THE QUALITATIVE ANALYSIS OF TWO SPECIES PREDATOR-PREY MODEL WITE HOLLING’S TYPE Ⅲ FUNCTIONAL RESPONSE

This paper is denoted to the qualitative analysis of two species predator-prey modelwith Holling’s type Ⅲ functional response.Conditions for the global stability of nontrivialequilibrium points and conditions for the existence and uniqueness of limit cycles around thepositive equilibrium point are obtained.The biological interpretations of these conditionsare discussed.The authors believe that the conditions established in this paper are new toliterature.     

Existence results for generalized vector equilibrium problems with applications

By a coincidence theorem, some existence theorems of solutions are proved for four types of generalized vector equilibrium problems with moving cones. Applications to the generalized semi-infinite programs with the generalized vector equilibrium constraints under the mild conditions are also given. The results of this paper unify and improve the corresponding results in the previous literature.     

A CRITERION FOR THE STABILITY OF MOTION OF NONLINEAR SYSTEM

As to an autonomous nonlinear system, the stability of the equilibrium state in a sufficiently small neighborhood of the equilibrium state can be determined by eigenvalues of the linear part of the nonlinear system provided that the eigenvalues are not in a critical case. Many methods may be used to detect the stability for a linear system. A lot of researches for determining the stability of a nonlinear system are completed by mathematicians and mechanicians but most of them are methods for the special forms of nonlinear systems. Till now, none of these methods can be conveniently applied to all nonlinear systems. The method introduced by this paper gives the necessary and sufficient conditions of the stability of a nonlinear system. The familiar Krasovski's method is a special case of this method     

The equilibrium stability for a smooth and discontinuous oscillator with dry friction

In this paper,we investigate the equilibrium stability of a Filippov-type system having multiple stick regions based upon a smooth and discontinuous(SD) oscillator with dry friction.The sets of equilibrium states of the system are analyzed together with Coulomb friction conditions in both( f_n,f_s) and(x,˙x) planes.In the stability analysis,Lyapunov functions are constructed to derive the instability for the equilibrium set of the hyperbolic type and La Salle's invariance principle is employed to obtain the stability of the nonhyperbolic type.Analysis demonstrates the existence of a thick stable manifold and the interior stability of the hyperbolic equilibrium set due to the attractive sliding mode of the Filippov property,and also shows that the unstable manifolds of the hyperbolic-type are that of the endpoints with their saddle property.Numerical calculations show a good agreement with the theoretical analysis and an excellent efficien y of the approach for equilibrium states in this particular Filippov system.Furthermore,the equilibrium bifurcations are presented to demonstrate the transition between the smooth and the discontinuous regimes.     

On the truth of nanoscale for nanobeams based on nonlocal elastic stress field theory： equilibrium, governing equation and static deflection

This paper has successfully addressed three critical but overlooked issues in nonlocal elastic stress field theory for nanobeams： （i） why does the presence of increasing nonlocal effects induce reduced nanostructural stiffness in many, but not consistently for all, cases of study, i.e., increasing static deflection, decreasing natural frequency and decreasing buckling load, although physical intuition according to the nonlocal elasticity field theory first established by Eringen tells otherwise？ （ii） the intriguing conclusion that nanoscale effects are missing in the solutions in many exemplary cases of study, e.g., bending deflection of a cantilever nanobeam with a point load at its tip; and （iii） the non-existence of additional higher-order boundary conditions for a higher-order governing differential equation. Applying the nonlocal elasticity field theory in nanomechanics and an exact variational principal approach, we derive the new equilibrium conditions, do- main governing differential equation and boundary conditions for bending of nanobeams. These equations and conditions involve essential higher-order differential terms which are opposite in sign with respect to the previously studies in the statics and dynamics of nonlocal nano-structures. The difference in higher-order terms results in reverse trends of nanoscale effects with respect to the conclusion of this paper. Effectively, this paper reports new equilibrium conditions, governing differential equation and boundary condi- tions and the true basic static responses for bending of nanobeams. It is also concluded that the widely accepted equilibrium conditions of nonlocal nanostructures are in fact not in equilibrium, but they can be made perfect should the nonlocal bending moment be replaced by an effective nonlocal bending moment. These conclusions are substantiated, in a general sense, by other approaches in nanostructural models such as strain gradient theory, modified couple stress models and experiments.     

