Controlling Chaos

We have proposed a stabilization method of unstable periodic orbits embedded within a chaos attractor[1].

Example of Duffing's equation

Before the controlling: A chatic attractor (Red line) with its Poincare mapping (Blue points) After the controlling: Stabilized a 3-periodic orbit (Blue line) embedded within the chaotic attractor.
Now, we are developping practical engineering applications; chaotic circuits, stepping motors, the pendulum driven by an external periodic force, etc., and also investigate to apply this method for higer-order or autonomous chaotic systems. As a second project, we try to stabilize a chaos by continuous state feedback. (from Oct. 1998)


  1. T.Ueta and H.Kawakami, ``Composite Dynamical System for Controlling Chaos,'' IEICE Trans. Fundamentals, Vol. E78-A, No.6, pp.708-714, 1995.
  2. T.Ueta and H.Kawakami, ``A Study of the Pendulum Equation with a Periodic Impulsive Force -- Bifurcation and Control --,'' IEICE Trans. Fundamentals, Vol. E78-A, No.10, 1995.
  3. T. Ueta, G. Chen and T. Kawabe, ``A Simple Approach to Calculation and Control of Unstable Periodic Orbits in Chaotic Piecewise Linear Systems,'' International Journal of Bifurcation and Chaos, Vol. 11, No.1, 2001. (in press).

Tetsushi UETA(