Some dynamical properties of a viscoelastic cylindrical shell

IntroductionTherearerarepapersonthedynamicPropertiesofviscoelasticshells.~ulosl']discussesthecaseofshallowsphericalshellandDrozdov[ZIgivesasufficientcondihonofstabilityfortheviscoelasticcylindershellbyusingtheLyapunovfunchonal.UsingtheLyapunovdirectmethod,Tyllkowski[']establishesasufficientconditionfortheasymptohcstabilityofviscoelasticcylindricalshell.ItisnotdifficulttofindthattheseexistingresultSmainlyconcentrateonthedynamicstabilityofviscoelasticshell.Thediscussionaboutthedynamicalsyste…     

结构气浮的力学特性研究

对结构气浮的静力和动力力学特性以及稳定性问题进行了研究。假设浮筒内的气体为理想气体，建立了气浮力的计算式；引进气浮力折减系数并结合试验，对气浮结构的动力学特性进行了分析；基于静力平衡，得到了非对称多体气浮结构的初稳性高参数的计算式。理论计算值和试验测算值吻合。提出的气浮力折减系数对气浮体的浮态、稳性和动力学特性都有很大的影响；气浮结构的稳性低于同等情况的普通浮体，采用分舱方法可以提高单体气浮筒的浮稳性。     

三纵列液压模块组合挂车侧倾稳定性计算

研究了三纵列任意轴线的液压模块组合挂车的侧倾稳定性问题, 分别推导了 面向侧翻稳定性及爆胎稳定性的关于装载量、装载货物质心高度及路面横向倾角的通用计算 公式. 最后用推导的通用公式对典型三纵列液压模块组合挂车的侧倾稳定性进行了实际计算, 并绘制了装载量、装载货物质心高度及路面横向倾角的关系图.     

Global stability and Hopf bifurcation of a predator-prey model with stage structure and delayed predator response

A Holling type predator-prey model with stage structure for the predator and a time delay due to the gestation of the mature predator is investigated. By analyzing the characteristic equations, the local stability of a predator-extinction equilibrium and a coexistence equilibrium of the model is addressed and the existence of Hopf bifurcations at the coexistence equilibrium is established. By means of the persistence theory on infinite dimensional systems, it is proven that the system is permanent if the coexistence equilibrium is feasible. By using Lyapunov functionals and the LaSalle invariance principle, it is shown that the predator-extinction equilibrium is globally asymptotically stable when the coexistence equilibrium is not feasible, and sufficient conditions are derived for the global stability of the coexistence equilibrium. Numerical simulations are carried out to illustrate the main theoretical results.     

Asymptotic Stability of Transiently Chaotic Neural Networks

The asymptotic stability of transiently chaotic neural networks is considered in this paper. By utilizing a Lyapunov function and then applying LaSalle's invariance principle, we present several sufficient conditions that guarantee the stability. These results are less conservative than those established in the earlier references. Two numerical examples are given to illustrate the applicability of these conditions.     

A note on Poisson stability and controllability

The connection between Poisson stability and controllability is revisited. For the controllability criterion based on weakly positive Poisson stability (WPPS) and Lie algebra rank condition (LARC), it is shown that two natural assumptions about the set of input values are necessary for strictness. By using the relationship between conservative property and WPPS, sufficient conditions for controllability of affine nonlinear systems are further discussed. At last, for systems defined on compact Riemannian manifold, the WPPS is proved to be equivalent to Poisson stability.     

Global stability of a delayed SEIRS epidemic model with saturation incidence rate

In this paper, an SEIRS epidemic model with a saturation incidence rate and a time delay describing a latent period is investigated. By analyzing the corresponding characteristic equations, the local stability of an endemic equilibrium and a disease-free equilibrium is established. When the basic reproduction number is greater than unity, by means of an iteration technique, sufficient conditions are obtained for the global asymptotic stability of the endemic equilibrium. By comparison arguments, it is proved that if the basic reproduction number is less than unity, the disease-free equilibrium is globally asymptotically stable. Numerical simulations are carried out to illustrate the main theoretical results.     

