Journal ArticleDOI
Study for the bifurcation topological structure and the global complicated character of a kind of nonlinear finance system (I)
TLDR
In this article, a mathematical model of a kind of complicated financial system, and all possible things that the model shows in the operation of our country's macro-financial system are analyzed.Abstract:
Based on the work discussed on the former study, this article first starts from the mathematical model of a kind of complicated financial system, and analyses all possible things that the model shows in the operation of our country's macro-financial system: balance, stable periodic, fractal, Hopf-bifurcation, the relationship between parameters and Hopf-bifurcation, and chaotic motion etc. By the changes of parameters of all economic meanings, the conditions on which the complicated behaviors occur in such a financial system, and the influence of the adjustment of the macro-economic policies and adjustment of some parameter on the whole financial system behavior have been analyzed. This study will deepen people's understanding of the lever function of all kinds of financial policies.read more
Citations
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Journal ArticleDOI
Nonlinear dynamics and chaos in a fractional-order financial system
TL;DR: A fractional-order financial system is proposed, a generalization of a dynamic financial model recently reported in the literature, that displays many interesting dynamic behaviors, such as fixed points, periodic motions, and chaotic motions.
Journal ArticleDOI
Analysis of nonlinear dynamics and chaos in a fractional order financial system with time delay
Zhen Wang,Xia Huang,Guodong Shi +2 more
TL;DR: It is found that an approximate time delay can enhance or suppress the emergence of chaos, and the lowest orders for chaos to exist in the delayed fractional order financial systems are determined, respectively.
Journal ArticleDOI
Chaos and Hopf bifurcation of a finance system
TL;DR: In this paper, the Ruelle-Takens route to chaos and strange non-chaotic attractors (SNA) are found through numerical simulations of a finance system with time-delayed feedback.
Journal ArticleDOI
Control of an uncertain fractional order economic system via adaptive sliding mode
Zhen Wang,Xia Huang,Hao Shen +2 more
TL;DR: This paper addresses the design of sliding mode controller (SMC) for an uncertain chaotic fractional order economic system and an adaptive SMC is designed in the case that the upper bound of the uncertainties is unknown.
Journal ArticleDOI
The effect of market confidence on a financial system from the perspective of fractional calculus: Numerical investigation and circuit realization
Shu-Bo Chen,Hadi Jahanshahi,Oumate Alhadji Abba,J.E. Solís-Pérez,Stelios Bekiros,Stelios Bekiros,José Francisco Gómez-Aguilar,Amin Yousefpour,Yu-Ming Chu +8 more
TL;DR: The effect of market confidence on a financial system from the perspective of fractional calculus is investigated, and it is shown that the system enters chaos through experiencing a cascade of period doublings, and the existence of chaos is verified.
References
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Journal ArticleDOI
Predictability and unpredictability in financial markets
TL;DR: The role of derivatives in solving the financial predictability problem is discussed and how they can be treated in the rigorous framework of modern applied mathematics is demonstrated.
Journal ArticleDOI
Mathematical models of population distribution within a culture group
TL;DR: In this article, models for the distribution and movement of populations within a culture group are proposed for two and three subcultures and questions of equilibria, periodic solutions, stability, and persistence versus extinction are considered.
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Nonlinear dynamics in foreign exchange markets
TL;DR: Four types of nonlinear dynamics are empirically analysed here in respect of the current international foreign exchange markets, e.g. autoregressive heteroscedasticity model, Lorenz-type chaos, hysteresis and the positive feedback model, providing strong support to the existence of significant nonlinearities in the exchange market dynamics in an international framework.