标题： 确定性模型在竞争市场中的微观系统跃迁现象 显示英文标题

标题： Leapfrogging of a deterministic model for microeconomic systems in competitive markets

摘要： Behrens-Feichtinger 模型为两个生产相同商品并在共同市场中竞争的公司销售的共同演变提供了一个确定性的图景。该模型涉及一种积极的投资策略，使得每家公司在市场中的相对位置决定了其临时投资。在这项工作中，我们关注的是一个特定的演化阶段，称为轮流领先阶段，在这个阶段，每家公司都有可能在一段有限的时间内交替主导市场。我们通过引入两个适当的变量，即两家公司在任意时间点的销售额差和总销售额，来研究有利于模型的轮流领先动态的条件。我们对由此产生的耦合离散非线性方程的不动点稳定性进行了分析，并生成了销售差和销售和相对于弹性系数的分岔图。时间序列分析表明，由销售额差从正到负分支的周期性振荡所表征的轮流领先阶段，通过模型特征参数的特定值得到稳定，并且当此外弹性系数（与两家公司的投资策略差异有关）足够高时也是如此。为了确保轮流领先动态期间商品的可用性，需要在任意时间点累积销售额为正值。 显示英文摘要

摘要： The Behrens-Feichtinger model provides a deterministic picture for the co-evolution of sales of two firms, producing the same goods and competing in a common market. The model involves an active investment strategy such that the temporary investment of each of the two firms depends on its relative position in the market. In this work we are interested in a specific regime of evolution referred to as leapfrogging regime, in which each firm has the possibility to dominate the market alternately during some finite period of time. We examine conditions favoring the leapfrogging dynamics of the model by introducing two appropriate variables, namely the sale difference and total sale of the two firms at any time. An analysis of stability of fixed points of the resulting coupled discrete nonlinear equations is carried out, and the bifurcation diagrams of the sale difference and sum with respect to the elasticity coefficient, are generated. A time-series analysis suggests that the leapfrogging regime, characterized by periodic oscillations of the sale difference from positive to negative branches, is stabilized by specific values of characteristic parameters of the model and when in addition the elasticity coefficient, related to the difference in investment strategies of the two firms, is reasonably high. A positive sign of cumulated sales at any time is required to ensure the availability of goods during the leapfrogging dynamics.