Response of nonlinear random business cycle model with time delay state feedback

The steady state response and bifurcation of nonlinear random business cycle model to random narrow-band excitation with time delay state feedback are studied in this paper. The method of multiple scales is used to determine the business cycle model of modulation of amplitude and phase. The effects of delay, detuning, bandwidth and magnitude of random excitation on dynamics of the business cycle system are investigated. The results show that the complex dynamics such as bifurcation, jump domain and so on are induced by time delay and the phenomena that multiple solution or bifurcation is induced by noise.     

一类准周期参激非线性相对转动动力系统的稳定性与时滞反馈控制

建立了一类含准周期参数激励和时滞反馈的相对转动非线性系统的动力学方程. 采用多尺度法求解1/2亚谐波主参数共振下的分岔响应方程,并分析了系统的稳定性. 在求解非受控系统的定常解的基础上,通过讨论系统的动力学特性,研究了准周期参数激励对系统响应的影响. 采用时滞反馈控制的方法对系统分岔和极限环(域)进行控制,数值模拟的结果表明通过改变时滞参数可以实现对系统分岔的控制,并能有效地控制极限环(域)的幅值和稳定性. 关键词： 相对转动 准周期参激 时滞反馈 极限环     

Nonlinear analysis of a maglev system with time-delayed feedback control

This paper undertakes a nonlinear analysis of a model for a maglev system with time-delayed feedback. Using linear analysis, we determine constraints on the feedback control gains and the time delay which ensure stability of the maglev system. We then show that a Hopf bifurcation occurs at the linear stability boundary. To gain insight into the periodic motion which arises from the Hopf bifurcation, we use the method of multiple scales on the nonlinear model. This analysis shows that for practical operating ranges, the maglev system undergoes both subcritical and supercritical bifurcations, which give rise to unstable and stable limit cycles respectively. Numerical simulations confirm the theoretical results and indicate that unstable limit cycles may coexist with the stable equilibrium state. This means that large enough perturbations may cause instability in the system even if the feedback gains are such that the linear theory predicts that the equilibrium state is stable.     

Act-and-wait time-delayed feedback control of autonomous systems

Recently an act-and-wait modification of time-delayed feedback control has been proposed for the stabilization of unstable periodic orbits in nonautonomous dynamical systems (Pyragas and Pyragas, 2016 [30]). The modification implies a periodic switching of the feedback gain and makes the closed-loop system finite-dimensional. Here we extend this modification to autonomous systems. In order to keep constant the phase difference between the controlled orbit and the act-and-wait switching function an additional small-amplitude periodic perturbation is introduced. The algorithm can stabilize periodic orbits with an odd number of real unstable Floquet exponents using a simple single-input single-output constraint control.     

晶闸管混沌行为的延迟反馈控制与尖峰电流抑制

应用延迟反馈控制法(time-delayed feedback control,TDFC),有效地控制了晶闸管中出现的混沌行为,由此提出一种基于Floquet定理的延迟反馈控制法的优化设计方法.为进一步抑制延迟反馈控制出现的尖峰电流现象,根据相空间压缩原理对反馈信号进行相空间压缩,从而很好地抑制尖峰电流.     

Computational and experimental study of a melt-hardened zone on a roller modified by wide-band laser treatment

A three-dimensional finite element model has been developed to simulate the wide-band laser remelting process and predict the thermal and mechanical properties in the melt-hardened zone. The simulation of the laser remelting process was performed using the nonlinear thermo-mechanical properties, based on a wide-band heat source model. The temperature fields, phase transformations, hardness and residual stress distributions in the melt-hardened zone were analyzed. In the remelting zone, the transformed volumetric percentage of martensite is beyond 80% and the excessive transformed martensitic structure greatly affects the mechanical properties in the melt-hardened zone with its volumetric expansion effect. After remelting, the hardness can be improved and the residual stress distributed within the melted zone is mainly of the compressive type, while the tensile stress in the heat-affected zone (HAZ) may cause the initiation of cracks. The computational results are in good agreement with experimental measurements.     

