This letter proposes a numerical method for approximating the location of and dynamics on a class of chaotic saddles. In contrast to the conventional strategy of maximizing the escape time, our proposal is to impose a zero-expansion condition along transversely repelling directions of chaotic saddles. This strategy exploits the existence of skeleton-forming unstable periodic orbits embedded in chaotic saddles, and thus can be conveniently implemented as a variant of subspace Newton-type methods. The algorithm is examined through an illustrative and another standard example.

A dynamic controller, based on the Stability Transformation Method (STM), has been used to stabilize unknown and unstable periodic orbits (UPOs) in dynamical systems. An advantage of the control method is that it can stabilize unknown UPOs. In this study, we introduce a novel control method, based on STM, to stabilize UPOs in DC-DC switching power converters. The idea of the proposed method is to apply temporal perturbations to the switching time. These perturbations are calculated without information of the locations of the target orbits. The effectiveness of the proposed method is verified by numerical simulations and laboratory measurements.

We consider an improved control method based on the Stability Transformation Method. Stability Transformation Method detects unknown and unstable periodic orbits of chaotic dynamical systems. Based on the approach to realize the Stability Transformation Method in real systems, we have proposed a control method which can stabilize unknown and unstable periodic orbits embedded in chaotic attractors. However, setting of the control parameters of the control system has remained as unsolved issue. When the dynamics of a target system are unknown, the control parameters have to be set by trial and error. In this paper, we improve the control method with the automatic adjustment function of the control parameters. We show an example of stabilizing unstable periodic orbits of the 3-dimensional hysteresis chaos generator by using the proposed control method. Some results are confirmed by laboratory measurements. The results imply that any unknown and unstable periodic orbits can be stabilized by using the proposed method, if the target chaos system is reduced to 1-dimensional return map.

This letter proposes a pulse width modulated (PWM) control method which can stabilize chaotic orbits onto unstable fixed points and unstable periodic orbits. Some numerical experiments using the Lorenz equation show that chaotic orbits can be stabilized by the PWM control method. Furthermore, we investigate the stability in the neighborhood of an unstable fixed point and discuss the stability condition of the PWM control method.

In this letter a new method for controlling chaos is proposed. Although different several methods based on the OGY- and the OPF-method perturb a value of an accessible system parameter, the proposed method perturbs the only timing of switching three values of a parameter. We apply the proposed method to the well-known Chua's circuit on computer simulations. The chaotic orbits in the Rössler type- and the double scroll type-attractor can be stabilized on several unstable periodic orbits embedded within these attractors.