Michiru Katayama, Kenji Ikeda, Tetsushi Ueta, Stabilization of laminars in chaos intermittency, World Scientific, International Journal of Bifurcation and Chaos, Vol.34, No.2, pp.(in-press), Feb. 2024.
Abstract: Chaos intermittency is composed of a laminar regime, which exhibits almost periodic motion, and a burst regime, which exhibits chaotic motion; it is known that in chaos intermittency, switching between these regimes occurs irregularly. In the laminar regime of chaos intermittency, the periodic solution before the saddle node bifurcation is closely related to its generation, and its behavior becomes periodic in a short time; the laminar is not, however, a periodic solution, and there are no unstable periodic solutions nearby. Most chaos control methods cannot be applied to the problem of stabilizing a laminar response to a periodic solution since they refer to information about unstable periodic orbits. In this paper, we demonstrate a control method that can be applied to the control target that laminar phase of a dynamical system exhibiting chaos intermittency. This method records the time series of a periodic solution prior to the saddle node bifurcation as a pseudo-periodic orbit and feeds it to the control target back. We report that when this control method is applied to a circuit model, laminar motion can be stabilized to a periodic solution via control inputs of very small magnitude, and robust control can be obtained.