The influence of the first integrals and the rolling resistance model on tippe top inversion

Nonlinear Dynamics - In this paper, we analyze the effect which the choice of a friction model has on tippe top inversion in the case where the resulting action of all dissipative forces is...     

Various friction models in two-sphere top dynamics

The dynamics of a two-sphere tippe top on a rough horizontal plane is considered. The top is bounded by a nonconvex surface consisting of two spherical segments of distinct radii and a cylinder; the cylinder axis coincides with the common symmetry axis of the segments. If the top is initially placed so that its center of mass is almost in the lowest position, the symmetry axis is almost vertical, and a high angular velocity of rotation about the vertical symmetry axis is imparted to the top, then it turns upside down from its base to the leg and starts to rotate on the leg. Then the top gradually returns to the stable equilibrium. The problem of the top motion is often used to demonstrate the efficiency of various proposed friction models [1–3]. The effects arising in the two-sphere top dynamics with various dry friction models are compared in the present paper. Both analytic methods based on the theory of stability and bifurcations and numerical calculations are used. The numerical study is performed under the assumption that the supporting plane is deformable, which permits one to describe transient processes accompaniedwith impacts by using a single system of equations.     

Global analysis of the dynamics of a mathematical model to intermittent HIV treatment

The aim of this paper is to study the qualitative dynamics of a piecewise smooth system modeling the intermittent treatment of the human immunodeficiency virus. Typical singularities and closed orbits are observable, and we quantitatively explore the dynamics around those singularities and closed orbits. Moreover, we conclude that this protocol always will be successful since the trajectory passing through any initial condition converges to one of these distinguished orbits. Our formal mathematical results corroborate the real-world observation, where the virus is not eliminated, but the number of infected cells is controlled around a specific value.

     

翻身陀螺简史及其力学分析

叙述了翻身陀螺的发明过程及其研究简史. 从物理概念出发分析了翻身陀螺的力学原理.     

Global dynamics of a flexible asymmetrical rotor

Nonlinear Dynamics - Global dynamics of a flexible asymmetrical rotor resting on vibrating supports is investigated. Hamilton’s principle is used to derive the partial differential governing...     

Global dynamics perspective on macro- to nano-mechanics

Nonlinear Dynamics - In about the last two decades, global nonlinear dynamics has been evolving in a revolutionary way, with the development of sophisticated techniques employing concepts/tools of...     

Global transient dynamics of nonlinear parametrically excited systems

In this paper we examine the response of a typical nonlinear system that is subjected to parametric excitation. Particular attention is paid to how basins of attraction evolve such that the global transient stability of the system may be assessed. We show that at a forcing level that is considerably smaller than that at which the steady-state attractor loses its stability, there may exist a rapid erosion and stratification of the basin, signifying a global loss of engineering integrity of the system.We also show, for a system near its equilibrium state, that the boundaries in parameter space can become fractal. The significance of such an analysis is not only that it corresponds to a failure locus for a system subjected to a sudden pulse of excitation, but since the phase-space basin is often eroded throughout its central region, the determination of basin boundaries in control space can often reflect the characteristics of the phase-space basin structure, and hence on the macroscopic level they provide information regarding the global transient stability of the system.     

Global qualitative analysis of new Monod type chemostat model with delayed growth response and pulsed input in polluted environment

In this paper, we consider a new Monod type chemostat model with time delay and impulsive input concentration of the nutrient in a polluted environment. Using the discrete dynamical system determined by the stroboscopic map, we obtain a ＂microorganism-extinction＂ periodic solution. Further, we establish the sufficient conditions for the global attractivity of the microorganism-extinction periodic solution. Using new computational techniques for impulsive and delayed differential equation, we prove that the system is permanent under appropriate conditions. Our results show that time delay is ＂profitless＂.     

Global dynamics in the simplest models of three-dimensional water-wave patterns

We explore the idea that periodic or chaotic finite motions corresponding to attractors in the simplest models of resonant wave interactions might shed light on the problem of pattern formation. First we identify those dynamical regimes of interest which imply certain specific relations between physically observable variables, e.g. between amplitudes and phases of Fourier harmonics comprising the pattern. To be of relevance to reality, the regimes must be robust.The issue of structural stability of low-dimensional dynamical models is central to our work. We show that the classical model of three-wave resonant interactions in a non-conservative medium is structurally unstable with respect to small cubic interactions. The structural instability is found to be due to the presence of certain extremely sensitive points in the unperturbed system attractors. The model describing the horse-shoe pattern formation due to non-conservative quintet interactions [11] is also analyzed and a rich family of attractors is mapped. The absence of such sensitive points in the found attractors thus indicates the robustness of the regimes of interest. Applicability of these models to the problem of 3-D water wave patterns is discussed. Our general conclusion is that extreme caution is necessary in applying the dynamical system approach, based upon low-dimensional models, to the problem of water wave pattern formation.     

