具有相对利润委托的离散分数阶库诺二元垄断博弈模型:稳定性、分岔、混沌、0-1 检验和控制

IF 4.6 Q2 MATERIALS SCIENCE, BIOMATERIALS
Senol Kartal
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引用次数: 0

摘要

由于记忆效应,分数阶动力系统与普通动力系统相比能提供更真实的结果。在本研究中,我们考虑了一个具有卡普托分数导数意义上的相对利润委托的库诺-双寡头博弈模型。为了描述模型中更丰富的动态行为(如混沌),需要一个离散的动态系统。由于采用了基于片断常数参数的离散化方法,我们得到了一个二维差分方程系统。全面给出了离散动力系统所有平衡点的稳定条件。从理论上证明了系统中翻转分岔的存在。李亚普诺夫指数和 0-1 检验混沌意味着该分岔会形成混沌结构。此外,我们还提出了混沌控制技术,如 Pyragas 方法,以消除模型中的混沌。所有涉及模型稳定性、分岔和混沌的理论结果都是通过数值模拟得到的。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
A discrete fractional order cournot duopoly game model with relative profit delegation: Stability, bifurcation, chaos, 0-1 testing and control
Due to the memory effect, fractional order dynamical systems provide more realistic results compared with ordinary counterparts. In this study, we consider a Cournot-duopoly game model with relative profit delegation in the sense of Caputo fractional derivative. To describe richer dynamical behavior such as chaos in the model, a discrete dynamical system is needed. As a result of the discretization method based on the use of piecewise constant arguments, we obtain a two dimensional system of difference equations. The stability conditions of all equilibrium points of the discrete dynamical system are given comprehensively. The existence of the flip bifurcation in the system has been demonstrated theoretically. Lyapunov exponents and 0–1 test chaos imply that chaotic structures are formed as a result of this bifurcation. In addition, we present the chaos control technique such as Pyragas method to eliminate chaos in the model. All theoretical results dealing with the stability, bifurcation and chaos in the model are stimulated by numerical simulations.
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来源期刊
ACS Applied Bio Materials
ACS Applied Bio Materials Chemistry-Chemistry (all)
CiteScore
9.40
自引率
2.10%
发文量
464
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