Electronic Operation of Chaotic Systems: Part 1, Quadratic Analogues
DOI:
https://doi.org/10.29105/ingenierias25.92-55Keywords:
Chaotic systems, Analog computation, Operational amplifiers, Quadratic nonlinearityAbstract
Some applications of chaotic systems require their implementation through analog or digital electronics. In this first part, the electronic realization of some well-known chaotic systems with quadratic nonlinearities is summarized, by means of circuits with multipliers and operational amplifiers. The equivalence of its variables and electronic components with the normalized variables and parameters of chaotic mathematical models is demonstrated. In addition, the behavior of each circuit is compared to simulations of their mathematical models. In the following parts of this work, the electronic realization of piecewise linear chaotic systems and implementation in digital devices will be shown.
Downloads
Metrics
References
Lorenz, E.N. Deterministic Nonperiodic Flow. Journal of the Atmospheric Sciences, (1963) 20: 130-141. DOI: https://doi.org/10.1175/1520-0469(1963)020<0130:DNF>2.0.CO;2
Kevin M. Cuomo and Alan V. Oppenheim. Circuit implementation of Synchronized Chaos with Applications to Communications. Physical Review Letters. (1993) 71(65). DOI: https://doi.org/10.1103/PhysRevLett.71.65
Olivares, D. Aplicación de sistemas caóticos en control automático. Tesis, Universidad Autónoma de Nuevo León, San Nicolás de los Garza, NL, México. (1994).
Pecora, L. M., Carroll, T. L., Johnson, G. A., Mar, D. J., and Heagy, J. F. Fundamentals of synchronization in chaotic systems, concepts, and applications. Chaos: An Interdisciplinary Journal of Nonlinear Science. (1997) 7(4): 520-543. DOI: https://doi.org/10.1063/1.166278
Jaimes-Reátegui, R. et. al. Secure optoelectronic communication using laser diode by chaotic Rössler circuits. Journal of Physics: Conference Series. (2001) 274: 012024. DOI: https://doi.org/10.1088/1742-6596/274/1/012024
García-Lopez, J. H. et. al. Novel communication scheme based on chaotic Rössler circuits. Journal of Physics: Conference Series. (2005) 23: 029 DOI: https://doi.org/10.1088/1742-6596/23/1/029
García-López, J. H. et. al. Synchronization of chaotic systems with coexisting attractors. Physical Review Letters. (2006) 96(24): 244102. DOI: https://doi.org/10.1103/PhysRevLett.96.244102
Rodriguez-Liñan, A., de León Morales, J. Sincronización de caos mediante observadores para cifrado en comunicaciones. Ingenierías. (2007) 10(34): 44-50.
Rössler, O. E. An equation for continuous chaos. Physics Letters A. (1976) 57(5): 397-398. DOI: https://doi.org/10.1016/0375-9601(76)90101-8
Braun, T. and Heisler, I. A. A comparative investigation of controlling chaos in a Rössler system. Physica A: Statistical Mechanics and its Applications. (2000) 283: 136-19. DOI: https://doi.org/10.1016/S0378-4371(00)00140-0
L. Pecora, T. Caroll, & J. Heagy. Synchronization in Chaotic Systems, Concepts and Applications. (2006). DOI: https://doi.org/10.1002/3527607455.ch10
Chiu, R., Mora-González, M., and Lopez-Mancilla, D. Osciladores Caóticos implementados en Microcontrolador PIC18F. Nova scientia. (2013) 6(12): 60-77. DOI: https://doi.org/10.21640/ns.v6i12.24
P. Salas C. Análisis y diseño de sistemas caóticos clásicos con base en filtros pasa-bajas. Tesis, Universidad Autónoma de San Luis Potosí, San Luis Potosí, México (2018).
Wang, M.J. Chaotic Control of Lü System via Three Methods. International Journal of Modern Nonlinear Theory and Application, (2014) 3: 29-36. DOI: https://doi.org/10.4236/ijmnta.2014.32005
Malasoma, J.M. A new class of minimal chaotic flows. Physics Letters A, 2002; 305: 52-58. DOI: https://doi.org/10.1016/S0375-9601(02)01412-3
Hambley, A.R., Electronics, (2000) Upper Saddle River, N.J., Prentice Hall.
Lü, J. and Chen, G. A New Chaotic Attractor Coined. International Journal of Bifurcation and Chaos, (2002) 12, 659-661. DOI: https://doi.org/10.1142/S0218127402004620
Chen, G. and Ueta, T. Yet Another Chaotic Attractor. International Journal of Bifurcation and Chaos, (1999) 9, 1465-1466. DOI: https://doi.org/10.1142/S0218127499001024
Pehli̇van İ, Kurt E, Lai̇ Q, Basaran A, Kutlu M. A Multiscroll Chaotic Attractor and its Electronic Circuit Implementation, Chaos Theory and Applications. 2019; 1(1): 29-37.
Méndez-Ramírez, R., Cruz-Hernández, C., Arellano-Delgado, A. and Martínez-Clark, R. A new simple chaotic Lorenz-type system and its digital realization using a TFT touch-screen display embedded system. Complexity, 2017(6820492): 1–13. DOI: https://doi.org/10.1155/2017/6820492
Downloads
Published
How to Cite
Issue
Section
License
Copyright (c) 2022 Francisco Antonio Rodríguez Cruz, César de Jesús Chacón Rendón, Angel Rodriguez-Liñan
This work is licensed under a Creative Commons Attribution 4.0 International License.