A new micromechanical approach of micropolar continuum modeling for 2-D periodic cellular material

In this paper, we present a new united approach to formulate the equivalent micropolar constitutive relation of two-dimensional (2-D) periodic cellular material to capture its non-local properties and to explain the size effects in its structural analysis. The new united approach takes both the displacement compatibility and the equilibrium of forces and moments into consideration, where Taylor series expansion of the displacement and rotation fields and the extended aver-aging procedure with an explicit enforcement of equilibrium are adopted in the micromechanical analysis of a unit cell. In numerical examples, the effective micropolar constants obtained in this paper and others derived in the literature are used for the equivalent micropolar continuum simulation of cellular solids. The solutions from the equivalent analysis are compared with the discrete simulation solutions of the cellu-lar solids. It is found that the micropolar constants developed in this paper give satisfying results of equivalent analysis for the periodic cellular material.     

FREE VIBRATION ANALYSIS OF LATTICE SANDWICH BEAMS UNDER SEVERAL TYPICAL BOUNDARY CONDITIONS

Free vibration problems of lattice sandwich beams under several typical boundary conditions are investigated in the present paper. The lattice sandwich beam is transformed to an equivalent homogeneous three-layered sandwich beam. Unlike the traditional analytical model in which the rotation angles of the face sheets and the core are assumed the same, different rotation angles are considered in this paper to characterize the real response of sandwich beams. The analytical solutions of the natural frequencies for several typical boundary conditions are obtained. The effects of material properties and geometric parameters on the natural frequencies are also investigated.     

Perturbation formulation of continuation method including limit and bifurcation points

This paper gives the perturbation formulation of continuation method for nonlinear equations. Emphasis is laid on the discussion of searching for the singular points on the equilibrium path and of tracing the paths over the limit or bifurcation points. The method is applied to buckling analysis of thin shells. The pre-and post-buckling equilibrium paths and deflections can be obtained, which are illustrated in examples of buckling analysis of cylindrical and toroidal shells.     

BASIC THEORY AND APPLICATIONS OF PROBABILISTIC METRIC SPACES(Ⅰ)

This paper is devoted to the study of the basic theory and applications of probabilistic metric spaces (PM-space). In this paper the topological structure and properties for PM-space are considered. The conditions of metrization and the form of metric functions for PM-spaces. Menger PM-spaces and probabilistic normed linear spaces (PN-space ) are given and the characterizations of various probabilistically bounded sets are presented. As applications we utilize these results obtained in this paper to study the linear operator theory and fixed point theory on PM-spaces.     

Stability and Hopf bifurcation of a delayed ratio-dependent predator-prey system

Since the ratio-dependent theory reflects the fact that predators must share and compete for food, it is suitable for describing the relationship between predators and their preys and has recently become a very important theory put forward by biologists. In order to investigate the dynamical relationship between predators and their preys, a so-called Michaelis-Menten ratio-dependent predator-prey model is studied in this paper with gestation time delays of predators and preys taken into consideration. The stability of the positive equilibrium is investigated by the Nyquist criteria, and the existence of the local Hopf bifurcation is analyzed by employing the theory of Hopf bifurcation. By means of the center manifold and the normal form theories, explicit formulae are derived to determine the stability, direction and other properties of bifurcating periodic solutions. The above theoretical results are validated by numerical simulations with the help of dynamical software WinPP. The results show that if both the gestation delays are small enough, their sizes will keep stable in the long run, but if the gestation delays of predators are big enough, their sizes will periodically fluc-tuate in the long term. In order to reveal the effects of time delays on the ratio-dependent predator-prey model, a ratiodependent predator-prey model without time delays is considered. By Hurwitz criteria, the local stability of positive equilibrium of this model is investigated. The conditions under which the positive equilibrium is locally asymptotically stable are obtained. By comparing the results with those of the model with time delays, it shows that the dynamical behaviors of ratio-dependent predator-prey model with time delays are more complicated. Under the same conditions, namely, with the same parameters, the stability of positive equilibrium of ratio-dependent predator-prey model would change due to the introduction of gestation time delays for predators and preys. Moreover, with the variation of time delays, the positive equilibrium of the ratio-dependent predator-prey model subjects to Hopf bifurcation.     

