci sequences $a(n) = a(n-1)+a(\\lfloor n/k\\rfloor)$ for $k > 1$. We show that $\\lim_{n\\to\\infty} a(kn)/a(n)\\cdot\\ln n/n = k\\ln k$ and we demonstrate the slow numerical convergence to this limit and how to deal with this slow convergence. We also discuss the connection between two classical results of N.G. de Bruijn and K. Mahler on the asymptotics of $a(n)$.
Asymptotic behaviour of a family of gradient algorithms in R^d and Hilbert spaces
Pronzato, Luc; Zhigljavsky, Anatoly A
2008-01-01
The asymptotic behaviour of a family of gradient algorithms (including the methods of steepest descent and minimum residues) for the optimisation of bounded quadratic operators in R^d and Hilbert spaces is analyzed. The results obtained generalize those of Akaike (1959) in several directions. First, all algorithms in the family are shown to have the same asymptotic behaviour (convergence to a two-point attractor), which implies in particular that they have similar asymptotic convergence rates. Second, the analysis also covers the Hilbert space case. A detailed analysis of the stability property of the attractor is provided.
Stability Tests of Positive Fractional Continuous-time Linear Systems with Delays
Tadeusz Kaczorek
2013-06-01
Full Text Available Necessary and sufficient conditions for the asymptotic stability of positive fractional continuous-time linear systems with many delays are established. It is shown that: 1 the asymptotic stability of the positive fractional system is independent of their delays, 2 the checking of the asymptotic stability of the positive fractional systems with delays can be reduced to checking of the asymptotic stability of positive standard linear systems without delays.
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.
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.
Zhang, Baoyong; Lam, James; Xu, Shengyuan
2015-07-01
This paper revisits the problem of asymptotic stability analysis for neural networks with distributed delays. The distributed delays are assumed to be constant and prescribed. Since a positive-definite quadratic functional does not necessarily require all the involved symmetric matrices to be positive definite, it is important for constructing relaxed Lyapunov-Krasovskii functionals, which generally lead to less conservative stability criteria. Based on this fact and using two kinds of integral inequalities, a new delay-dependent condition is obtained, which ensures that the distributed delay neural network under consideration is globally asymptotically stable. This stability criterion is then improved by applying the delay partitioning technique. Two numerical examples are provided to demonstrate the advantage of the presented stability criteria.
On the minimal speed and asymptotics of the wave solutions for the lotka volterra system
Hou, Xiaojie
2010-01-01
e study the minimal wave speed and the asymptotics of the traveling wave solutions of a competitive Lotka Volterra system. The existence of the traveling wave solutions is derived by monotone iteration. The asymptotic behaviors of the wave solutions are derived by comparison argument and the exponential dichotomy, which seems to be the key to understand the geometry and the stability of the wave solutions. Also the uniqueness and the monotonicity of the waves are investigated via a generalized sliding domain method.
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.
Asymptotically Free Gauge Theories. I
Wilczek, Frank; Gross, David J.
1973-07-01
Asymptotically free gauge theories of the strong interactions are constructed and analyzed. The reasons for doing this are recounted, including a review of renormalization group techniques and their application to scaling phenomena. The renormalization group equations are derived for Yang-Mills theories. The parameters that enter into the equations are calculated to lowest order and it is shown that these theories are asymptotically free. More specifically the effective coupling constant, which determines the ultraviolet behavior of the theory, vanishes for large space-like momenta. Fermions are incorporated and the construction of realistic models is discussed. We propose that the strong interactions be mediated by a "color" gauge group which commutes with SU(3)xSU(3). The problem of symmetry breaking is discussed. It appears likely that this would have a dynamical origin. It is suggested that the gauge symmetry might not be broken, and that the severe infrared singularities prevent the occurrence of non-color singlet physical states. The deep inelastic structure functions, as well as the electron position total annihilation cross section are analyzed. Scaling obtains up to calculable logarithmic corrections, and the naive lightcone or parton model results follow. The problems of incorporating scalar mesons and breaking the symmetry by the Higgs mechanism are explained in detail.
Asymptotic safety goes on shell
Benedetti, Dario
2011-01-01
It is well known in quantum field theory that the off-shell effective action depends on the gauge choice and field parametrization used in calculating it. Nevertheless, the typical scheme in which the scenario of asymptotically safe gravity is investigated is an off-shell version of the functional renormalization group equation. Working with the Einstein-Hilbert truncation as a test bed, we develop a new scheme for the analysis of asymptotically safe gravity in which the on-shell part of the effective action is singled out and we show that the beta function for the essential coupling has no explicit gauge-dependence. In order to reach our goal, we introduce several technical novelties, including a different decomposition of the metric fluctuations, a new implementation of the ghost sector, and a new cut-off scheme. We find a non-trivial fixed point, with a value of the cosmological constant which is independent of the gauge-fixing parameters.