Stabilization of Unstable Periodic Orbits in a Three-Dimensional Chaotic System Using Time-Delay Autosynchronization Control Method

This paper is concerned with controlling complex dynamics of a threedimensional chaotic system consisting of two quadratic cross-products and one square term. We use Pyragas' time-delayed feedback control (TDFC) known as time delay autosynchronization (TDAS) method to stabilize the unstable equilibrium point and unstable periodic orbits of the system. An explicit formula is derived to determine the critical value of time delay tau 0 for which when the delay passes through a certain threshold critical value, the chaotic dynamical system undergoes a Hopf bifurcation. Furthermore, by choosing the appropriate range of feedback strength K and control parameter tau as a free parameters, existence of Hopf bifurcation is investigated theoretically and numerically. Finally, some numerical simulations are presented to verify the analytical results.(c) 2023 L&H Scientific Publishing, LLC. All rights reserved.