STUDY FOR THE BIFURCATION TOPOLOGICAL STRUCTURE AND THE GLOBAL COMPLICATED CHARACTER OF A KIND OF NONLINEAR FINANCE SYSTEM (Ⅰ)

Based on the mathematical model of a kind of complicated financial system, all possible things that the model shows in the operation of our country’s macro-financial system were analyzed, such as balance, stable periodic, fractal, Hopf-bifurcation, the relationship between parameters and Hopf-bifurcations,and chaotic motion etc. By the changes of parameters of all economic meanings, the conditions on which the complicated behaviors occur in such a financial system, and the influence of the adjustment of the macro-economic policies and adjustment of some parameter on the whole financial system behavior were analyzed. This study will deepen people’s understanding of the lever function of all kinds of financial policies.     

CONSOLIDATION HEORY OF UNSATURATED SOIL BASED ON THE THEORY OF MIXTURE(Ⅰ)

Unsaturated soil is a three-phase media and is composed of soil grain, water and gas. In this paper, the consolidation problem of unsaturated soil is investigated based on the theory of mixture. A theoretical formula of effective stress on anisotropic porous media and unsaturated soil is derived. The principle of effective stress and the principle of Curie symmetry are taken as two fundamental constitutive principles of unsaturated soil. A mathematical model of consolidation of unsaturated soil is proposed, which consists of 25 partial differenfial equations with 25 unknowns. With the help of increament linearizing method, the model is reduced to 5 governing equations with 5 unknowns, i.e., the three displacement components of solid phase, the pore water pressure and the pore gas pressure. 7 material parameters are involved in the model and all of them can he measured using soil tests. It is convenient to use the model to engineering practice. The well known Biot’s theory is a special case of the model.     

QUALITATIVE INVESTIGATION OF DYNAMICAL EQUATION SYSTEM OF HEMOGLOBIN (OR ALLOSTERIC ENZYMES)

For the dynamical equation system (a three-dimensional autonomous system) of hemoglobin given in , we make the following qualitative investigations: (1) point out that all meaningful solutions should be in a tetrahedroid, and that its four surfaces are without contact; (2) find all singular points, and prove that only two of them are respectively situated on a pair of them are respectively situated on a pair of separate edges,and that other singular points are outside the tetrahedroid and meaningless; (3) prove that, among seven physical parameters of this system, only the sign of a parameter determines the properties of these two singular points; (4) clear up the relation between this system and MWC model, The investigation shows that this system reflects the dynamical properties of hemoglobin satisfactorily.     

How does a woodpecker work? An impact dynamics approach

To understand how a woodpecker is able accelerate its head to such a high velocity in a short amount of time,a multi-rigid-segment model of a woodpecker’s body is established in this study.Based on the skeletal specimen of the woodpecker and several videos of woodpeckers pecking,the parameters of a three-degree-of-freedom system are determined.The high velocity of the head is found to be the result of a whipping effect,which could be affected by muscle torque and tendon stiffness.The mechanism of whipping is analyzed by comparing the response of a hinged rod to that of a rigid rod.Depending on the parameters,the dynamic behavior of a hinged rod is classified into three response modes.Of these,a high free-end velocity could be achieved in mode II.The model is then generalized to a multihinge condition,and the free-end velocity is found to increase with hinge number,which explains the high free-end velocity resulting from whipping.Furthermore,the effects of some other factors,such as damping and mass distribution,on the velocity are also discussed.     

CONSOLIDATION HEORY OF UNSATURATED SOIL BASED ON THE THEORY OF MIXTURE(Ⅰ)

Unsaturated soil is a three-phase media and is composed of soil grain,water andgas.In this paper,the consolidation problem of unsaturated soil is investigated basedon the theory of mixture.A theoretical formula of effective stress on anisotropicporous media and unsaturated soil is derived.The principle of effective stress and theprinciple of Curie symmetry are taken as two fundamental constitutive principles ofunsaturated soil.A mathematical model of consolidation of unsaturated soil isproposed,which consists of25 partial differenfial equations with25 unknowns.Withthe help of increament linearizing method,the model is reduced to5 governingequations with5 unknowns,i.e.,the three displacement components of solid phase,thepore water pressure and the pore gas pressure.7 material parameters are involved inthe model and all of them can be measured using soil tests.It is convenient to use themodel to engineering practice.The well known Biot’s theory is a special case of themodel.     

