Control of unstable high-period orbits in complex systems

We apply the discrete parametric control (Ott-Brebogi-York method) to stabi lize the high-order (k = 34) unstable periodic orbit of a 2D chaotic map. T he map describes a complex reversible system, the phase space of which cont ains elements typical for both Hamiltonian and dissipative dynamics. Stabil ization was achieved (even with external noise) for the unstable orbit wher e the amplitude of chaotic oscillations shows variations by 4 orders of mag nitude.