We propose a prototype model of market dynamics in which all functional relationships are linear. We take into account three borders, defined by linear functions, that are intrinsic to the economic reasoning: non-negativity of prices; downward rigidity of capacity (depreciation); and a capacity constraint for the production decision. Given the linear specification, the borders are the only source for the emerging of cyclical and more complex dynamics. In particular, we discuss centre bifurcations, border collision bifurcations and degenerate flip bifurcations—dynamic phenomena the occurrence of which are intimately related to the existence of borders.

中文翻译：

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关于边界的重要性：内生动力的出现

我们提出了一种市场动力学的原型模型，其中所有功能关系都是线性的。我们考虑了由线性函数定义的三个边界，它们是经济推理所固有的：价格的非负性；能力的下降刚性（折旧）；以及生产决策的产能限制。给定线性规范，边界是出现周期性且更复杂的动力学的唯一来源。特别是，我们讨论了中心分叉，边界碰撞分叉和简并的翻转分叉-动力学现象的发生与边界的存在密切相关。