Chaos control of a new 3D autonomous system by stability transformation method

This paper sheds new insights into the stability transformation method (STM) for chaos control of dynamical system. The STM is applied to stabilize both multiple equilibrium points and unstable periodic orbits (UPOs) embedded in the chaotic attractor of a new 3D autonomous system. Firstly, the different equilibrium points of chaotic system are stabilized with STM by choosing specific initial points and involutory matrices. Then, the stability matrix is derived based on a priori information of equilibrium points, which indicates that the non-involutory matrix can also be used to control the unstable equilibrium points of chaotic systems. Finally, it is found that the STM can be regarded as a special form of speed feedback control method (SFCM), which facilitates the practical implementation of STM scheme. The chaotic system can be controlled by adopting the corresponding feedback control strategy once the stability matrices are determined. In this way, the blindness of choice for control strategy in the SFCM is avoided, and the difficulty for determining the state variables to be controlled is overcome.