Endogenous fluctuations induced by nonlinear pollution accumulation in an OLG economy and the bifurcation control

This paper aims to study the influence of nonlinear pollution accumulation on economic growth by incorporating the nonlinear pollution accumulation into an OLG model. It is shown that the nonlinearity can yield very complex dynamics, including the flip bifurcation resulting in sustained fluctuations in economy. This indicates that the nonlinear pollution accumulation can be a source of intergenerational inequity. To stabilize the complex motion and thus to control the fluctuations, a bifurcation control method from control theory is proposed. The welfare analysis shows the sustainable development criterion can be met in the controlled system but not in the original system.     

Analysis on the dynamics of a Cournot investment game with bounded rationality

In this work, a dynamic system of investment game played by two firms with bounded rationality is proposed. It is assumed that each firm in any period makes a strategy for investment and uses local knowledge to make investment strategy according to the marginal profit observed in the previous period. Theoretic work is done on the existence of equilibrium solutions, the instability of the boundary equilibriums and the stability conditions of the interior equilibrium. Numerical simulations are used to provide experimented evidence for the complicated behaviors of the system evolution. It is observed that the equilibrium of the system can loose stability via flip bifurcation or Neimark–Sacher bifurcation and time-delayed feedback control can be used to stabilize the chaotic behaviors of the system.     

Empirical assessment of bifurcation regions within New Keynesian models

As is well known in systems theory, the parameter space of most dynamic models is stratified into subsets, each of which supports a different kind of dynamic solution. Since we do not know the parameters with certainty, knowledge of the location of the bifurcation boundaries is of fundamental importance. Without knowledge of the location of such boundaries, there is no way to know whether the confidence region about the parameters’ point estimates might be crossed by one or more such boundaries. If there are intersections between bifurcation boundaries and a confidence region, the resulting stratification of the confidence region damages inference robustness about dynamics, when such dynamical inferences are produced by the usual simulations at the point estimates only. Recently, interest in policy in some circles has moved to New Keynesian models, which have become common in monetary policy formulations. As a result, we explore bifurcations within the class of New Keynesian models. We study different specifications of monetary policy rules within the New Keynesian functional structure. In initial research in this area, Barnett and Duzhak (Physica A 387(15):3817–3825, 2008) found a New Keynesian Hopf bifurcation boundary, with the setting of the policy parameters influencing the existence and location of the bifurcation boundary. Hopf bifurcation is the most commonly encountered type of bifurcation boundary found among economic models, since the existence of a Hopf bifurcation boundary is accompanied by regular oscillations within a neighborhood of the bifurcation boundary. Now, following a more extensive and systematic search of the parameter space, we also find the existence of Period Doubling (flip) bifurcation boundaries in the class of models. Central results in this research are our theorems on the existence and location of Hopf bifurcation boundaries in each of the considered cases. We also solve numerically for the location and properties of the Period Doubling bifurcation boundaries and their dependence upon policy-rule parameter settings.     

Complex dynamics of monopolies with gradient adjustment

This paper aims to show that delay matters in continuous- and discrete-time framework. It constructs a simple dynamic model of a boundedly rational monopoly. First the existence of the unique equilibrium state is proved under general price and cost function forms. Conditions are derived for its local asymptotical stability with both continuous and discrete time scales. The global dynamic behavior of the systems is then numerically examined, demonstrating that the continuous system is globally asymptotically stable without delay and in the presence of delay if the delay is sufficiently small. Then stability of the continuous system is lost via Hopf bifurcation. In the discrete case without delay, the steady state is locally asymptotically stable if the speed of adjustment is small enough, then stability is lost via period-doubling bifurcation. If the delay is one or two steps, then stability loss occurs via Neimark–Sacker bifurcation.     

Stability and bifurcation in a simple heterogeneous asset pricing model

Stability and bifurcation analysis of deterministic systems has been widely used in modeling financial markets. We develop a simple pricing model with two types of rational traders, fundamentalists and chartists, in order to study well price behavior in financial markets, we use student t distribution to replace traditional normal distribution to describe fundamental price process. We study the stability and bifurcation of the underling deterministic system and use numerical simulation to study the dynamic of the stochastic system, including autocorrelations structures and high kurtosis of the returns. It is found that the fundamental price becomes stable (unstable) when the activities from both types of traders are balanced (unbalanced).     

“Period three to period two” bifurcation for piecewise linear models

In Hommes, Nusse, and Simonovits (1990) the dynamics of a simple economic model was studied. Although this piecewise linear model is quite simple, its dynamics shows different kinds of behavior such as periodic, quasiperiodic, and chaotic behavior. In particular, a new kind of bifurcation, namely a period three to period two bifurcation, was observed numerically. This paper deals with this new bifurcation phenomenon and we show that the period three to period two bifurcation occurs and is a structurally stable phenomenon in a class of two-dimensional continuous, piecewise linear systems. In particular, the period three to period two bifurcation is a structurally stable phenomenon in economic models with Hicksian nonlinearities.Research in part supported by the Department of Energy (Scientific Computing Staff Office of Energy Research).     

