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This document shows a software that shows different chaotic generator, as continuous as discrete time. The software gives the option for obtain the different signals, using different parameters and initial condition value. The program shows then critical parameter for each model. All theses models are capable of encrypter information, this software show it too., {"references":["L.M... Pechora and T.L. Carroll, \"Synchronization in chaotic\nsystems,\"Phys. Rev. Lett. 64, 821-824 (1990).","L. M. Pecora and T. L. Carroll, \"Circuit implementation of\nsynchronizedchaos with applications to communications,\" Phys. Rev. A\n44, (1991).","Special Issue on Chaos synchronization and control: Theory and\napplications IEEE Trans. Circuits Syst. I, 44, (1997).","Special Issue on Control and synchronization of chaos, Int. J. Bifurc.\nChaos, 10, (2000).","C. Cruz-Hern├índez and H. Nijmeijer, \"Synchronization through\nfiltering,\" Int. J. Bifurc. Chaos, 10, 763-775 (2000). Synchronization\nthrough extended Kalman filtering. In: Nijmeijer H, Fossen TI, editors.\nNew trends in nonlinear observer design. Lecture notes in control and\ninformation sciences, 244 London: Springer; 469-490, (1999).","H. Sira-Ram├¡rez and C. Cruz-Hern├índez, \"Synchronization of\nchaotic systems: a generalized Hamiltonian systems approach,\" Int. J.\nBifurc. Chaos, 11, 1381-1395 (2001). And in: Proceedings of the\nAmerican Control Conference, Chicago, USA, 769-773 (2000).","D. L├│pez-Mancilla and C. Cruz-Hern├índez, \"Output synchronization\nof chaotic systems: model-matching approach with application to secure\ncommunication,\" Nonlinear Dynamics and Systems Theory, 5, 141-15\n(2005).","U. Feldmann, M. Hasler and W. Schwarz, \"Communication by\nchaotic signals: the inverse system approach,\" Int. J. Circuits Theory and\nApplications, 24, 551-579 (1996).","H. Nijmeijer and I. M. Y. Mareels, \"An observer looks\natsynchronization,\" IEEE Trans. Circuits Syst. I, 44, 882-890 (1997).\n[10] Lorenz, E. N. , \"Deterministic nonperiodic flow\". J. Atmos. Sci. 20: 130-\n141. doi:10.1175/1520-0469(1963)0202.0.CO;2., (1963).\n[11] Matsumoto, Takashi , \"A Chaotic Attractor from Chua's Circuit\". IEEE\nTransactions on Circuits and Systems (IEEE) CAS-31 (12): 1055-1058.\n(1984).\n[12] Madan, Rabinder N., \"Chua's circuit: a paradigm for chaos\". River\nEdge, N.J.: World Scientific Publishing Company. ISBN 9810213662,\n(1993).\n[13] O. E. Rössler, \"An Equation for Continuous Chaos\".\nPhysics Letters 57A (5): 397-398M., (1976).\n[14] Hénon, \"A two-dimensional mapping with a strange attractor\".\nCommunications in Mathematical Physics 50: 69-77.\ndoi:10.1007/BF01608556, (1976).\n[15] Eric W. Weisstein, Logistic Equation at MathWorld.\n[16] R.M. May, \"Simple mathematical models with very complicated\ndynamics\". Nature 261: 459. doi:10.1038/261459a0, 1976"]}

In this paper, we use Generalized Hamiltonian systems approach to synchronize a modified sixth-order Chua's circuit, which generates hyperchaotic dynamics. Synchronization is obtained between the master and slave dynamics with the slave being given by an observer. We apply this approach to transmit private information (analog and binary), while the encoding remains potentially secure., {"references":["L. M. Pecora and T.L. Carroll, \"Synchronization in chaotic systems,\" Phys.