NONLINEAR SATURATION OF BAROCLINIC INSTABILITY IN THE GENERALIZED PHILLIPS MODEL(Ⅱ)-THE LOWER BOUND ON THE DISTURBANCE ENERGY AND POTENTIAL ENSTROPHY TO THE NONLINEARLY UNSTABLE BASIC FLOW

On the basis of the nonlinear stability theorem in the context of Arnol’d’s second theorem for the generalized Phillips model,nonlinear saturation of baroclinic instability in the generalized Phillips model is investigatedThe lower bound on the disturbance energy and potential enstrophy to the nonlinearly unstable basic flow in the generalized Phillips model is presented,which indicates that there may exist an allocation between a nonlinearly unstable basic flow and a growing disturbance     

THE CRITERION ALGORITHM OF RELATION OF IMPLICATION BETWEEN PERIODIC ORBITS(Ⅱ)

In recent years,there is a wide interest in Sarkovskii’s theorem and related study.According to Sarkovskii’s theorem,if the continuous self-map f of the closed interval has a3-periodic orbit,then f must has an n-periodic orbit for any positive integer n.But f can nothave all n-periodic orbits for some n.Example.LetEvidently f has only one kind of3-periodic orbit in the two kinds of3-periodic orbits,whichexplains that it isn’t far enough to uncover the relation between periodic orbits by theinformation which Sarkovskii’s theorem has offered.In this paper,we raise the concept oftype of periodic orbits,and give a feasible algorithm which decldes the relation ofimplication between the two kinds of periodic orbits.     

Effects of bottom shear stresses on the wave-induced dynamic response in a porous seabed：PORO-WSSI （shear） model

When ocean waves propagate over the sea floor,dynamic wave pressures and bottom shear stresses exert on the surface of seabed.The bottom shear stresses provide a horizontal loading in the wave-seabed interaction system,while dynamic wave pressures provide a vertical loading in the system.However,the bottom shear stresses have been ignored in most previous studies in the past.In this study,the effects of the bottom shear stresses on the dynamic response in a seabed of finite thickness under wave loading will be examined,based on Biot’s dynamic poro-elastic theory.In the model,an "u-p" approximation will be adopted instead of quasi-static model that have been used in most previous studies.Numerical results indicate that the bottom shear stresses has certain influences on the wave-induced seabed dynamic response.Furthermore,wave and soil characteristics have considerable influences on the relative difference of seabed response between the previous model(without shear stresses) and the present model(with shear stresses).As shown in the parametric study,the relative differences between two models could up to 10% of p0,depending on the amplitude of bottom shear stresses.     

Analysis of limit cycle oscillations of a typical airfoil section with freeplay

A typical airfoil section system with freeplay is investigated in the paper. The classic quasi-steady flow model is applied to calculate the aerodynamics, and a piecewise-stiffness model is adopted to characterize the nonlinearity of the airfoil section’s freeplay. There are two critical speeds in the system, i.e., a lower critical speed, above which the system might generate limit cycle oscillation, and an upper critical one, above which the system will flutter. Then a Poincaré map is constructed for the limit cycle oscillations by using piecewise-linear solutions with and without contact in the system. Through analysis of the Poincaré map, a series of equations which can determine the frequencies of period-1 limit cycle oscillations at any flight velocity are derived. Finally, these analytic results are compared to the results of numerical simulations, and a good agreement is found. The effects of freeplay value and contact stiffness ratio on the limit cycle oscillation are also analyzed through numerical simulations of the original system. Moreover, there exist multi-periods limit cycle oscillations and even complicated "chaotic" oscillations may occur, which are usually found in smooth nonlinear dynamic systems.     

