Kumbhakar Ruma, Karmakar Sarbari, Pal Nikhil, Kurths Jürgen
Department of Mathematics, Visva-Bharati, Santiniketan 731235, India.
Potsdam Institute for Climate Impact Research (PIK)-Member of the Leibniz Association, Telegrafenberg A56, Potsdam 14473, Germany.
Chaos. 2024 Oct 1;34(10). doi: 10.1063/5.0226934.
A beautiful feature of nature is its complexity. The chaos theory has proved useful in a variety of fields, including physics, chemistry, biology, and economics. In the present article, we explore the complex dynamics of a rather simple one-dimensional economic model in a parameter plane. We find several organized zones of "chaos and non-chaos" and different routes to chaos in this model. The study reveals that even this one-dimensional model can generate intriguing shrimp-shaped structures immersed within the chaotic regime of the parameter plane. We also observe shrimp-induced period-bubbling phenomenon, three times self-similarity of shrimp-shaped structures, and a variety of bistable behaviors. The emergence of shrimp-shaped structures in chaotic regimes can enable us to achieve favorable economic scenarios (periodic) from unfavorable ones (chaotic) by adjusting either one or both of the control parameters over broad regions of these structures. Moreover, our results suggest that depending on the parameters and initial conditions, a company may go bankrupt, or its capital may rise or fall in a regular or irregular manner.
大自然的一个美妙特征在于其复杂性。混沌理论已在包括物理、化学、生物和经济学等多个领域证明了其有用性。在本文中，我们在参数平面中探究一个相当简单的一维经济模型的复杂动力学。我们在该模型中发现了几个“混沌与非混沌”的有组织区域以及通向混沌的不同路径。研究表明，即使是这个一维模型也能在参数平面的混沌区域内产生有趣的虾形结构。我们还观察到虾形结构引发的周期泡现象、虾形结构的三次自相似性以及各种双稳行为。混沌区域中虾形结构的出现使我们能够通过在这些结构的广阔区域内调整一个或两个控制参数，从不利的（混沌的）经济情景实现有利的（周期性的）经济情景。此外，我们的结果表明，根据参数和初始条件，一家公司可能破产，或者其资本可能以规则或不规则的方式上升或下降。
