Chaos and Hopf bifurcation of a finance system

Gao, Qin; Ma, Junhai

doi:10.1007/s11071-009-9472-5

Cited by 151 publications

(86 citation statements)

References 13 publications

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“…All three parameters possess a positive value (a 0, b 0, c 0). Also, the finance system (1) has been studied by other researchers in the same or in other mathematical forms [11,12,26], by extracting interesting results about its dynamical behavior.…”

Section: The Novel Nonlinear Finance Modelmentioning

confidence: 99%

Analysis, adaptive control and circuit simulation of a novel finance system with dissaving

Tacha¹,

Volos²,

Stouboulos³

et al. 2016

Archives of Control Sciences

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Analysis, adaptive control and circuit simulation of a novel finance system with dissaving OURANIA I. TACHA, CHRISTOS K. VOLOS, IOANNIS N. STOUBOULOS and IOANNIS M. KYPRIANIDISIn this paper a novel 3-D nonlinear finance chaotic system consisting of two nonlinearities with negative saving term, which is called 'dissaving' is presented. The dynamical analysis of the proposed system confirms its complex dynamic behavior, which is studied by using wellknown simulation tools of nonlinear theory, such as the bifurcation diagram, Lyapunov exponents and phase portraits. Also, some interesting phenomena related with nonlinear theory are observed, such as route to chaos through a period doubling sequence and crisis phenomena. In addition, an interesting scheme of adaptive control of finance system's behavior is presented. Furthermore, the novel nonlinear finance system is emulated by an electronic circuit and its dynamical behavior is studied by using the electronic simulation package Cadence OrCAD in order to confirm the feasibility of the theoretical model.

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Section: The Novel Nonlinear Finance Modelmentioning

confidence: 99%

Analysis, adaptive control and circuit simulation of a novel finance system with dissaving

Tacha¹,

Volos²,

Stouboulos³

et al. 2016

Archives of Control Sciences

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“…Gao qin et al [8] formulated a financial model, studied the chaos and bifurcations problems of this financial model, and got some good results. In this paper, we study the stability of this chaotic financial model by using the pulse control method, and obtain the sufficient conditions for asymptotic stability of the financial system.…”

Section: Introductionmentioning

confidence: 99%

Impulsive Control of a Chaotic Financial System

Yong¹

2018

Proceedings of the 2017 4th International Conference on Machinery, Materials and Computer (MACMC 2017)

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Abstract. The impulsive control of a finance system is investigated in this paper, and the finance system can be asymptotically controlled to the origin by using impulsive control. Based on the new comparison theorem of impulsive system, this paper obtains some sufficient for the stabilization of the finance system via impulsive control with varying impulsive intervals, A numerical simulation illustrates the effectiveness of the proposed result.

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“…An effective and rapid control method is very important for the government when some chaotic phenomenon appears [2][3][4][5]. A classical three-dimensional financial dynamic model describing the time variations of state adjustment has been reported [3], which includes the interest rate, the price index, and the investment demand.…”

Section: Introductionmentioning

confidence: 99%

Hopf Bifurcation, Positively Invariant Set, and Physical Realization of a New Four‐Dimensional Hyperchaotic Financial System

Kai

Zhang

Wei

et al. 2017

Mathematical Problems in Engineering

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This paper introduces a new four-dimensional hyperchaotic financial system on the basis of an established three-dimensional nonlinear financial system and a dynamic model by adding a controller term to consider the effect of control on the system. In terms of the proposed financial system, the sufficient conditions for nonexistence of chaotic and hyperchaotic behaviors are derived theoretically. Then, the solutions of equilibria are obtained. For each equilibrium, its stability and existence of Hopf bifurcation are validated. Based on corresponding first Lyapunov coefficient of each equilibrium, the analytical proof of the existence of periodic solutions is given. The ultimate bound and positively invariant set for the financial system are obtained and estimated. There exists a stable periodic solution obtained near the unstable equilibrium point. Finally, the dynamic behaviors of the new system are explored from theoretical analysis by using the bifurcation diagrams and phase portraits. Moreover, the hyperchaotic financial system has been simulated using a specially designed electronic circuit and viewed on an oscilloscope, thereby confirming the results of the numerical integrations and its real contribution to engineering.

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Chaos and Hopf bifurcation of a finance system

Cited by 151 publications

References 13 publications

Analysis, adaptive control and circuit simulation of a novel finance system with dissaving

Analysis, adaptive control and circuit simulation of a novel finance system with dissaving

Impulsive Control of a Chaotic Financial System

Hopf Bifurcation, Positively Invariant Set, and Physical Realization of a New Four‐Dimensional Hyperchaotic Financial System

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