Dynamical Models For Prices With Distributed Delays

G. Mircea, M. Neamţu, L. Cismaș
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Abstract

Abstract In the present paper we study some models for the price dynamics of a single commodity market. The quantities of supplied and demanded are regarded as a function of time. Nonlinearities in both supply and demand functions are considered. The inventory and the level of inventory are taken into consideration. Due to the fact that the consumer behavior affects commodity demand, and the behavior is influenced not only by the instantaneous price, but also by the weighted past prices, the distributed time delay is introduced. The following kernels are taken into consideration: demand price weak kernel and demand price Dirac kernel. Only one positive equilibrium point is found and its stability analysis is presented. When the demand price kernel is weak, under some conditions of the parameters, the equilibrium point is locally asymptotically stable. When the demand price kernel is Dirac, the existence of the local oscillations is investigated. A change in local stability of the equilibrium point, from stable to unstable, implies a Hopf bifurcation. A family of periodic orbits bifurcates from the positive equilibrium point when the time delay passes through a critical value. The last part contains some numerical simulations to illustrate the effectiveness of our results and conclusions.
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具有分布时滞的价格动力学模型
摘要本文研究了单一商品市场价格动态的几个模型。供给量和需求量被认为是时间的函数。同时考虑了供给函数和需求函数的非线性。考虑库存和库存水平。由于消费者行为影响商品需求,而且消费者行为不仅受瞬时价格的影响,还受加权过去价格的影响,因此引入了分布式时滞。考虑了需求价格弱核和需求价格狄拉克核。只找到一个正平衡点,并对其稳定性进行了分析。当需求价格核弱时,在参数的某些条件下,平衡点是局部渐近稳定的。当需求价格核为狄拉克时,研究了局部振荡的存在性。平衡点的局部稳定性从稳定到不稳定的变化意味着Hopf分岔。当时滞超过一个临界值时,一组周期轨道从正平衡点分叉。最后通过一些数值模拟来说明我们的结果和结论的有效性。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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