Master – Slave Configuration of Fractional – Order Lorenz Chaotic Oscillators Embedded in FPGA

Resumen: In this paper, the FPGA implementation for a chaotic communication system using chaos is presented. Fractional-order nonlinear systems are used as chaos generators. Specially, fractional-order Lorenz chaotic oscillators are arranged as network in master-slave configuration, where the synchronization is achieved based on the coupling matrix from complex systems theory.

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A. D. Cortes-Preciado, C. Posadas-Castillo, M. A. Platas-Garza, A. G. Soriano-S´anchez, C. Elizondo-Gonzalez & A.E. Loya-Cabrera. Master – Slave Configuration of Fractional – Order Lorenz Chaotic Oscillators Embedded in FPGA. Memorias del Congreso Nacional de Control Automático, pp. 713-719, 2019.

Palabras clave

Sincronización de Sistemas, Sistemas Caóticos, Otros Tópicos Afines

• Angulo-Guzman, S., Posadas-Castillo, C., Platas-Garza, M.A., Diaz-Romero, D.A., and Lopez-Mancilla, D. (2016). Chaotic Synchronization of Regular and Irregular Complex Networks with Fractional Order Oscillators. International Journal of Control, Automation and Systems, 14(4), 1114–1123.
• Anzo-Hernández, A., García-Martínez, M., Campos Cantón, E., and Ontaon-García, L.J. (2018a). Electronic implementation of a dynamical network with nearly identical hybrid nodes via unstable dissipative systems. arXiv, 1–23.
• Anzo-Hernández, A., Gilardi-Velázquez, H.E., and Campos-Cantón, E. (2018b). On multistability behavior of Unstable Dissipative Systems. Chaos, 28(3), 1–22.
•  Arellano-Delgado, A., López-Gutierrez, R.M., Martínez Clark, R., and Cruz-Hernández, C. (2018). SmallWorld Outer Synchronization of Small-World Chaotic Networks. Journal of Computational and Nonlinear Dynamics, 13(101008), 1–1.
• Echenausía-Monroy, J.L., García-López, J.H., Jaimes Reategui, R., López-Mancilla, D., and Huerta-Cuellar, G. (2018). Family of Bistable Attractors Contained in an Unstable Dissipative Switching System Associated to a SNLF. Complexity, 1–9.
• Jiang, C., Liu, C., Liu, S., and Zhang, F. (2016). Combination complex synchronization among three incommensurate fractional-order chaotic systems. Journal of Mathematics and Computer Science, 16, 308–323.
• Kassim, S., Hamiche, H., Djennoune, S., and Bettayeb, M. (2017). A novel secure image transmission scheme based on synchronization of fractional-order discretetime hyperchaotic systems. Nonlinear Dyn, 2473–2489.
• Li, X., Wang, X., and Chen, G. (2003). Synchronization in complex dynamical networks and its applications. Conference on Growing Networks and Graphs in Statistical Physics, Finance, Biology and Social Systems.
• López-Mancilla, D., López-Cahuich, G., Posadas-Castillo, C., García-López, J.H., Vázquez-Gutierrez, J.L., and Tlelo-Cuautle, E. (2019). Synchronization of complex networks of identical and nonidentical chaotic systems via model-matching control. PLOS ONE, 145, 1–16.
• M., P.L. and L., C.T. (1990). Synchronization in chaotic systems. Review Letters, 64(8), 821–824.
• Méndez-Ramírez, R., Arellano-Delgado, A., Murillo Escobar, M.A., and Cruz-Hernández, C. (2018). Multimedia Contents Encryption Using the MACM System, chapter Cryptographic and Information Security Approaches for Images and Videos, 263–295. Elsevier.
• Pena-Ramírez, J., Arellano-Delgado, A., and Nijmeijer, H. (2018). Enhancing master-slave synchronization: The effect of using a dynamic coupling. PHYSICAL REVIEW E, 1–10.
• Petrás, I. (2011). Fractional-order nonlinear systems: Modeling, analysis and simulation. Springer.
• Rajagopal, K., Karthikeyan, A., and Srinivasan, A.K. (2017). FPGA implementation of novel fractional-order chaotic systems with two equilibriums and no equilibrium and its adaptive sliding mode synchronization. Nonlinear Dynamics, 87, 2281–2304.
• Soriano-Sánchez, A.G., Posadas-Castillo, C., Platas Garza, M.A., and Arellano-Delgado, A. (2018). Synchronization and FPGA realization of complex networks with fractionalorder Liu chaotic oscillators. Applied Mathematics and Computation, 332, 250–262.
• Soriano-Sánchez, A.G., Posadas-Castillo, C., Platas Garza, M.A., and Diaz-Romero, D.A. (2015). Performance improvement of chaotic encryption via energy and frequency location criteria. Mathematics and Computers in Simulation, 112, 14–27.
• Soriano-Sánchez, A., Posadas-Castillo, C., Platas-Garza, M., and Elizondo-González, C. (2016). Chaotic Synchronization of CNNs in Small-World Topology Applied to Data Encryption, chapter Studies in Computational Intelligence 636, 337–362. Springer.
• Su, D., Bao, W., Liu, J., and Gong, C. (2016). An efficient simulation of the fractional chaotic system and its synchronization. Journal of the Franklin Institute, 355(18), 9072–9084.
• Tlelo-Cuautle, E., de Jesus Quintas-Valles, A., de la Fraga, L.G., and de Jesus Rangel-Magdaleno, J. (2016). VHDL Descriptions for the FPGA Implementation of PWL-Function-Based Multi-Scroll Chaotic Oscillators. PLOS ONE, 11(12), 1–32.
• Tolba, M.F., AbdelAty, A.M., Said, L.A., Madian, A.H., and Radwan, A.G. (2018). FPGA Implementation of Fractional-Order Chaotic Systems, chapter Fractional Order Systems, 33–62. Elsevier.
• Xiong, L., Lu, Y.J., Zhang, Y.F., Zhang, X.G., and P, G. (2016). Design and Hardware Implementation of a New Chaotic Secure Communication technique. PLOS ONE, 11(8), 1–19.