Proceeding of International Conference
Shota Mano, Daisuke Ito, Tetsushi Ueta, Pseudo periodic orbits and their stabilization, Proc. NOLTA2014, 775-778, Luzern, Sep. 2014.
Abstract: In a chaotic attractor, some orbits looking like unstable periodic orbit are recognized. We call them pseudo periodic orbits and they are not proper periodic orbits but, we consider that they pre- serve similar properties to unstable periodic orbits. In this paper, we propose the method stabilizing the pseudo periodic orbit by using the external force con- trol. Although, the pseudo periodic orbit is an approx- imative unstable periodic orbit but it is found easily without any analytic approaches. We demonstrate the chaos controlling by using the pseudo periodic orbit for the Duffing equation with hysteresis characteristics.