A NUMERICAL MODEL OF LEFT VENTRICLE AND AORTIC VALVE FUNCTION OF ITS AFTERLOAD(Ⅰ)

Due to the study of the function of heart and nortic valve,we set up a physical model of left ventricle,aortic valve and afterload and derive theoretical equation of each part from the model.Then we calculate the basic equations within phystology and impair parameters.Based this,we will discuss,fully in the next paper the effect of left ventricular afterload on valve opening,ejection and valve function ,etc.     

STUDY FOR THE BIFURCATION TOPOLOGICAL STRUCTURE AND THE GLOBAL COMPLICATED CHARACTER OF A KIND OF NONLINEAR FINANCE SYSTEM(Ⅰ)

ＩｎｔｒｏｄｕｃｔｉｏｎＣｈａｏｔｉｃｉｓｔｈｅｉｎｈｅｒｅｎｔｒａｎｄｏｍｎｅｓｓｉｎｔｈｅｄｅｆｉｎｉｔｅｓｙｓｔｅｍ .Ｔｈｅｄｅｆｉｎｉｔｅｎｅｓｓｉｓｃａｕｓｅｄｂｙｔｈｅｓｙｓｔｅｍｉｎｔｅｒｎａｌｓｂｕｔｎｏｔｂｙｔｈｅｅｘｔｅｒｎａｌｄｉｓｔｕｒｂａｎｃｅ[1- 4],ｗｈｉｌｅｔｈｅｉｎｈｅｒｅｎｔｒａｎｄｏｍｎｅｓｓｉｓｔｈｅｉｒｒｅｇｕｌａｒａｎｄｄｉｆｆｉｃｕｌｔ＿ｔｏ＿ｂｅ＿ｐｒｅｄｉｃｔｅｄｂｅｈａｖｉｏｒｏｆｔｈｅｓｙｓｔｅｍ[5 ,6 ].Ｗｈａｔｉｓｍｏｓｔａｔｔｒａｃｔｉｖｅ…     

STUDY FOR THE BIFURCATION TOPOLOGICAL STRUCTURE AND THE GLOBAL COMPLICATED CHARACTER OF A KIND OF NONLINEAR FINANCE SYSTEM(Ⅱ)

ＩｎｔｒｏｄｕｃｔｉｏｎＣｈａｏｔｉｃｉｓｔｈｅｉｎｈｅｒｅｎｔｒａｎｄｏｍｎｅｓｓｉｎｔｈｅｄｅｆｉｎｉｔｅｓｙｓｔｅｍ .Ｔｈｅｄｅｆｉｎｉｔｅｎｅｓｓｉｓｃａｕｓｅｄｂｙｔｈｅｓｙｓｔｅｍｉｎｔｅｒｎａｌｓｂｕｔｎｏｔｂｙｔｈｅｅｘｔｅｒｎａｌｄｉｓｔｕｒｂａｎｃｅ,ｗｈｉｌｅｔｈｅｉｎｈｅｒｅｎｔｒａｎｄｏｍｎｅｓｓｉｓｔｈｅｉｒｒｅｇｕｌａｒａｎｄｄｉｆｆｉｃｕｌｔ＿ｔｏ＿ｂｅ＿ｐｒｅｄｉｃｔｅｄｂｅｈａｖｉｏｒｏｆｔｈｅｓｙｓｔｅｍ .Ｗｈａｔｉｓｍｏｓｔａｔｔｒａｃｔｉｖｅｏｆｔｈｅｃ…     

On the stability boundary of hamiltonian systems

The criterion for the points in the parameter space being on the stability boundary of linear Hamiltonian system depending on arbitrary numbers of parameters was given, through the sensitivity analysis of eigenvalues and eigenvectors. The results show that multiple eigenvalues with Jordan chain take a very important role in the stability of Hamiltonian systems. Foundation item: the National Natural Science Foundation of China (10072012); the National Natural Science Foundation of Russia Biography: QI Zhao-hui (1964-)     

