Control And Synchronization Of A Class Of Nonlinear Financial Systems

In this paper, we will study stability, synchronization of a class of nonlinear financial system. For stability of the financial hyperchaotic system, we put forward two different methods to make sure that the financial hyperchaotic system achieves stability under different control schemes by using Lyapunov stability theory and differential equations inequality. For synchronization of the financial system, we propose a hybrid synchronization conception which is the first time that the hybrid synchronization is used in the financial system. Based on the complex network theory,we further establish a mathematical model for the evolution of the financial market.Besides, we study its stability by using impulse control.Firstly, we put forward a class of delay financial hyperchaotic system model. The stability criterions are obtained through the design of intermittent controller, adaptive intermittent controller, and the Lyapunov stability analysis. The simulation results are given to test the correctness of proposing scheme.Secondly, we explore the hybrid synchronization of a class of financial hyperchaotic system. We definite the conception of hybrid synchronization and construct the appropriate hybrid control. The sufficient hybrid synchronization conditions are achieved through detailed and strict theoretical analysis. The final numerical simulation is consistent of the theoretical analysis results.Thirdly, we build a delay complex financial network model. We propose principles of modeling a complex financial network based on the basic theory of complex network, network modeling method, process etc. We finally propose a delay complex financial model and explain its practical significance.Finally, we analyze the stability of a time-delay complex financial network model.Through theoretical analysis, some sufficient stability conditions are got based on impulsive stability theory. Numerical simulation results verified the accuracy of proposed theory.