Generating tri-chaos attractors with three positive Lyapunov exponents in new four order system via linear coupling

This paper presents a new hyperchaotic system with three positive Lyapunov exponents (called Tri-Chaos). Via linear coupling, Mathieu, and van der Pol systems are coupled with each other and then become a new four order system—Mathieu–van der Pol autonomous system. As we know, two positive Lyapunov exponents confirm hyperchaotic nature of its dynamics and it means that the system can present more complicated behavior than ordinary chaos. We further generate three positive Lyapunov exponents in a new coupled nonlinear system and anticipate the advanced application in secure communication. Not only a new chaotic system with three Lyapunov exponents is proposed, but also its implementation of an electronic circuit is put into practice in this article. The phase portrait, electronic circuit, power spectrum, Lyapunov exponents, and 2-D and 3-D parameter diagram of tri-chaos with three positive Lyapunov exponents of the new system will be shown in this paper. S.-Y. Li · Z.-M. Ge ( ) Department of Mechanical Engineering, National Chiao Tung University, Hsinchu, Taiwan, Republic of China e-mail: [email protected] S.-C. Huang Institute of Electrical Control Engineering, National Chiao Tung University, Hsinchu, Taiwan, Republic of China C.-H. Yang Department of Automatic Control, National Taiwan University of Science and Technology, Taipei City, Taiwan, Republic of China