Stochastic Hopf Bifurcation of a novel finance chaotic system
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Authors
Jiangang Zhang
- Department of Mathematics, Lanzhou Jiaotong University, Lanzhou, Gansu, 730070, China.
Juan Nan
- Department of Mathematics, Lanzhou Jiaotong University, Lanzhou, Gansu, 730070, China.
Yandong Chu
- Department of Mathematics, Lanzhou Jiaotong University, Lanzhou, Gansu, 730070, China.
Wenju Du
- School of Traffic and Transportation, Lanzhou Jiaotong University, Lanzhou, Gansu, 730070, China.
Xinlei An
- Department of Mathematics, Lanzhou Jiaotong University, Lanzhou, Gansu, 730070, China.
Abstract
The paper investigated the existence and stability of the Stochastic Hopf Bifurcation for a novel finance
chaotic system with noise by the orthogonal polynomial approximation method, which reduces the stochastic
nonlinear dynamical system into its equal deterministic nonlinear dynamical system. And according to the
Gegenbauer polynomial approximation in Hilbert space, the financial system with random parameter can
be reduced into the deterministic equivalent system. The parameter condition to ensure the appearance of
Hopf bifurcation in this novel finance chaotic system is obtained by the Hopf bifurcation theorem. We show
that a supercritical Hopf bifurcation occurs at systems' unique equilibriums \(s_0\). In addition, the stability
and direction of the Hopf bifurcation is investigated by the calculation of the first Lyapunov coefficient.
And the critical value of stochastic Hopf bifurcation is determined by deterministic parameters and the
intensity of random parameter in stochastic system. Finally, the simulation results are presented to support
the analysis.
Share and Cite
ISRP Style
Jiangang Zhang, Juan Nan, Yandong Chu, Wenju Du, Xinlei An, Stochastic Hopf Bifurcation of a novel finance chaotic system, Journal of Nonlinear Sciences and Applications, 9 (2016), no. 5, 2727--2739
AMA Style
Zhang Jiangang, Nan Juan, Chu Yandong, Du Wenju, An Xinlei, Stochastic Hopf Bifurcation of a novel finance chaotic system. J. Nonlinear Sci. Appl. (2016); 9(5):2727--2739
Chicago/Turabian Style
Zhang, Jiangang, Nan, Juan, Chu, Yandong, Du, Wenju, An, Xinlei. "Stochastic Hopf Bifurcation of a novel finance chaotic system." Journal of Nonlinear Sciences and Applications, 9, no. 5 (2016): 2727--2739
Keywords
- Stochastic chaos
- stability
- stochastic Hopf bifurcation
- Gegenbauer polynomial approximation.
MSC
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