A Dynamic Economic Model with Discrete Time and Consumer Sentiment

Abstract

The paper describes a dynamical economic model with discrete time and consumer sentiment in the deterministic and stochastic cases. We seek to demonstrate that consumer sentiment may create fluctuations in the economical activities. The model possesses a flip bifurcation and a Neimark-Sacker bifurcation, after which the stable state is replaced by a (quasi) periodic motion. We associate the difference stochastic equation to the model by randomizing the control parameter d and by adding one stochastic control. Numerical simulations are made for the deterministic and stochastic models, for different values of the control parameter d.