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Chaotic Map with No Fixed Points: Entropy, Implementation and Control
Van Van Huynh1, Adel Ouannas2, Xiong Wang3
1Modeling Evolutionary Algorithms Simulation and Artificial Intelligence, Faculty of Electrical and Electronics Engineering, Ton Duc Thang University, Ho Chi Minh City, Vietnam.
Abstract:
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.
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