Analysis of nonlinear dynamic stability of liquid-converying pipes

Nonlinearly dynamic stability of flexible liquid-conveying pipe in fluid structure interaction was analyzed by using modal disassembling technique. The effects of Poisson, Junction and Friction couplings in the wave-flowing-vibration system on the pipe dynamic stability were included in the analytical model constituted by four nonlinear differential equations. An analyzing example of cantilevered pipe was done to illustrate the dynamic stability characteristics of the pipe in the full coupling mechanisms, and the phase curves related to the first four modal motions were drawn. The results show that the dynamic stable characteristics of the pipe are very complicated in the complete coupling mechanisms, and the kinds of the singularity points corresponding to the various modal motions are different. Foundation items: the National Natural Science Foundation of China (50079007); the Hydraulic Science Foundation of China Hydraulic Ministry (SZ9830); the Natural Science Foundation of Yunnan Provicce (98E003G) Biographies: ZHANG Li-xiang (1959−) HUANG Wen-hu (1926−)     

IMPULSIVE CONTROL FOR THE STABILIZATION AND SYNCHRONIZATION OF LUR＇ E SYSTEMS

An impulsive control scheme of the Lur‘e system and several theorems on stability of impulsive control systems was presented, these theorems were then used to find the conditions under which the Lur‘e system can be stabilized by using impulsive control with varying impulsive intervals. The parameters of Lur‘e system and impulsive control law are given, a theory of impulsive synchronization of two Lur‘e system is also presented. A numerical example is used to verify the theoretical result.     

HYBRID PERTURBATION-GALERKIN SOLUTION OFTHE FLOW IN A CIRCULAR CROSS-SECTIONTUBE WITH CONSTRICTION~

Using hybrid perturbatin- Galerkin technique, a circular cross-section tube model with sinusoidal wall is studied. This technique can remove the limitation of small parametersfor perturbation and the difficulty of selecting good coordinate functions about Galerkintechnique. The effects caused by the boundary conditions and the Reynolds number on theflow were discussed. The position of the separate and reattachment points was obtained. The tendency of the variation about the shear stress on the wall and friction factor along the axisdirection were also analyzed, The results at a small parameter have good agreements withthe perturbation ones.     

Study on the Prediction Method of Low-Dimension Time Series that Arise from the Intrinsic Nonlinear Dynamics

The prediction methods and its applications of the nonlinear dynamic systems determined from chaotic time series of low-dimension are discussed mainly. Based on the work of the foreign researchers, the chaotic time series in the phase space adopting one kind of nonlinear chaotic model were reconstructed. At first, the model parameters were estimated by using the improved least square method. Then as the precision was satisfied, the optimization method was used to estimate these parameters. At the end by using the obtained chaotic model, the future data of the chaotic time series in the phase space was predicted. Some representative experimental examples were analyzed to testify the models and the algorithms developed in this paper. The results show that if the algorithms developed here are adopted, the parameters of the corresponding chaotic model will be easily calculated well and true. Predictions of chaotic series in phase space make the traditional methods change from outer iteration to interpolations. And if the optimal model rank is chosen, the prediction precision will increase notably. Long term superior predictability of nonlinear chaotic models is proved to be irrational and unreasonable. Paper from Chen Yu-shu, Member of Editorial of Committee, AMM Foundation item: the National Natural Science Foundation of China (19990510); the National Key Basic Research Special Fund(G1998020316) Biography: Ma Jun-hai(1965-), Professor, Doctor     

Abundance of unimodal maps with dense critical orbit and prefixed critica orbit

For the so-called quadratic family, it is proved that, there exists a positive Lebesgue measure set E in the parameter space such that the corresponding map has a dense critical orbit in the support set of the invariant measure for almost all parameters in E; it is also proved that there is a dense set in E such that the critical orbit of the corresponding map enter the reversed fixed point.     

Numerical study on the stability and mixing of vertical round buoyant jet in shallow water

IntroductionAsimplewaytodisposeofthelargequantitiesofwasteheatresultingfromsteamelectricpowergeneration ,istodischargetheheatedcondenserwaterthroughasubmergedroundoutfalllocatedatthebottomofthereceivingwater.Inrecentyears,suchkindsofhighvelocityinjectionsystemshaveincreasinglybeenusedaseffectivemixingdevices,frequently ,thesedevicesarelocatedinwatersofonlyafewportdiametersdeep ,anddischargingareaisrelativelysmall.Thusanunderstandingoftheinducedexcesstemperaturedistribution ,inrelationshiptothe…