Growth Dynamics and Returns to Scale: Bifurcation Analysis

We investigate the dependence of the dynamic behavior of an endogenous growth model on the degree of returns to scale. We focus on a simple (but representative) growth model with publicly funded inventive activity. We show that constant returns to reproducible factors (the leading case in the endogenous growth literature) is a bifurcation point, and that it has the characteristics of a transcritical bifurcation. The bifurcation involves the boundary of the state space, making it difficult to formally verify this classification. For a special case, we provide a transformation that allows formal classification by existing methods. We discuss the new methods that would be needed for formal verification of transcriticality in a broader class of models. Journal of Economic Literature Classification Numbers: O41, O30.     

A dynamic duopoly model with bounded rationality based on constant conjectural variation

In this paper, we construct dynamic models on the basis of constant conjectural variation. Duopolists with dynamic adjustment behavior of bounded rationality have been considered. Numerical simulation is used to illustrate the complexion of models. The existence of equilibrium points and their stability in this nonlinear system are discussed. We study two special cases of symmetry model and Bertrand model with conjectural variation. When the speed of output adjustment changes, a series of complex phenomena including bifurcation, chaos and strange attractors can be observed in our models. We also analyzed the importance of the initial conditions to the system that a tiny variation of the initial value will cause dramatic fluctuations in output.     

知识溢出下增长收敛的复杂性

在知识经济条件下,贸易自由化能否对一个国家的产出水平产生影响,能否为国际经济带来收敛,这是一个重要问题。文章通过假设国家之间构成一个知识网络,贸易中存在非线性的知识溢出,模拟了单边或多边关税下调对一个国际经济增长的收敛行为。研究结果表明,进入WTO体系后关税下调并不总意味着收敛的出现,收敛性依各经济体的初始状态和学习能力的大小而出现复杂行为,在知识网络体系单元取向上,网络的溢出参数——学习能力是决定性因素。多区域系统一旦出现收敛,则不会以牺牲富国利益为代价,即收敛是以低水平稳态向高水平稳态转移的形式出现的。     

Growing through chaotic intervals

We consider a growth model proposed by Matsuyama [K. Matsuyama, Growing through cycles, Econometrica 67 (2) (1999) 335-347] in which two sources of economic growth are present: the mechanism of capital accumulation (Solow regime) and the process of technical change and innovations (Romer regime). We will shown that no stable cycle can exist, except for a fixed point and a cycle of period two. The Necessary and Sufficient conditions for regular or chaotic regimes are formulated. The bifurcation structure of the two-dimensional parameter plane is completely explained. It is shown how the border-collision bifurcation leads from the stable fixed point to pure chaotic regime (which consists either in 4-cyclical chaotic intervals, 2-cyclical chaotic intervals or in one chaotic interval).     

基于尖点突变理论的知识型员工组织承诺建立—破坏的动力学分析

利用尖点突变理论来解释知识型员工组织承诺演化的动力学机制及其特征,把组织承诺作为状态变量,把能有效预测组织承诺的工作满意度和组织支持作为控制变量,针对武汉IT企业调研数据,利用cuspfit软件定量地拟合出了尖点突变模型。通过分析发现,工作满意度作为正则因子、组织支持作为分歧因子,共同影响组织承诺的突变机制:①组织承诺由建立到破坏的突变是源于工作满意度和组织支持变量穿过分歧集合时产生的自组织相变;②承诺一旦被破坏就很难重新建立起来,是源于这种突变机制的滞后效应;③当工作满意度和组织支持取值在分歧集合内部时,组织承诺演化均衡态的选择(建立或者破坏)取决于员工承诺的初始水平。     

Multiple equilibria and global indeterminacy in an endogenous growth model with congestible public goods

This paper extends the findings in Chen and Lee (2007) to show that the use of congestible public goods can produce both local and global indeterminacy in a two‐sector endogenous growth model with productive public services financed by income taxation. Basically, we observe the effects on growth rates by changing parameters, and compare the case of a single steady‐state with the emergence of dual steady‐states, identifying the feasible ways to avoid a possible low‐growth poverty trap. The novelty of our analysis is to detect the presence of global indeterminacy by making use of the Bogdanov‐Takens bifurcation theorem. Some examples are also provided to achieve concrete policy implications.     

