Nonlinear delay difference equations for housing dynamics assuming heterogeneous backward-looking expectations

China's first interest rate hike during the last decade, aiming to cool down the seemingly overheated real estate market, had aroused more caution on housing market. This paper aims to analyze the housing price dynamics after an unanticipated economic shock, which was believed to have similar properties with the back ward- looking expectation models. The analysis of the housing price dynamics is based on the cobweb model with a simple user cost affected demand and a stock-flow supply assumption. Several nth-order delay rational difference equations are set up to illustrate the properties of housing dynamics phenomena, such as the equilibrium or oscillations, overshoot or undershoot and convergent or divergent, for a kind of heterogeneous backward-looking expectation models. The results show that demand elasticity is less than supply elasticity is not a necessary condition for the occurrence of oscillation. The housing price dynamics will vary substantially with the heterogeneous backward-looking expectation assumption and some other endogenous factors.     

The application and complexity analysis about a high-dimension discrete dynamical system based on heterogeneous triopoly game with multi-product

In production practice, firms usually produce multi-products rather than single products to obtain cost-saving advantages, cater for the diversity of consumer tastes and provide a barrier to entry. Based on nonlinear and economics theories, this paper establishes a discrete triopoly dynamical model which considers multi-product firms with heterogeneous expectations: naïve, adaptive and bounded rationality expectations. The discrete model is described by a 6-dimensional dynamical system. Thesis explores the path of the complexity of evolution and its intrinsic regularity, studies the influence of parameter change on the sensitivity level. The stable conditions of Cournot Nash equilibrium point are analyzed. The route to complex dynamics is investigated using 2-D and creative 3-D bifurcation diagrams by numerical experiment. The results show: the adaptive parameters can modify the stability of the market, but cannot lead to chaos independently; the bounded rationality parameters can arouse chaos for the whole market; larger differentiated degree of multi-product can suppress instability which is caused by adaptive and bounded rationality adjustment parameters. These results have significant theoretical and practical value to multi-product triopoly game with heterogeneous expectations in related markets.     

Research on the price game and the application of delayed decision in oligopoly insurance market

In the oligopoly insurance market, we assumed that some oligarchs make two-period delay decisions in bounded rationality and expectation, respectively, and others make decisions with bounded rationality without the condition of delay. There also exist two cases in which only one oligarch makes a delayed decision and two oligarchs make delayed decisions at the same time. Based on the analysis of these situations, we established the corresponding dynamic price game models. We then performed a numerical simulation to the complexity state of the system with different conditions such as stability, bifurcation, and chaos, and analyzed the profits of different oligarchs when the system is in different states. The results showed that when only one oligarch makes a delayed decision, with the decrease in the price weight of period t and increase in that of periods t?1 and t?2, the system??s stable region in the direction of the price adjustment of the oligarch with a delayed decision gets smaller. However, when there are two oligarchs with a delayed decision in the system, in the case where the delay parameters of oligarch 1 remain unchanged and the price parameters of different periods of oligarch 2 change, the system??s stable region in the direction of the price adjustment of oligarch 1 does not have the obvious change as that when only one oligarch makes a delayed decision. This showed that the sensibility of one oligarch in the direction of its own price adjustment is lower than other oligarchs. In addition, in the same system with delay and when the system is in chaos, the total profit of the oligarchs is obviously less than that when the system is in a stable state. However, the use of a delayed decision may not enhance the oligarch??s competitive advantages. Finally, the variable feedback control method is used to effectively control the chaos in the system.     

Complexity analysis of a Cournot–Bertrand duopoly game with different expectations

In this paper, we consider a Cournot–Bertrand mixed duopoly model with different expectations, where the market has linear demand and the firms have fixed marginal cost functions. Two firms choose output and price as decision variables, respectively, under the assumption that there is a certain degree of differentiation between the products offered by firms to avoid the whole market is occupied by the one that applies a lower price. The two players are considered to have bounded rational and static expectations. The existence and local stability condition of Nash equilibrium is investigated. We find the stability region of Cournot–Bertrand system is bigger than that of Cournot or Bertrand system under the same conditions. Furthermore, there are two different kinds of bifurcations when the parameters pass through the different boundary curves of the stability region, which is different from the Cournot or Bertrand model. Numerical simulation method is used to display the dynamic behaviors of the dynamical system, such as periodic cycles, bifurcation diagrams and strange attractors of the systems. The economic explanations of the complex dynamic behaviors are also given.     