\nRev. Lett. 64, 821-824 (1990).","L. M. Pecora and T. L. Carroll, \"Circuit implementation of synchronized\nchaos with applications to communications,\" Phys. Rev. A 44, (1991).","Special Issue on Chaos synchronization and control: Theory and\napplications, IEEE Trans. Circuits Syst. I, 44, (1997).","Special Issue on Control and synchronization of chaos, Int. J. Bifurc.\nChaos, 10, (2000).","C. Cruz-Hern├índez and H. Nijmeijer, \"Synchronization through filtering,\"\nInt. J. Bifurc. Chaos, 10, 763-775 (2000). Synchronization through\nextended Kalman filtering. In: Nijmeijer H, Fossen TI, editors. New trends\nin nonlinear observer design. Lecture notes in control and information\nsciences, 244 London: Springer; 469-490, (1999).","H. Sira-Ram├¡rez and C. Cruz-Hern├índez, \"Synchronization of chaotic\nsystems: a generalized Hamiltonian systems approach,\" Int. J. Bifurc.\nChaos, 11, 1381-1395 (2001). And in: Proceedings of the American\nControl Conference, Chicago, USA, 769-773 (2000).","D. L├│pez-Mancilla and C. Cruz-Hern├índez, \"Output synchronization of\nchaotic systems: model-matching approach with application to secure\ncommunication,\" Nonlinear Dynamics and Systems Theory, 5, 141-15\n(2005).","U. Feldmann, M. Hasler and W. Schwarz, \"Communication by chaotic\nsignals: the inverse system approach,\" Int. J. Circuits Theory and\nApplications, 24, 551-579 (1996).","H. Nijmeijer and I. M. Y. Mareels, \"An observer looks at synchronization,\"\nIEEE Trans. Circuits Syst. I, 44, 882-890 (1997).\n[10] K. M. Cuomo and A.V. Oppenheim, \"Circuit implementation of\nsynchronized chaos with applications to communications,\" Phys. Rev.\nLett., 71, 65-68 (1993).\n[11] K. M. Cuomo, A.V. Oppenheim and S. H. Strogatz, \"Synchronization of\nLorenz-based chaotic circuits with applications to communications,\" IEEE\nTrans. Circuits Syst. I, 40, 626-633 (1993).\n[12] C. Posadas-Castillo, C. Cruz-Hern├índez and R. N├║├▒ez, \"Experimental\nrealization of binary signals transmission based on synchronized Lorenz\ncircuits,\" J Appl Res Technol, 2, 127-137 (2004).\n[13] C. Cruz-Hern├índez, D. L├│pez-Mancilla, V. Garc├¡a, H. Serrano and R.\nN├║├▒ez, \"Experimental realization of binary signal transmission using\nchaos,\" J. Circ. Syst. Comput, 14, 453-468 (2005).\n[14]Parlitz U., Chua L.O., Kocarev Lj., Halle K.S. and Shang, A. (1992).\nTransmission of digital signals by chaotic synchronization. Int. J. Bifurc.\nChaos 2(4):973-977.\n[15] Yang T. and Chua L.O. (1996). Secure communication via chaotic\nparameter modulation. IEEE Trans. Circuits Syst. I 44(5):817-819.\n[16] Short K. (1996). Unmasking a modulated chaotic communication scheme.\nInt. J. Bifurc. Chaos 6(2):367-375.\n[17] Pérez G. and Cerdeira H.A. Extracting messages masked by chaos Phys.\nRev. Lett. 74:1970-1973. (1995)\n[18] Cruz-Hern├índez C., Posadas C. and Sira-Ram├¡rez H. Synchronization of\ntwo hyperchaotic Chua Circuits: a generalized Hamiltonian systems\napproach, IFAC-2002, Barcelona, Spain. (2002).\n[19] Cruz-Hern├índez C. Synchronization of Time-Delay Chua-s Oscillator\nwith Application to Secure Communication, Nonlinear Dynamics and\nSystems Theory, 4(1) (2004) 1-13.\n[20] G├ímez-Guzm├ín L. Cruz-Hern├índez, L├│pez-Gutiérrez R.M. Garc├¡a-\nGuerrero E.E. Synchronization of Chua-s circuits with multi-scroll\nattractors: Application to communication, Commun Nonlinear Sci Numer\nSimulat 14 (2009) 2765-2775.\n[21] Suykens JAK, Huang A, Chua LO. A family of n-scroll attractors from a\ngeneralized Chua-s circuit. Archiv Ekektron Uberttragungstech\n1997;51(3):131-8.\n[22] Cruz-Hern├índez C., Martynyuk A., Advances in chaotic dynamics with\napplications, Cambridge Scientific Publishers Ltd., Vol. 4, 2009."]}