Bifurcations of travelling wave solutions for a coupled nonlinear wave system

Introduction FangShaomeiandGuoBoling[1]consideredthefollowingtimeperiodicproblemof dampedcouplednonlinearwaveequations:ut f(u)x-αuxx βuxxx 2vvx=G1(u,v) h1(x),vt-γvxx 2(uv)x g(v)x=G2(u,v) h2(x),(1)whereα,β,γareconstants,andγ>0,β≠0.Undertheperiodicboundaryconditions,the authorsobtainedtheuniqueexistenceofstrongsolutionsfortheabovesystem.InthispaperweshallconsiderbifurcationbehaviorofthetravellingwavesolutionsofEq.(1)inthecaseGi(u,v)≡0,hi(u,v)≡0(i=1,2).Letξ=x-ct,u=u(x-ct),where cis…     

On the general theory of stability for elastic bodies

This paper deals with the stability of loaded equilibrium configuration of elastic bodies, within the framework of nonlinear thermoelasticity. Although most of the results are obtained in the context of thermo-mechanical stability, the parallel developments for the purely mechanical stability are also considered. By use of an appropriate thermodynamic restriction, several theorems are proved concerning a sufficient condition for stability of the equilibrium configuration. These theorems hold under a general class of motions and their validity is not limited to small motions and small temperature changes from a loaded equilibrium state. Various generalizations of our main results are discussed and the reasonableness of the proposed stability criterion is demonstrated.     

STABILITY CRITERIA IN TERMS OF TWO MEASURES FOR DELAY DIFFERENTIAL EQUATIONS

ＩｎｔｒｏｄｕｃｔｉｏｎＡｓｗｅｋｎｏｗ ,ｉｎｔｈｅｉｎｖｅｓｔｉｇａｔｉｏｎｏｆｔｈｅｐｒｏｐｅｒｔｉｅｓｏｆｓｏｌｕｔｉｏｎｓｆｏｒｎｏｎｌｉｎｅａｒｄｉｆｆｅｒｅｎｔｉａｌｅｑｕａｔｉｏｎｓ,ｔｈｅｍｅｔｈｏｄｏｆｖａｒｉａｔｉｏｎｏｆｐａｒａｍｅｔｅｒｓｉｓａｎｅｆｆｅｃｔｉｖｅｔｏｏｌｉｎｔｈｅｃａｓｅｔｈａｔｔｈｅｃｏｒｒｅｓｐｏｎｄｉｎｇｕｎｐｅｒｔｕｒｂｅｄｔｅｒｍｓａｒｅｌｉｎｅａｒｏｒｏｆｃｅｒｔａｉｎｓｍｏｏｔｈｎｅｓｓｔｈｏｕｇｈｔｈｅｙａｒｅｎｏｎｌｉｎｅａｒ.Ｏｎｔｈｅ…     

Analysis of stability and bifurcation for an SEIV epidemic model with vaccination and nonlinear incidence rate

In this paper, a delay-differential mathematical model that described HIV infection of CD4⁺ T cells is analyzed. The effect of time delay on stability of the equilibria of the infection model has been studied. And the sufficient criteria for stability switch of the infected equilibrium and the local and global asymptotic stability of the uninfected equilibrium are given. By using the geometric stability switch criterion in the delay-differential system with delay-dependent parameters, we present that stable equilibria become unstable as the time delay increases. Numerical simulations are carried out to explain the mathematical conclusions.     

计及交叉扩散时热盐双扩散对流系统的非线性稳定性分析

对热盐双扩散对流系统的非线性稳定性进行了研究,其中考虑了交叉扩散的影响.利用一个有限表达式来求解非线性方程组,得到了较好的结果.只需将交叉扩散系数表示为两个参数,就得出了更一般的R_T-R_S关系式,以及定常有限振幅的表达式.而当交叉扩散系数取为零时,该式就还原为前人在不计及交叉扩散时导出的关系式.     

Secondary Instabilities of Wakes of a Circular Cylinder Using a Finite Element Method

This study investigates secondary instabilities of periodic wakes of a circular cylinder with infinitely long span. It has been known that after the wake undergoes a supercritical Hopf bifurcation (the primary instability) that leads to two-dimensional von Kantian vorlex street, the secondary instability occurs sequentially, which results in the onset of three-dimensional flow. Williamson (1996) has reviewed that the periodic wakes over a range of moderate Reynolds number from 140 to 300 are characterized by two critical modes. Mode A and Mode B, which are respectively associated with large-scale and fine-scale structures in span. In order to understand a sequence of bifurcation in transitional wake, in this paper, the stability of periodic Row governed by the linearized Navier-Stokes equations is analyzed by using the Floquet stability theory. By employing the finite elemental discretization with a fine mesh, the numerical results for both simulation and stability analysis have high spatio-resolution. The obtained stability results are in good agreement with experimental data and some relevant numerical results. By means of visualizations of the three-dimensionally critical flow structures. the existence of Mode A and Mode B is verified from the spatial structures in both the two modes.     

