Simultaneous stabilization of periodic orbits and fixed points in delay-coupled Lorenz systems
We study two delay-coupled Lorenz systems and demonstrate unified chaos control by noninvasive time-delayed coupling. Both an unstable periodic orbit and an unstable fixed point of the system can be stabilized close to a subcritical Hopf bifurcation. Using a multiple scales method, the systems are reduced to Hopf normal forms, and an analytical approach for stabilizing a periodic orbit as well as a fixed point of the system is developed. As a result, the equations for the characteristic exponents are derived in an analytical form, revealing the range of coupling parameters for successful stabilization. Finally, we illustrate the results with numerical simulations, which show good agreement with the theory. CYBERNETICS AND PHYSICS, VOL. 1, No. 3, 2012, 155–164.