Abstract

Time-delay autosynchronization (TDAS) can be used to stabilize unstable periodic orbits in dynamical systems. The technique involves continuous feedback of signals delayed by the orbit's period so that the feedback signal vanishes on the target periodic orbit and hence the stabilized periodic orbit is a solution of the original dynamical system. Furthermore, this control method only requires the knowledge of the period of the unstable orbit. The amount of feedback gain needed to achieve stabilization varies with the bifurcation parameter(s) of the system, resulting in a domain of control. We compute the domain of control of the unstable periodic orbits of the bud; converter for a given TDAS scheme. We obtain a closed analytical expression for the curve g : S-1 --> C whose index determines the stability, and this index is then numerically computed. We run several simulations of the controlled system and discuss the results.