Hopf bifurcation and topological horseshoe of a novel finance chaotic system

This paper deals with the existence of both Hopf bifurcation and topological horseshoe for a novel finance chaotic system. First, through rigorous mathematical analysis, we show that a Hopf bifurcation occurs at systems’ three equilibriums S0,1,2 and Hopf bifurcation at equilibrium S0 is non-degenerate and supercritical. Second, the computer-assisted verifications for horseshoe chaos in the system are given. Simulation results are presented to support the analysis.

► We study a financial chaotic system using a method which combines mathematics and computer in this paper. ► The Hopf bifurcation of the system is discussed by a rigorous mathematical analysis. ► The existence of the topological horseshoe in this system is proved by a computer-assisted method. ► The results obtained in this paper would benefit the further studies of this finance chaotic system.