Global dynamics of an autoparametric spring–mass–pendulum system

In this paper, a study of the global dynamics of an autoparametric four degree-of-freedom (DOF) spring–mass–pendulum system with a rigid body mode is presented. Following a modal decoupling procedure, typical approximate periodic solutions are obtained for the autoparametrically coupled modes in 1:2 internal resonance. A novel technique based on forward-time solutions for finite-time Lyapunov exponent is used to establish global convergence and domains of attraction of different solutions. The results are compared to numerically constructed domains of attraction in the plane of initial position and initial velocity for the pendulum. Simulations are also provided for a few interesting cases of interest near critical values of parameters. Results also shed some light on the role played by other modes present in a multi-DOF system in shaping the overall system response.     

Global dynamics of the cable under combined parametrical and external excitations

The chaotic dynamics and global bifurcations of the suspended elastic cable under combined parametric and external excitations are investigated. The non-linear equations of motion of the elastic cable to small vibration of one support are derived. The averaged equations are obtained by using the method of multiple scales. Based on the averaged equations, the theory of normal form and Maple program are used to obtain the explicit expressions of normal form associated with a double zero and a pair of pure imaginary eigenvalues. On the basis of the normal form, global bifurcation analysis of the parametrically and externally excited suspended elastic cable is given by a global perturbation method developed by Kovacic and Wiggins. The chaotic motion of the elastic cable is also found by numerical simulation.     

GLOBAL DYNAMICS OF DELAYED BIDIRECTIONAL ASSOCIATIVE MEMORY （BAM） NEURAL NETWORKS

IntroductionConsiderthebidirectionalassociativememory (BAM )neuralnetworkswithconstanttransmissiondelaysdescribedbyasystemofdelaydifferentialequationsoftheform[1,2 ]:dxi(t)dt =-aixi(t) nj=1bijfj(yj(t-σij) ) Ii,　　i=1 ,2 ,… ,m ,dyj(t)dt =-cjyj(t) mi=1djigi(xi(t-τji) ) Jj,　　j=1 ,2 ,… ,n ,fort >0 .Thesystem ( 1 )consistsoftwosetsofneurons (orunits)arrangedontwolayers,namely ,I_layerandJ_layer.Inthesystem ( 1 ) ,xi( ·)andyj( ·)denotemembranepotentialoftheithneuronsfromtheI_laye…     

Global sensitivity analysis of asymmetric energy harvesters

Nonlinear Dynamics - Parametric variability is inevitable in actual energy harvesters. It can significantly affect crucial aspects of the system performance, especially in harvesting systems that...     

螺杆泵动力学热力耦合分析方法研究

地面驱动螺杆泵是一种广泛应用于油田采油工程中的人工举升装置。由于螺杆泵深置地下的油管中,密封性很强,很难现场测试工作过程中定子橡胶材料的温度变化以及温度变化引起的定子变形。本文采用有限元方法分析螺杆泵定子的热力耦合效应,讨论定子橡胶材料温度变化的物理机理。用热力学单向解耦分析方法分析单螺杆泵定子橡胶材料的温度分布场以及温度分布引起的定子型线变化。讨论了过盈量、转子转速对温度分布和定子型线变化的影响。     

Global dynamics of a harmonically excited oscillator with a play: Numerical studies

In this paper a harmonically excited linear oscillator with a play is investigated. Direct numerical simulation and numerical continuation techniques were employed to study the system behaviour. To conduct the numerical analysis, the system differential equations were transformed into the autonomous form and were then solved using our newly developed in-house Matlab-based computational suite ABESPOL [1]. The results are presented in form of trajectories and Poincaré maps on the phase plane, bifurcation diagrams and basins of attraction. The bifurcation analysis was supported by a path following method. The influence of each system parameter (except gap) on the system dynamics was studied in detail. The bifurcations known as interior crisis and boundary crisis were observed and discussed in this work. Notably, the parameter regions where various types of grazing induced bifurcations occurred were detected and investigated.     

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.