Dynamical Analysis on a Finance System with Nonconstant Elasticity of Demand

Abstract

This paper investigates a finance system with nonconstant elasticity of demand. First, under some conditions, the system has invariant algebraic surfaces and the analytic expressions of the surfaces are given. Furthermore, when the two surfaces coincide and become one surface, the dynamics on the surface are analyzed and a globally stable equilibrium is found. Second, by using the normal form theory, the Hopf bifurcation is studied and the approximate expression and stability of the bifurcating periodic orbit are obtained. Third, the chaotic behaviors are investigated and the route to chaos is period-doubling bifurcations. Moreover, it is found that the system has coexisting attractors, including periodic attractor and periodic attractor, chaotic attractor and chaotic attractor. With the change of parameter, the two chaotic attractors coincide and then a symmetrical chaotic attractor arises.