The microcontroller implementation, controls, and synchronization of a three-dimensional (3D) autonomous system with a parabolic equilibrium point are investigated in this paper. The system in question displays a reverse period doubling route hidden chaotic attractors with two different shapes. Then, the partial and total amplitude controls of the system are achieved by inserting two parameters. A microcontroller implementation is performed in order to confirm the results obtained from the numerical simulations. It is found that the results from the numerical simulations and microcontroller implementation qualitatively agree with each other. The sliding mode controllers are designed to control chaos in the system under study. With the sliding mode control method, the numerical simulations confirm that chaos can be controlled in the 3D autonomous system with a parabolic equilibrium point. In addition, two chaotic 3D autonomous systems with a parabolic equilibrium point and the same parameters are synchronized by the use of a unidirectional linear error feedback coupling scheme. Finally, an active control technique is applied to bring about chaos synchronization between two chaotic 3D autonomous systems with a parabolic equilibrium and different parameters.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.