The Determinants of Stock Price Volatility: An Industry Study

The currently ongoing IT-revolution is a great challenge for economists. The industry displays ever arising new technologies, unstable market shares, long-term swings, and short-term volatility of stock prices. Yet, to study those phenomena empirically one is constrained by a lack of data. The U.S. auto industry, for which long-term time series are available, has shared a similar experience since its early development. This paper studies how long-term swings and short-term stock price volatility in the U.S. auto industry is related to innovative efforts and switching of market shares of firms. The early period of the life-cycle of the industry was characterized by high product innovation, high market share instability, volatile stock prices, and the later period by fewer firms, process innovation, more stable market shares and less stock price volatility. In this paper we focus on the transition period leading from the first to the second period and study the relation of innovative effort, market share fluctuations and stock price dynamics. After presenting stylized facts on the life-cycle of the industry we introduce a dynamic model that is able to replicate some of the stylized facts. The dynamic model admits heterogeneous firms and encompasses both evolutionary as well as optimizing approaches.     

Complexity analysis of the dual-channel supply chain model with delay decision

In the oligopoly e-commerce market, the oligarch retailers sell products through traditional channel, while others through both network and traditional channel in order to obtain greater profits. Instead of discussing classic Bertrand game model, which past studies have done, we considered dual-channel retailer who makes price decision through both in network channel and traditional channel. This paper used the bifurcation theory of dynamical system, considering dual-channel retailer who makes delay decision. We performed a numerical simulation on system with different conditions, and some complex phenomenons occured, such as bifurcation and chaos. The results showed that adopting price delay decision in tradition channel would make the system more stable. While, adopting price delay decision in network channel makes the system less stable. When the market is in chaotic state, the using of delay decision would have an effect on the system stability in either traditional or network channels. The system become stable from chaos and would return to chaotic again with the increasing of weight in past period. Some interesting phenomenons happened when dual-channel retailer adopted delay decision in both channels. The superposition of delay decision would make the system more complex. At last, we measured the system’s performance by using profit index. We analyzed the profits of different oligarchs when the system is in different states. When the system is in chaos, the total profits of the oligarchs are obviously less than that in a stable state. Adopting delay decision is a way to avoid profit loss when system is in chaotic period, but this requires the retailer has rich operational experience. That is because adopting delayed decision may not always enhance the competitive strength of oligarchs.     

On the dynamics of compressor surge

Investigations concerned with the stability of stationary states and the possibility of self-excited oscillation (surge) occurring in systems with a centrifugal compressor (or a centrifugal pump) lead, for a simplified model, to an analysis of a set of two first-order differential equations. The paper presents such an analysis for the case when the machine characteristic can be expressed by a continuous unique curve as well as for that when the characteristic is neither a unique nor even a smooth curve. It is shown which of the singular points is the saddle point and in the case of the latter type of characteristic, which point can be taken for the saddle; this approach is believed to make practical analyses more straightforward.     

Backward and forward-looking expectations in a chaotic cobweb model

In this study we research the dynamics shown by a cobweb-type model with linear demand, non-invertible supply function and with forward-looking expectations associated to backward looking ones. The study of the dynamics exhibited by our model will show how the presence of forward-looking expectations represents a stabilising factor: As the weight attributed to the above mentioned foreseeing form increases, the system becomes less and less complex until it only generates orbits converging either to the fixed point or to a cycle-2. It is particularly interesting to analyse at the same time the role played by the two forms of expectations considered, both of which contribute to market stabilization.     

The Complexity of Collective Decision

This paper is about the dynamics of collective decision when an individual adapts his rational decision to the others'. We consider an organization of heterogeneous agents, in which each agent faces the binary decision problem. The standard way of modeling a collective decision is to assume everyone has the same value or payoff structure. This paper considers collective decision of agents with heterogeneous payoffs. We obtain and classify rational decision rules of heterogeneous agents into a few categories depending on their idiosyncratic payoff structure. We also obtain the micro–macro dynamics that relate the aggregate collective decision with the underlying individual decisions. We investigate the roles of particular types of agents such as hardcore, conformists, and nonconformists. We show that agents' rational behavior combined with the others produce stable orders, and sometimes complex cyclic behavior.     

