Two-phase oscillatory patterns in a positive feedback agent model

We present in this paper a multi-agent model of an economic system driven by a simple positive feedback rule of price updating, which exhibits Lévy statistics for all the ranges of index α. We have observed by means of computer simulations two distinct phases of oscillatory patterns in the parameter space. One phase has the price fluctuations following the Cauchy distribution (α=1), and the other phase has the price fluctuations following the Gauss distribution (α=2). Near the boundary region they follow the Lévy distribution index around α=1.7, consistent to the real financial data.