Chaotic Map with No Fixed Points: Entropy, Implementation and Control
Van Van Huynh,
Adel Ouannas,
Xiong Wang,
Viet-Thanh Pham,
Xuan Quynh Nguyen,
Fawaz E. Alsaadi
Affiliations
Van Van Huynh
Modeling Evolutionary Algorithms Simulation and Artificial Intelligence, Faculty of Electrical and Electronics Engineering, Ton Duc Thang University, Ho Chi Minh City, Vietnam
Adel Ouannas
Department of Mathematics and Computer Science, University of Larbi Tebessi, Tebessa 12002, Algeria
Xiong Wang
Institute for Advanced Study, Shenzhen University, Shenzhen 518060, China
Viet-Thanh Pham
Nonlinear Systems and Applications, Faculty of Electrical and Electronics Engineering, Ton Duc Thang University, Ho Chi Minh City, Vietnam
Xuan Quynh Nguyen
National Council for Science and Technology Policy, Hanoi, Vietnam
Fawaz E. Alsaadi
Department of Information Technology, Faculty of Computing and IT, King Abdulaziz University, Jeddah 21589, Saudi Arabia
A map without equilibrium has been proposed and studied in this paper. The proposed map has no fixed point and exhibits chaos. We have investigated its dynamics and shown its chaotic behavior using tools such as return map, bifurcation diagram and Lyapunov exponents’ diagram. Entropy of this new map has been calculated. Using an open micro-controller platform, the map is implemented, and experimental observation is presented. In addition, two control schemes have been proposed to stabilize and synchronize the chaotic map.