The research on price game model and its complex characteristics of triopoly in different decision-making rule

Based on a detailed analysis of the international market, we establish a decentralized dynamics model to describe the situation that a new oligarch wishes to enter into a market which has been occupied by two oligarchs, so they have different decision rules. Then we establish and analyze the corresponding continuity system, and in detail discuss the Lyapunov exponent of this system, studying the influence of the parameter’s change to the Lyapunov exponent in three situations. Proceeding to the next step, we make the analysis of the complex dynamics behavior, such as Hopf bifurcation, chaos attractor and initial sensibility. We make a numerical simulation under different conditions, and the result shows that the process of game will tend to a Nash equilibrium at a lower price adjustment speed, and with the increase of the value, the system will appear to be unstable and go into a chaos state gradually. However, for the new entrant, the influence of chaos is not huge, and the new entrant can be seen as a stable element in the chaotic market. The research leads to a good guidance to the market with a new entrant to do the best decision-making.     

结构可靠度FORM方法的混沌动力学分析

引入混沌动力学理论讨论了FORM收敛失败的非线性动力学根源. 给出了几个典 型函数在参数区间上的可靠指标分岔图，展示了极限状态函数经过FORM迭代成为 非线性映射后计算结果的周期振荡、分岔和混沌等复杂动力学现象，计算了非线性映射的 Lyapunov指数. 结果表明，极限状态函数设计点的曲率大小与FORM的收敛性没有简单的联 系，判别FORM迭代计算收敛性的指标是非线性映射的Lyapunov指数.     

Brownian dynamics simulation of rodlike polymers under shear flow

The highly nonlinear behaviors of rodlike polymers in nematic phase under shear flow are studied with Brownian dynamics simulation. The LebwohlLasher nematogen model is taken as the prototype of the simulation and the mean-field approximation is avoided. By considering the nearest-neighbor intermolecular interaction, the spatial orientational correlation is introduced and therefore the spatial inhomogeneity such as the multiple-domain effect can automatically be incorporated. The transient order parameters, birefringence axes, shear stresses and first normal stress differences are calculated. The important finding of this work is that the director wagging and damped oscillation share the same molecular origin as director tumbling. The only difference is that the system is split into micro-domains which tumble with different phase angles in the wagging and damped oscillation regimes. The tumbling of the director of the whole system is suppressed due to the spatial inhomogeneity of director fields and then the damped oscillation of macroscopic stresses becomes predominant. The negative first normal stress difference exists at moderate shear rates, where both elasticity and viscosity play important role. Our simulation results including some dimensionless scaling parameters find good agreement with experimental observations in literature.     

Experimental study of regular and chaotic transients in a non-smooth system

This paper focuses on thoroughly exploring the finite-time transient behaviors occurring in a periodically driven non-smooth dynamical system. Prior to settling down into a long-term behavior, such as a periodic forced oscillation, or a chaotic attractor, responses may exhibit a variety of transient behaviors involving regular dynamics, co-existing attractors, and super-persistent chaotic transients. A simple and fundamental impacting mechanical system is used to demonstrate generic transient behavior in an experimental setting for a single degree of freedom non-smooth mechanical oscillator. Specifically, we consider a horizontally driven rigid-arm pendulum system that impacts an inclined rigid barrier. The forcing frequency of the horizontal oscillations is used as a bifurcation parameter. An important feature of this study is the systematic generation of generic experimental initial conditions, allowing a more thorough investigation of basins of attraction when multiple attractors are present. This approach also yields a perspective on some sensitive features associated with grazing bifurcations. In particular, super-persistent chaotic transients lasting much longer than the conventional settling time (associated with linear viscous damping) are characterized and distinguished from regular dynamics for the first time in an experimental mechanical system.     

概率约束评估的功能度量法的混沌控制

功能度量法是基于可靠度的结构优化设计中评估概率约束的一种方法,其改进均值(AMV)迭代格式具有简洁、高效的优点,但对一些非线性功能函数搜索最小功能目标点时可能陷入周期振荡或混沌解,本文利用混沌反馈控制的稳定转换法对功能度量法的AMV迭代格式实施收敛控制.首先展示一些功能函数应用功能度量法AMV格式迭代计算产生了周期解和混沌解现象,并对迭代算法进行了混沌动力学分析.然后利用稳定转换法对功能度量法迭代失败的参数区间进行混沌控制,使嵌入周期和混沌轨道的不稳定不动点稳定化,获得了稳定收敛解,实现了迭代解的周期振荡、分岔和混沌控制.     