Some Non-linear Elastic Solutions for Masonry Solids*

ABSTRACT

This paper deals with equilibrium problems for solids made of elastic materials of bounded tensile strength and for which exact solutions are achieved. A constitutive equation is adopted and its main properties with regard to uniqueness of the solution to boundary problems are also analyzed. Four distinct equilibrium problems are then considered. The first three are characterized by specific symmetry conditions—polar, spherical, and cylindrical, respectively.     

NONLINEAR THEORY OF MULTILAYER SANDWICH SHELLS AND ITSAPPLICATION (Ⅱ)──FUNDAMENTAL EQUATIONS FOR ORTHOTROPIC SHALLOW SHELLS

InPartl,anonlineartheoryformultilayersand`"ichshellsundergoingsmallstrainsandmoderaterotatiol1sisgiven-inwhichtranst'ersesheardeformationisconsidered.Thesimplifiedtheoryfortheshellsundergoingmoderateormoderate/smallrotationsisalsoPresented.Theexpressionsi…     

NONLINEAR THEORY OF MULTILAYER SANDWICH SHELLS AND ITS APPLICATION (Ⅱ)──FUNDAMENTAL EQUATIONS FOR ORTHOTROPIC SHALLOW SHELLS

This paper applied the simplified theory for multilayer sandwich shells undergoing moderate/small rotations in Ref. [1] to shallow shells. The equilibrium equations and boundary conditions of large deflection of orthotropic and the special case, isotropic shells, are presented.     

Time-Reversible Hamiltonian Vector Fields with Symplectic Symmetries

This paper deals with the dynamics of time-reversible Hamiltonian vector fields with two degrees of freedom around an elliptic equilibrium point in presence of 1–1 resonance. The main result says that under certain conditions there are two one-parameter families of reversible periodic solutions terminating at the equilibrium.     

Bifurcation and stability analysis of a neural network model with distributed delays

In this paper, the dynamics of a generalized two-neuron model with self-connections and distributed delays are investigated, together with the stability of the equilibrium. In particular, the conditions under which the Hopf bifurcation occurs at the equilibrium are obtained for the weak kernel. This means that a family of periodic solutions bifurcates from the equilibrium when the bifurcation parameter exceeds a critical value. Explicit algorithms for determining the stability of the bifurcating periodic solutions and the direction of the Hopf bifurcation are derived by using the theory of normal form and center manifold [20]. Some numerical simulations are given to illustrate the effectiveness of the results found. The obtained results are new and they complement previously known results.This work was supported by the National Natural Science Foundation of China under Grants 60574043 and 60373067, the Natural Science Foundation of Jiangsu Province, China under Grants BK2003053.     

边坡三维极限平衡法的通用形式

基于以下假定条件:(1) 稳定系数定义为材料的强度折减系数;(2) 土体为刚体,底滑面服从Mohr-Columb强度破坏准则;(3) 微条柱底部法向力dNz的作用点处于条柱底部中点;(4)滑面剪力与底滑面和xoz平面交线的夹角为θ。本文建立了边坡三维极限平衡法的通用形式,通过给定不同的限制条件,可分别得到三维普通条分法 、三维简化毕肖普法 、三维简化简布法 、三维Spencer法 等三维极限平衡的具体算法。     

Global dynamical behavior of a three-body system with flexible connection in the gravitational field

Summary In this paper, the global behavior of relative equilibrium states of a three-body satellite with flexible connection under the action of the gravitational torque is studied. With geometric method, the conditions of existence of nontrivial solutions to the relative equilibrium equations are determined. By using reduction method and singularity theory, the conditions of occurrence of bifurcation from trivial solutions are derived, which agree with the existence conditions of nontrivial solutions, and the bifurcation is proved to be pitchfork-bifurcation. The Liapunov stability of each equilibrium state is considered, and a stability diagram in terms of system parameters is presented. Received 10 March 1998; accepted for publication 21 July 1998     

弹性力学的平衡差分解法

本文从基本的平衡方程出发,导出了含边界条件的弹性力学差分方程;给出了平面问题,梁弯曲问题,薄板弯曲问题的具体形式和算例。这种方法适用各种边界和荷载情况,而且放松了对位移连续性的要求。