Study On The Time-delayed Feedback Control Of The Two Typical Sprott Chaotic Systems

Sprott system is a kind of typical chaotic system which has good values for researchbecause of its simple equation structure and complicated dynamical behaviors. In this paper, wefocus our attention on Sprott N and Sprott F systems and investigate their dynamical behaviorsas well as the time-delayed feedback control of the two chaotic systems. The latency time ofthe closed loop and low-pass filter are considered and their influences on time-delayedfeedback control technique are compared. The main research work contains:(1) By using time-delayed feedback control technique, we first analyze the relationshipbetween the characteristic roots and feedback gain k、time delay around the equilibriumpoints of Sprott N and Sprott F systems, as well as the controllable area of parameters. Then,we consider the influences of latency time on the performance of time-delayed feedbackcontrol technique. The research results show that latency time has little influence on Sprott Nsystem, but it weakens the controllability of DFC on. Sprott F system.Low-pass filter is usedto filter high-frequency signals emerged from signal extraction which improves the effects oftime-delayed feedback control technique and largens the controllable area of parameters indifferent extent. Numerical simulations validate that time-delayed feedback control techniquesuccessfully turn the unstable equilibrium points into stable ones.(2) We discuss the tracking control of Sprott N system under time-delayed feedbackcontrol technique. In line with Lyapunov stability theory, we prove the feasibility of assuagingthe unstable periodical orbits which embed in chaotic attractor. Through computer calculation,the method of determining time delay is presented. As for a certain periodical orbit, weobtain the controllable domain of parameter k from the bifurcation diagram. Tracking controlof period1and2orbits of Sprott N system are realized through numerical simulations.