Global Attractivity and Global Exponential Stability for Delayed Hopfield Neural Network Models

ＩｎｔｒｏｄｕｃｔｉｏｎＨｏｐｆｉｅｌｄｎｅｕｒａｌｎｅｔｗｏｒｋｍｏｄｅｌｉｓｏｎｅｏｆｔｈｅｍｏｓｔｐｏｐｕｌａｒｍｏｄｅｌｓｉｎｔｈｅｌｉｔｅｒｒａｔｕｒｅｏｆａｒｔｉｆｉｃｉａｌｎｅｕｒａｌｎｅｔｗｏｒｋｓ,ｗｈｉｃｈｉｓｄｅｓｃｒｉｂｅｄｂｙｔｈｅｆｏｌｌｏｗｉｎｇｎｏｎｌｉｎｅａｒｄｙｎａｍｉｃｓｅｑｕａｔｉｏｎｓ[1,2 ]:Ｃｉｄｕｉ(ｔ)ｄｔ =-ｕｉ(ｔ)Ｒｉ ∑ｎｊ=1Ｔｉｊｇｊ(ｕｊ(ｔ) ) Ｉｉ　　 (ｉ=1 ,2 ,… ,ｎ) ,( 1 )ｗｈｅｒｅｎ≥ 2ｉｓｔｈｅｎｕｍｂｅｒｏｆｎｅｕｒｏｎｓｉｎｔｈｅ…     

Delay induced stability switches in a viral dynamical model

In this paper, a delay-differential mathematical model that described HIV infection of CD4⁺ T cells is analyzed. The effect of time delay on stability of the equilibria of the infection model has been studied. And the sufficient criteria for stability switch of the infected equilibrium and the local and global asymptotic stability of the uninfected equilibrium are given. By using the geometric stability switch criterion in the delay-differential system with delay-dependent parameters, we present that stable equilibria become unstable as the time delay increases. Numerical simulations are carried out to explain the mathematical conclusions.

     

Global analysis of Ivlev's type predator-prey dynamic systems

Consider a class of Ivlev's type predator-prey dynamic systems with prey and predator both having linear density restricts. By using the qualitative methods of ODE, the global stability of positive equilibrium and existence and uniqueness of non-small amplitude stable limit cycle are obtained. Especially under certain conditions, it shows that existence and uniqueness of non-small amplitude stable limit cycle is equivalent to the local un-stability of positive equilibrium and the local stability of positive equilibrium implies its global stability. That is to say, the global dynamic of the system is entirely determined by the local stability of the positive equilibrium.     

Global stability of periodic solutions for a discrete predator–prey system with functional response

The purpose of this paper is to study the existence and global stability of a periodic solution for a discrete predator–prey system with the Beddington–DeAngelis functional response and predator cannibalism. By using the continuation theorem, the existence conditions of at least one periodic solution are obtained, and the sufficient conditions, which ensure the global stability of the positive periodic solution, are derived by constructing a special Lyapunov function.     

Global analysis of Ivlev＇s type predator-prey dynamic systems

Consider a class of Ivlev＇s type predator-prey dynamic systems with prey and predator both having linear density restricts. By using the qualitative methods of ODE, the global stability of positive equilibrium and existence and uniqueness of non-small amplitude stable limit cycle are obtained. Especially under certain conditions, it shows that existence and uniqueness of non-small amplitude stable limit cycle is equivalent to the local un-stability of positive equilibrium and the local stability of positive equilibrium implies its global stability. That is to say, the global dynamic of the system is entirely determined by the local stability of the positive equilibrium.     

时间无关不可逆过程及不可逆系统的稳定性

在不可逆热力学框架内引入了四条基本假设，建立了宏观本构关系的新的逻辑系统．在假设3中通过引入一种新的运算，把内变量演化方程定义在时间的点集上．结合讨论C1ausius-Dubem不等式，得到了假设4，它把时间点集的性质与系统状态联起来．以此为基础，证明了一致性条件成立的判别准则和加卸载准则，并成功地解释了实验现象存在有一个应变速率的临界值，当加载应变速率低于该值时，材料的应力—应变关系基本上与速率无关；当高于该值时，则明显与速率相关、更富有力学含义地给出了不可逆系统稳定性的一种定义，并证明了判别稳定性的一个准则．此外，还得出系统稳定是不可逆行为与时间无关的前提条件．     

Hopf Bifurcation and Stability of Periodic Solutions for van der Pol Equation with Distributed Delay

The van der Pol equation with a distributed time delay is analyzed. Itslinear stability is investigated by employing the Routh–Hurwitzcriteria. Moreover, the local asymptotic stability conditions are alsoderived. By using the mean time delay as a bifurcation parameter, themodel is found to undergo a sequence of Hopf bifurcations. The directionand the stability criteria of the bifurcating periodic solutions areobtained by the normal form theory and the center manifold theorem. Somenumerical simulation examples for justifying the theoretical analysisare also given.