HOPF BIFURCATION AND CHAOS OF FINANCIAL SYSTEM ON CONDITION OF SPECIFIC COMBINATION OF PARAMETERS

Junhai MA;Yaqiang CUI;Lixia LIU

系统科学与复杂性(英文) ›› 2008, Vol. 21 ›› Issue (2) : 250-259.

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系统科学与复杂性(英文) ›› 2008, Vol. 21 ›› Issue (2) : 250-259.
论文

HOPF BIFURCATION AND CHAOS OF FINANCIAL SYSTEM ON CONDITION OF SPECIFIC COMBINATION OF PARAMETERS

    Junhai MA(1)(2), Yaqiang CUI(1), Lixia LIU(1)
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HOPF BIFURCATION AND CHAOS OF FINANCIAL SYSTEM ON CONDITION OF SPECIFIC COMBINATION OF PARAMETERS

    Junhai MA(1)(2), Yaqiang CUI(1), Lixia LIU(1)
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摘要

This paper studies the global bifurcation and Hopf bifurcation of one kind of complicated financial system with different parameter combinations. Conditions on which bifurcation happens, and the critical system structure when the system
transforms from one kind of topological structure to another are studied as well. The criterion for identifying Hopf bifurcation under different parameter combinations is also given. The chaotic character of this system under quasi-periodic force is finally studied. The bifurcation structure graphs are given when two parameters of the combination are fixed while the other parameter varies. The presence and stability of 2 and 3 dimensional torus bifurcation are studied. All of the Lyapunov exponents of the system with different bifurcation parameters and routes leading
the system to chaos with different parameter combinations are studied. It is of important theoretical and practical meaning to probe the intrinsic mechanism of such continuous complicated financial system and to find the macro control policies for such kind of system.

Abstract

This paper studies the global bifurcation and Hopf bifurcation of one kind of complicated financial system with different parameter combinations. Conditions on which bifurcation happens, and the critical system structure when the system
transforms from one kind of topological structure to another are studied as well. The criterion for identifying Hopf bifurcation under different parameter combinations is also given. The chaotic character of this system under quasi-periodic force is finally studied. The bifurcation structure graphs are given when two parameters of the combination are fixed while the other parameter varies. The presence and stability of 2 and 3 dimensional torus bifurcation are studied. All of the Lyapunov exponents of the system with different bifurcation parameters and routes leading
the system to chaos with different parameter combinations are studied. It is of important theoretical and practical meaning to probe the intrinsic mechanism of such continuous complicated financial system and to find the macro control policies for such kind of system.

关键词

Chaos / complicated financial system / equilibrium ``drift'' / Hopf bifurcation / strange non-chaotic attractor

Key words

Chaos / complicated financial system / equilibrium``drift'' / Hopf bifurcation / strange non-chaotic attractor

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Junhai MA , Yaqiang CUI , Lixia LIU. HOPF BIFURCATION AND CHAOS OF FINANCIAL SYSTEM ON CONDITION OF SPECIFIC COMBINATION OF PARAMETERS. 系统科学与复杂性(英文), 2008, 21(2): 250-259
Junhai MA , Yaqiang CUI , Lixia LIU. HOPF BIFURCATION AND CHAOS OF FINANCIAL SYSTEM ON CONDITION OF SPECIFIC COMBINATION OF PARAMETERS. Journal of Systems Science and Complexity, 2008, 21(2): 250-259
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