Heterogeneous triopoly game with isoelastic demand function

In this paper, we analyze a triopolistic market with heterogeneous firms when the demand function is isoelastic. We consider the same heterogeneous firms as Elabbasy et al. (Comput. Math. Appl. 57:488?C499, 2009) introducing a nonlinearity in the demand function instead of the cost function. Stability conditions of the two equilibrium points and complex dynamics are studied. The main novelty consists of the double route to chaos, via period-doubling bifurcations and via Neimark?CSacker bifurcation. The two routes have important differences from the economic point of view.     

ANALYSIS OF FINANCIAL DERIVATIVES BY MECHANICAL METHOD (Ⅱ)-BASIC EQUATION OF MARKET PRICE OF OPTION

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Heterogeneity and evolution of expectations in a model of currency crisis

A simple model of a portfolio allocation between mature and emerging markets is specified. The representative-agent, rational expectations version of the model has an unlimited number of equilibria, providing no reason to expect that heterogeneous agents would all coordinate on one or another equilibrium. Therefore, the model is simulated with heterogeneous expectations based on ex post returns, imitation, and experimentation. Solutions produce periodic crises, as periods of excessive optimism plant the seed for their reversal, despite the fact that interest rates fall before crises, instead of rising.     

Consumer memory and price fluctuations in commodity markets: An integrodifferential model

A model for the dynamics of price adjustment in a single commodity market is developed. Nonlinearities in both supply and demand functions are considered explicitly, as are delays due to production lags and storage policies, to yield a nonlinear integrodifferential equation. Conditions for the local stability of the equilibrium price are derived in terms of the elasticities of supply and demand, the supply and demand relaxation times, and the equilibrium production-storage delay. The destabilizing effect of consumer memory on the equilibrium price is analyzed, and the ensuing Hopf bifurcations are described.     

交变电场作用下单液滴蒸发的分子动力学模拟

利用分子动力学方法研究了正弦形式的交变电场对三维悬浮水滴在超临界氮气环境下蒸发特性的影响, 主要考虑了电场幅值和频率对液滴蒸发寿命和液滴瞬时蒸发速率的影响. 其中水滴由8000个水分子组成, 环境气体由27000个氮气分子组成. 首先利用分子动力学方法模拟计算了不同状态下水的物性参数以及亚临界条件下匀强电场对液滴蒸发特性的影响, 从而验证了分子模型和蒸发模型的正确性. 接着模拟了在不同幅值和频率的交变电场作用下水滴在氮气环境下的蒸发过程, 结果表明, 相比于无电场或匀强电场, 交变电场能够更显著地促进水滴的蒸发. 在频率一定时, 随着电场幅值的增大, 液滴的蒸发速率不断升高, 蒸发寿命不断下降, 且液滴的瞬时蒸发速率、液滴温度、水分子的排列结构等参数都会产生频率为所加电场二倍的振荡特性, 且电场幅值越大, 振荡幅值也越大. 而在电场幅值一定时, 随着频率的增大, 液滴蒸发寿命和速率并不是单调变化的, 而是在频率$f=5$GHz时, 分别达到一个极大值和极小值, 文中从液滴能量和分子排列结构两个方面解释了产生了这一现象的原因.      

Modeling of the dynamic behavior of systems with rolling elements

Bearings, friction wheels, cams, etc. are widely employed elements in machine construction. The modeling of the dynamics of rolling friction plays therefore a crucial role in the simulation and optimization of such systems. This paper describes a recently developed transient-rolling-friction model with its application to different generic dynamical systems, to simulate the effects of rolling friction or traction on the dynamics of mechanical systems. The results, which are expressed in terms of the complex stiffness arising in the rolling-contact patches, show that the behavior depends on both the amplitude and the frequency of oscillation. For low amplitudes and frequencies, the behavior is quasi-linear. For increasing amplitudes and frequencies, however, strong non-linearities appear, leading to complex behavior.