Stability, Multi-Stability and Complexity Analysis in a Dynamic Economic
Model with Exponential Term
Abstract
In this paper, a discrete-time dynamic economic system, with exponential
demand term and quadratic cost term, is established. We have spent great
lot efforts in verifying the properties of existence and local stability
of equilibrium points by Medium Theory and Zero-Point Theory.
Immediately, the stability conditions are given in details. And then, by
changing the valuesof parameters, the system shows some new and
interesting phenomena in terms to stability and multi-stability, like
different shape basin of coexisting attractors. Even some changes in the
topological structure of basin have beenintuitively and more deeply
analyzed by using numerical simulation. Finally, we utilize critical
curves to analyze the reason of “hole” formation and to descript their
evolution process. As a result, we can intuitively find that the
generation of global bifurcation, like contact bifurcation or final
bifurcation,is usually accompanied by the contact of critical curve and
boundary.