An improved car-following model with consideration of the lateral effect and its feedback control research

A car-following model is presented, in which the effects of non-motor vehicles on adjacent lanes are taken into ac- count. A control signal including the velocity differences between the following vehicle and the target vehicle is introduced according to the feedback control theory. The stability condition for the new model is derived. Numerical simulation is used to demonstrate the advantage of the new model including the control signal; the results are consistent with the analytical ones     

Modified coupled map car-following model and its delayed feedback control scheme

A modified coupled map car-following model is proposed, in which two successive vehicle headways in front of the considering vehicle is incorporated into the optimal velocity function. The steady state under certain conditions is obtained. An error system around the steady state is studied further. Moreover, the condition for the state having no traffic jam is derived. A new control scheme is presented to suppress the traffic jam in the modified coupled map car-following model under the open boundary. A control signal including the velocity differences between the following and the considering vehicles, and between the preceding and the considering vehicles is used. The condition under which the traffic jam can be well suppressed is analysed. The results are compared with that presented by Konishi et al. (the KKH model). The simulation results show that the temporal behaviour obtained in our model is better than that in the KKH model. The simulation results are in good agreement with the theoretical analysis.     

一类相对转动系统Hopf分岔的非线性反馈控制

研究一类非线性摩擦阻尼力作用下的相对转动系统的Hopf分岔现象,给出系统产生Hopf分岔的充要条件,提出一种非线性反馈控制方法对系统的Hopf分岔点进行转移,并控制极限环的稳定性和幅值,数值模拟说明该方法对一类相对转动系统的Hopf分岔控制是有效的. 关键词： 相对转动 非线性反馈控制 Hopf分岔 极限环     

A fractal comparison of real and Austrian business cycle models

Rescaled range and power spectral density analysis are applied to examine a diverse set of macromonetary data for fractal character and stochastic dependence. Fractal statistics are used to evaluate two competing models of the business cycle, Austrian business cycle theory and real business cycle theory. Strong evidence is found for antipersistent stochastic dependence in transactions money (M1) and components of the monetary aggregates most directly concerned with transactions, which suggests an activist monetary policy. Savings assets exhibit persistent long memory, as do those monetary aggregates which include savings assets, such as savings money (M2), M2 minus small time deposits, and money of zero maturity (MZM). Virtually all measures of economic activity display antipersistence, and this finding is invariant to whether the measures are adjusted for inflation, including real gross domestic product, real consumption expenditures, real fixed private investment, and labor productivity. This strongly disconfirms real business cycle theory.     

Generating Li-Yorke chaos in a stable continuous-time T-S fuzzy model via time-delay feedback control

This paper investigates the chaotification problem of a stable continuous-time T-S fuzzy system.A simple nonlinear state time-delay feedback controller is designed by parallel distributed compensation technique.Then,the asymptotically approximate relationship between the controlled continuous-time T-S fuzzy system with time-delay and a discrete-time T-S fuzzy system is established.Based on the discrete-time T-S fuzzy system,it proves that the chaos in the discretetime T-S fuzzy system satisfies the Li-Yorke definition by choosing appropriate controller parameters via the revised Marotto theorem.Finally,the effectiveness of the proposed chaotic anticontrol method is verified by a practical example.     

Bifurcation and stability of an improved time-delayed fluid flow model in internet congestion control

Based on the fluid flow time-delayed model proposed by Misra et al in internet congestion control, one modified time-delayed model is presented, where the influence of the communication delay on the router queue length is investigated in detail. The main advantage of the new model is that its stability domain is larger even without an extra controller. By linear stability analysis and numerical simulation, the effectiveness and feasibility of the novel model in internet congestion control are verified.     

Nonlinear feedback control of a novel hyperchaotic system and its circuit implementation

This paper reports a new hyperchaotic system by adding an additional state variable into a three-dimensional chaotic dynamical system. Some of its basic dynamical properties, such as the hyperchaotic attractor, Lyapunov exponents, bifurcation diagram and the hyperchaotic attractor evolving into periodic, quasi-periodic dynamical behaviours by varying parameter k are studied. An effective nonlinear feedback control method is used to suppress hyperchaos to unstable equilibrium. Furthermore, a circuit is designed to realize this new hyperchaotic system by electronic workbench (EWB). Numerical simulations are presented to show these results.     

