Stochastic Hopf Bifurcation of a novel finance chaotic system

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.

[Retracted] Prediction and Application of Computer Simulation in Time‐Lagged Financial Risk Systems

“…However, due to the complexity and vagaries of financial markets, financial risks are always present, and if they are too large and not handled properly, they can also affect the sustainable development of the national economy [1]. However, financial risks exist objectively in the financial market, and because of their uncertainty, high leverage, correlation, and contagiousness, they can easily lead to losses in financial institutions and, in serious cases, to the disruption of the social and financial system and financial crises [2]. erefore, to maintain the stability of the financial system, it is necessary to adopt appropriate methods to predict and control financial risks.…”

PDϑ Control Strategy for a Fractional‐Order Chaotic Financial Model

“…Remark . In [4][5][6][7][13][14][15][16][17][18][19][20], the authors studied the various dynamics of integer-order financial models. They did not involve the fractional-order forms.…”

“…For instance, Zhang et al [1] discussed the stability of a financial hyperchaotic model, Serletic [2] investigated the chaos in economic system, Lin et al [3] made an detailed analysis on chaotic behavior of a financial complex model, and Gao and Ma [4] studied the chaotic phenomenon and bifurcation of a finance model. For more information on financial models, one can see [5][6][7][8][9].…”

“…In 2014, Zhao et al [19] investigated the the anticontrol of Hopf bifurcation and chaos control of model (1) by applying delayed washout filters. For details, one can see [5][6][7][20][21][22][23][24][25][26][27][28][29][30].…”