scispace - formally typeset
Search or ask a question
Journal ArticleDOI

Study for the bifurcation topological structure and the global complicated character of a kind of nonlinear finance system (I)

陈予恕1, 马军海1
18 Nov 2001-Applied Mathematics and Mechanics-english Edition (Kluwer Academic Publishers)-Vol. 22, Iss: 11, pp 1240-1251
TL;DR: 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.
Citations
More filters
Journal ArticleDOI
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.
Abstract: This study examines the two most attractive characteristics, memory and chaos, in simulations of financial systems. A fractional-order financial system is proposed in this study. It is a generalization of a dynamic financial model recently reported in the literature. The fractional-order financial system displays many interesting dynamic behaviors, such as fixed points, periodic motions, and chaotic motions. It has been found that chaos exists in fractional-order financial systems with orders less than 3. In this study, the lowest order at which this system yielded chaos was 2.35. Period doubling and intermittency routes to chaos in the fractional-order financial system were found.

381 citations

Journal ArticleDOI
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.
Abstract: In this paper, a delayed fractional order financial system is proposed and the complex dynamical behaviors of such a system are discussed by numerical simulations. A great variety of interesting dynamical behaviors of such a system including single-periodic, multiple-periodic, and chaotic motions are displayed. In particular, the effect of time delay on the chaotic behavior is investigated, it is found that an approximate time delay can enhance or suppress the emergence of chaos. Meanwhile, corresponding to different values of delay, the lowest orders for chaos to exist in the delayed fractional order financial systems are determined, respectively.

253 citations


Cites background from "Study for the bifurcation topologic..."

  • ...Dynamics in a fractional order financial system The authors [34,35] reported a model composed of three first order differential equations to describe the running of financial system: ẋ = z + (y − a)x, ẏ = 1 − by − x2, ż = −x − cz....

    [...]

Journal ArticleDOI
Qin Gao1, Junhai Ma1
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.
Abstract: The complex dynamical behavior of a finance system is investigated in this paper The Ruelle–Takens route to chaos and strange nonchaotic attractors (SNA) are found through numerical simulations Then the system with time-delayed feedback is considered and the stability and Hopf bifurcation of the controlled system are investigated This research has important theoretical and practical meanings

141 citations


Cites background or result from "Study for the bifurcation topologic..."

  • ...By choosing an appropriate coordinates and setting proper dimensions for every state variable, [9–13] offer the simplified finance model as...

    [...]

  • ...This is just the case which is not considered in [9–11]....

    [...]

  • ...From the analysis of [9–11] we can see that the unique equilibrium (0, 1 b ,0) of the system is a stable sink when c − b − abc < 0 and c + a − 1 b > 0....

    [...]

  • ...For system (1), we have the following result [9–11]....

    [...]

  • ...References [9–13] have reported a dynamic model of finance which is composed of four sub-blocks: production, money, stock and labor force, and expressed as three first-order differential equations....

    [...]

Journal ArticleDOI
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.

119 citations

Journal ArticleDOI
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.
Abstract: Modeling and analysis of financial systems have been interesting topics among researchers. The more precisely we know dynamic of systems, the better we can deal with them. This way, in this paper, we investigate the effect of market confidence on a financial system from the perspective of fractional calculus. Market confidence, which is a significant concern in economic systems, is considered, and its effects are comprehensively investigated. The system has been studied through numerical simulations and analyses, such as the Lyapunov exponents, bifurcation diagrams, and phase portrait. It is shown that the system enters chaos through experiencing a cascade of period doublings, and the existence of chaos is verified. Finally, an analog circuit of the chaotic system is designed and implemented to prove its feasibility in real-world applications. Also, through the circuit implementation, the effects of different factors on the behavior of the systems are investigated.

100 citations

References
More filters
01 Jan 2001
TL;DR: Based on the mathematical model of a kind of complicated financial system, all possible things that the model shows in the operation of our country's macro-financial system were analyzed, such as balance, stable periodic, fractal,Hopf-bifurcation, the relationship between parameters and Hopf-Bifurcations, and chaotic motion etc as mentioned in this paper.
Abstract: Based on the mathematical model of a kind of complicated financial system, all possible things that the model shows in the operation of our country's macro-financial system were analyzed, such as balance, stable periodic, fractal,Hopf-bifurcation, the relationship between parameters and Hopf-bifurcations, 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 were analyzed. This study will deepen people ' s understanding of the lever function of all kinds of financial policies.

114 citations

Journal ArticleDOI
TL;DR: In this article, the singularities of vector fields associated with Newton polyhedra are blown up in the space of the exponents, by means of which it is shown that a vector field possessing characteristic orbits is locally topologically equivalent with its principal part, under suitable non-degeneracy hypotheses.

79 citations

Journal ArticleDOI
TL;DR: In this article, the authors describe the two generic instabilities which arise in quasireversible systems and show that their normal forms are the well-known real Lorenz equations and the Maxwell-Bloch equations.
Abstract: We describe the two generic instabilities which arise in quasireversible systems and show that their normal forms are the well-known real Lorenz equations and the Maxwell-Bloch equations. We present for the first time analytic predictions for the appearance of Lorenz chaos and we describe a simple mechanical system which experimentally displays this chaotic behavior.

39 citations

Journal ArticleDOI
Ömer Morgül1
TL;DR: It is shown by examples that many response systems proposed in the literature are of this form, and a necessary condition for synchronization and a selection criterion for appropriate synchronization signal are given.
Abstract: We consider observer-based synchronization of chaotic systems. In this scheme, for a given chaotic drive system, response system is chosen in observer form. We show by examples that many response systems proposed in the literature are of this form. We give a necessary condition for synchronization and a selection criterion for appropriate synchronization signal in this case. We apply this idea to synchronization of well-known hyperchaotic R\"ossler system.

24 citations