当前位置: X-MOL 学术Complexity › 论文详情
Our official English website, www.x-mol.net, welcomes your feedback! (Note: you will need to create a separate account there.)
Analysis of a Four-Dimensional Hyperchaotic System Described by the Caputo–Liouville Fractional Derivative
Complexity ( IF 2.3 ) Pub Date : 2020-11-28 , DOI: 10.1155/2020/8889831
Ndolane Sene 1
Affiliation  

A new four-dimensional hyperchaotic financial model is introduced. The novelties come from the fractional-order derivative and the use of the quadric function in modeling accurately the financial market. The existence and uniqueness of its solutions have been investigated to justify the physical adequacy of the model and the numerical scheme proposed in the resolution. We offer a numerical scheme of the new four-dimensional fractional hyperchaotic financial model. We have used the Caputo–Liouville fractional derivative. The problems addressed in this paper have much importance to approach the interest rate, the investment demand, the price exponent, and the average profit margin. The validation of the chaotic, hyperchaotic, and periodic behaviors of the proposed model, the bifurcation diagrams, the Lyapunov exponents, and the stability analysis has been analyzed in detail. The proposed numerical scheme for the hyperchaotic financial model is destined to help the agents decide in the financial market. The solutions of the 4D fractional hyperchaotic financial model have been analyzed, interpreted theoretically, and represented graphically in different contexts. The present paper is mathematical modeling and is a new tool in economics and finance. We also confirm, as announced in the literature, there exist hyperchaotic systems in the fractional context, which admit one positive Lyapunov exponent.

中文翻译:

Caputo-Liouville分式导数描述的四维超混沌系统的分析

介绍了一种新的四维超混沌金融模型。新颖性来自分数阶导数和二次函数的使用准确建模金融市场。研究了其解决方案的存在性和唯一性,以证明模型的物理充分性和该决议中提出的数值方案的合理性。我们提供了新的四维分数超混沌金融模型的数值方案。我们使用了Caputo-Liouville分数导数。本文所解决的问题对于确定利率,投资需求,价格指数和平均利润率非常重要。详细分析了所提出模型的混沌,超混沌和周期性行为,分叉图,Lyapunov指数以及​​稳定性分析的有效性。拟议的超混沌金融模型数值方案旨在帮助代理商确定金融市场。已对4D分数超混沌金融模型的解决方案进行了分析,理论解释并在不同环境下以图形方式表示。本文是数学建模,是经济学和金融学的新工具。我们还确认,正如文献中所宣布的那样,在分数环境中存在超混沌系统,它们承认一个正Lyapunov指数。
更新日期:2020-12-01
down
wechat
bug