Stochastic Hopf Bifurcation of a novel finance chaotic system

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