Susceptibility and magnetisation of a random ising model

The susceptibility of a bond disordered Ising model is calculated by configurationally averaging an Ornstein-Zernike type of equation for the two spin correlation function. The equation for the correlation function is derived using a diagrammatic method due to Englert. The averaging is performed using bond CPA. The magnetisation is also calculated by averaging in a similar manner a linearised molecular field equation. Part of the work was done, while one of the authors (DK) was visiting International Centre for Theoretical Physics, Trieste, Italy.     

A study of detonation diffraction and failure for a model of compressible two-phase reactive flow

A two-phase model of heterogeneous explosives, with a reaction rate that is proportional to the gas-phase pressure excess above an ignition threshold, is examined computationally. The numerical approach, a variant of Godunov's method designed to accommodate nonconservative terms in the hyperbolic model, extends previous work of the authors to two-dimensional configurations. The focus is on the behavior of an established detonation as it rounds a 90° corner and undergoes diffraction. The dependence of the post-diffraction conduct on the reaction rate is explored by varying the reaction-rate prefactor and the ignition threshold. The aim is to determine whether the model, as postulated, can capture dead zones, which are pockets of unreacted or partially reacted explosive observed in the vicinity of the corner in diffraction experiments. Results of this study are compared with those of a similar investigation on the one-phase ignition-and-growth model.     

CO2 emission control in new CM car-following model with feedback control of the optimal estimation of velocity difference under V2X environment

A new coupled map car-following model in this paper is proposed by considering the influence of the difference of the estimated optimal speed based on the coupled map (CM) car-following model under V2X environment. The stability of the new model is analyzed by applying the control theory, and the conditions are obtained for the stability of the traffic system. And the two scenes of vehicle stopping once and four times have been simulated. The simulation results show that the control term considered with optimal estimation of speed difference can effectively improve the stability of vehicle running and reduce CO₂ emissions in the CM car-following model.     

Output-only identification and dynamic analysis of time-varying mechanical structures under random excitation: A comparative assessment of parametric methods

This article addresses the problem of parametric time-domain identification and dynamic analysis for time-varying (TV) mechanical structures under unobservable random excitation. The methods presented are based on time-dependent autoregressive moving average (TARMA) models, and are classified according to the mathematical structure imposed on the TV parameter evolution as unstructured parameter evolution, stochastic parameter evolution, and deterministic parameter evolution. The features and relative merits of each class are outlined. A representative method from each is then assessed through its application to the identification and dynamic analysis of a laboratory TV structure consisting of a beam with a mass moving on it. The results are mutually compared and contrasted to those obtained through “frozen-configuration” (multiple experiment) baseline identification.     

Effects of Levy noise and immune delay on the extinction behavior in a tumor growth model

The combined effects of Ltvy noise and immune delay on the extinction behavior in a tumor growth model are explored, The extinction probability of tumor with certain density is measured by exit probability. The expression of the exit probability is obtained using the Taylor expansion and the infinitesimal generator theory. Based on numerical calculations, it is found that the immune delay facilitates tumor extinction when the stability index α〈 1, but inhibits tumor extinction when the stability index α 〉 1. Moreover, larger stability index and smaller noise intensity are in favor of the extinction for tumor with low density. While for tumor with high density, the stability index and the noise intensity should be reduced to promote tumor extinction.     

一类分时冗余系统的累伤可靠性模型及其参数估计

在不考虑部件每一次修如新的条件下,给出了物理系统状态失效时间的一种等效方法,建立了需要周期更换部件状态的分时冗余系统的累积损伤可靠性模型,并基于Weibull分布对相应模型参数进行了估计,并给出了一个用于评价系统可靠性的仿真方法. 为验证模型与仿真方法的有效性,对一个1/3型机械系统的可靠性进行了分析. 关键词： 分时冗余系统 可靠性 累积损伤模型 物理失效