On the Dynamics of Complex Valued Nonlinear Autoregressive Time Series Models and Stochastic Limit Cycles

摘要

This paper introduces a new simple complex valued functional coefficients autoregressive time series model (FCAR). The dynamical behavior of the proposed system is studied. The existence and local stability of the only equilibrium point of the system are analyzed. For one control parameter, the chaotic behaviour of the system is discussed by means of phase portraits, bifurcation diagram, time series portraits and Lyapunov exponents. The correlation structure is obtained. Numerical simulation is used to verify the theoretical study.