Input-to-state stability and no-inputs stabilization of delayed feedback chaotic financial system involved in open and closed economy
Ruofeng Rao, Shouming Zhong
Abstract
The stochastic inflow or withdrawal of funds in the international financial market are both positive or negative external inputs to the domestic financial system. So, in this paper, input-to-state stability criterion of delayed feedback chaotic financial system is investigated, and derived by counterevidence method, Lyapunov functional method, variational method and regional control technique, which was involved to equilibrium solution with the positive interest rate. On the other hand, if these inputs are too small to be ignored, impulse control can be applied to stability analysis of the delayed feedback system, in which the delayed impulse allows the pulse effect to lag for a period of time. The obtained stability criteria show that no matter how complex and chaos the financial system is, high-frequency effective macro-control is conducive to the global asymptotical stability of the economic system, including the open economic model with foreign investment fund inputs. Finally, numerical examples illustrate the effectiveness of all the proposed methods.