The bifurcation control for a Lorenz system with time delay

Abstract

2Faculty of Science, Jiangsu University, Zhenjiang Jiangsu 212013, China, (Received September 03 2019, accepted October 27 2019) The main aim of this manuscript is to investigate the control issue for a Lorenz system with time delay applying a hybrid control method based on state feedback and parameter perturbation. By choosing the time delay as the bifurcation parameter and utilizing stability theory for delay differential equation, the local stability in two different cases with time delay equal to 0 and not equal to 0 is discussed. With the help of Hopf bifurcation theorem, the beingness of Hopf bifurcation is established by combining the distribution results of the \u00a0characteristic \u00a0roots. \u00a0And \u00a0the \u00a0hybrid \u00a0control \u00a0method \u00a0can \u00a0availably \u00a0postpone \u00a0the \u00a0Hopf \u00a0bifurcation \u00a0by numerical simulations. \u00a0