非共识研究与高校原始创新能力提升

非共识研究是从事兼具不确定性和创新性且在初期评审专家难以对项目达成一致意见的研究行为或活动。从非共识研究视角探索高校原始创新能力提升的制约因素及其应对策略，可为中国高校破解原始创新问题提供思路。研究发现，非共识研究与高校原始创新能力提升具有紧密联系，其在开辟新的理论疆域、推动原创成果生产、营造包容型创新环境等方面为高校原始创新能力提升提供了可能。然而，在实践过程中，非共识研究在评价环境、干预行为、学术司法、多元参与等方面存在的问题制约着高校原始创新能力提升。因此，在非共识研究视角下，高校原始创新能力提升可以从创新包容的评价机制、构建科学的干预模式、建立开放的申诉程序以及拓展多元支持体系等方面进行尝试。     

Endogenous fluctuations under evolutionary pressure in Cournot competition

An evolutionary game theoretic model of Cournot competition is investigated. Individuals choose from a finite set of different behavioral rules. Each rule specifies the quantity to be produced in the current period as a function of past quantities. Using more sophisticated rules may require extra information costs. Based upon realized payoffs, the fractions of the population choosing a certain behavioral rule are updated according to the replicator equation with noise. The long-run behavior of the evolutionary system consisting of the population dynamics coupled with the quantity dynamics of the Cournot game may be complicated and endogenous fluctuations may arise. We consider a typical example where firms can choose between two rules: the Nash rule and the best-reply rule. We show that a homoclinic tangency between the stable and unstable manifold of the equilibrium occurs as evolutionary pressure increases, implying bifurcation routes to complicated dynamics and strange attractors.     

Exchange rate fluctuations in an economy with noise traders

This paper analyzes the stability of the exchange rate in an economy with noise traders. Noise trading is restricted to agents investing in the domestic stock market. The agents pricing foreign exchange hold rational expectations. Monetary policy is affected by the behavior of investors in the domestic stock market and in turn affects fundamental stock evaluations as well as noise trading. We show that when monetary policy affects only fundamentalists bifurcation appears in the exchange rate. When monetary policy also affects noise trading, fixing the exchange rate or switching to a low money growth rule imply stock bubbles converge to zero.     

Dynamic inefficiency in an overlapping generations economy with production

Reichlin [Equilibrium cycles in an overlapping generations economy with production, J. Econ. Theory 40 (1986) 89-102] has shown in an OLG model with productive capital that whenever the steady state is locally indeterminate and undergoes a Hopf bifurcation, it is Pareto-optimal. While these results were established under the assumption of Leontief technology, the author has partially extended them to show that the Hopf bifurcation is robust with respect to the introduction of capital-labor substitution. In this note, we prove that the Pareto-optimality of the steady state does not extend to technologies with capital-labor substitution. When the steady state is a sink or undergoes a Hopf bifurcation, it is characterized by over-accumulation with respect to the Golden Rule—the interest rate is negative—hence not Pareto-optimal. Most importantly, it follows that stabilization policies targeting the steady state leave room for welfare losses associated with productive inefficiency, apart from the very special case of Leontief technology.     

Border collision bifurcations in boom and bust cycles

Boom and bust cycles are widely documented in the literature on industry dynamics. Rigidities and delays in capacity adjustment in combination with bounded rational behavior have been identified as central driving forces. We construct a model that features only these two elements and we show that this is indeed sufficient to reproduce some stylized facts of a boom and bust cycle. The bifurcation diagrams summarizing the dynamic behavior reveal complex cycles and in particular also abrupt changes in the nature of these cycles. We apply new insights from the mathematical theory of piecewise smooth dynamic systems—in particular, results from the theory of border collision bifurcations—and show that the very existence of borders such as capacity constraints or nonnegativity constraints may lie behind abrupt changes in the dynamic behavior of economic variables.     

On a master-slave Bertrand game model

A master-slave Bertrand game model is proposed for upstream and downstream monopolies owned by different parties, in which the upstream monopolist's output is used as the main factor of production by the downstream monopolist who is a small purchaser of the upstream monopolist's output. The bifurcation of the Bertrand-Nash equilibrium is analyzed with Schwarzian derivative. Numerical simulations are employed to show the model's complex dynamics by means of the largest Lyapunov exponents (LLEs), bifurcation, time series diagrams and phase portraits. With the modified straight-line stabilization method, chaos control is used to improve the aggregate profits of the two oligopolists. Lastly the welfare impacts of price fluctuations and chaos controls are briefly discussed.     

Existence and uniqueness of stochastic equilibrium in a simple macro model

This paper demonstrates that even the simplest rational expectations macro model may be plagued by nonexistent or multiple equilibria. The reason for these problems is the postulated existence of risk-averse behavior on the part of labor suppliers and purchasers of durable commodities. This risk-averse behavior introduces the price forecast variance into the behavioral parameters of the model, thus leading to a simultaneous nonlinear system.     

Lock-in and break-out from technological trajectories: Modeling and policy implications

The prevailing models explaining how technologies develop along a specific trajectory largely focus on the circumstances that lead to technological lock-in. We contribute substantially to this area of research by investigating the circumstances under which technological development may break-out of a trajectory. We argue that for this to happen, a third selection mechanism—beyond those of the market and of technology—needs to upset the lock-in. We model the interaction, or mutual shaping among three selection mechanisms, and thus this paper also allows for a better understanding of when a technology will lock-in into a trajectory, when a technology may break-out of a lock-in, and when competing technologies may co-exist in a balance. As a system is conceptualized to gain a (third) degree of freedom, the possibility of bifurcation is introduced into the model. The equations, in which interactions between competition and selection mechanisms can be modeled, allow one to specify conditions for lock-in, competitive balance, and break-out.