Services on Demand
Journal
Article
Indicators
- Cited by SciELO
- Access statistics
Related links
- Similars in SciELO
Share
Journal of applied research and technology
On-line version ISSN 2448-6736Print version ISSN 1665-6423
J. appl. res. technol vol.7 n.1 Ciudad de México Apr. 2009
Automatic synthesis of 2Dnscrolls chaotic systems by behavioral modeling
J. M. MuñozPacheco*1, E. TleloCuautle2
1,2 Department of Electronics, INAOE, Luis Enrique Erro No. 1, Tonantzintla, Puebla, 72840 MEXICO; Tel/Fax: 522222470517; *Email: mpacheco@inaoep.mx, e.tlelo@ieee.org
ABSTRACT
This paper introduces the guidelines to synthesize 2D chaotic systems by means of highlevel descriptions. The aim of this investigation is to synthesize 2Dnscrolls chaotic systems based on saturated functions with multisegments. The new methodology of circuit synthesis is performed by three hierarchical levels. First, the 2D chaotic oscillator is numerically simulated at the electronic system level by applying state variables and piecewiselinear approximation. Second, the excursion levels of the chaotic signals are scaled to control the breaking points and slopes of the saturated functions within practical values. Additionally, the frequency scaling of 2Dnscrolls chaotic attractors is performed. Finally, current and voltage saturated functions are synthesized using VerilogA models for the operational amplifiers and in this manner a 2D chaotic system is synthesized using operational amplifiers to generate 2Dnscrolls attractors. Numerical results are confirmed by HSPICE simulations to show the usefulness of the proposed synthesis approach.
Keywords: Chaos, 2Dnscroll attractors, behavioral modeling, circuit synthesis, opamp.
RESUMEN
El presente artículo introduce una guía para sintetizar sistemas caóticos en 2D a través de descripciones de alto nivel. El objetivo de esta investigación es sintetizar sistemas caóticos de 2Dnenrollamientos basados en funciones saturadas con multisegmentos. La nueva metodología para síntesis de circuitos se desarrolla en tres niveles jerárquicos. Primero, el oscilador caótico en 2D se simula numéricamente a nivel de sistema electrónico aplicando variables de estado y aproximación lineal a tramos. Segundo, los niveles de excursión de las señales caóticas se escalan para controlar los puntos de rompimiento y las pendientes de las funciones saturadas dentro de valores prácticos. Adicionalmente, se desarrolla un escalamiento en frecuencia de los atractores caóticos de 2Dnenrollamientos. Finalmente, las funciones saturadas de corriente y voltaje se sintetizan usando modelos en VerilogA de amplificadores operacionales para que de esta manera se sintetice un sistema caótico en 2D usando amplificadores operacionales para generar atractores de 2Dnenrollamientos. Los resultados numéricos se confirman con simulaciones en HSPICE para mostrar la utilidad del enfoque de síntesis propuesta.
DESCARGAR ARTÍCULO EN FORMATO PDF
Acknowledgment
J.M. MuñozPacheco acknowledges CONACyT for support granted through Ph. D. scholarship #204409. This research is supported by CONACyT/MEXICO under project number 48396Y.
References
[1] JiHuan He, Nonlinear science as a fluctuating research frontier, Chaos, Solitons & Fractals, In Press, Available online 9 October (2008). [ Links ]
[2] Zelinka, G.R. Chen, S. Celikovsky, Chaos synthesis by means of evolutionary algorithms, International Journal of Bifurcation and Chaos, vol. 18, no. 4, pp. 911942, (2008). [ Links ]
[3] J. Lu, G. Chen, Generating multiscroll chaotic attractors: theories, methods and applications, Int. J. Bifurcat. Chaos, vol. 16, no. 4, pp. 775858, (2006). [ Links ]
[4] Jinhu Lü, K. Muralib, Sudeshna Sinhac, Henry Leungd and M.A. AzizAlaouie, Generating multiscroll chaotic attractors by thresholding, Physics Letters A, vol. 372, no. 18, pp. 32343239, (2008). [ Links ]
[5] F.Q. Wang, C.X. Liu, Generation of multiscroll chaotic attractors via the sawtooth function, International Journal of Modern Physics B, vol. 22, no. 15, pp. 23992405, (2008). [ Links ]
[6] W. Liu, W.K.S. Tang, G. Chen, 2x2scroll attractors generated in a threedimensional smooth autonomous system, International Journal of Bifurcation and Chaos, Volume: 17, Issue: 11, Pages: 41534157, (2007). [ Links ]
[7] E. TleloCuautle, J.M. MuñozPacheco, Numerical simulation of Chua's circuit oriented to circuit synthesis, International Journal of Nonlinear Sciences and Numerical Simulation, vol. 8, no. 2, pp. 249256, (2007) [ Links ].
[8] J. Lu, G. Chen, Design and Analysis of Multiscroll Chaotic Attractors from Saturated Function Series, IEEE TCASI, vol. 51, no. 12, pp. 24762490, (2004). [ Links ]
[9] C. Liu, T. Liu, L. Liu, Y. Su, A New Nonlinear Chaotic System, International Journal of Nonlinear Sciences and Numerical Simulation, vol. 7, no. 3, pp. 345352, (2006). [ Links ]
[10] D. Cafagna, G. Grassi, Adomian decomposition for studying hyperchaotic 2Dscroll attractors with application to synchronization, IEICE Transactions on Fundamentals of Electronics Communications and Computer Sciences, vol. E89A, no. 10, pp. 27522758, (2006). [ Links ]
[11] C. CruzHernandez, A.A. Martynyuk, Advance in chaotic dynamics with applications, Cambridge Scientific Publishers Ltd., (2008) in press. [ Links ]
[12] L. GamezGuzman, C. CruzHernandez, R.M. LopezGutierrez, Synchronization of multiscroll chaos generators: application to private communication, Revista Mexicana de Fisica, vol. 54, no. 4, pp. 299305, (2008). [ Links ]
[13] D. Materassi, M. Basso, Time scaling of chaotic systems: Application to secure communications, International Journal of Bifurcation and Chaos, vol. 18, no. 2, pp. 567575, (2008). [ Links ]
[14] M.E. Yalcin, Increasing the entropy of a random number generator using nscroll chaotic attractors, International Journal of Bifurcation and Chaos, vol. 17, no. 12, pp. 44714479, (2007). [ Links ]
[15] ChuanKuei Huang, ShuhChuan Tsay and YuRen Wu, Implementation of chaotic secure communication systems based on OPA circuits, Chaos, Solitons & Fractals, vol. 23, no. 2, pp. 589600, (2005). [ Links ]
[16] M. Romera, M. Small, M.F. Danca, Deterministic and random synthesis of discrete chaos, Applied Mathematics and Computation, vol. 192, no. 1, pp. 283297, (2007). [ Links ]
[17] W.J. Zhou, S.M. Yu, Design and implementation of chaotic generators based on IEEE754 standard and field programmable gate array technology, Acta Physica Sinica, vol. 57, no. 8, pp. 47384747, (2008). [ Links ]
[18] R. NúñezPérez, Measurement of Chua chaos and its applications, Journal of Applied Research and Technology, vol. 6, no. 1, pp. 4553, (2008). [ Links ]
[19] C. PosadasCastillo, C. CruzHernández, R. NúnezPérez, Experimental realization of binary signals transmission based on synchronized Lorenz circuits, Journal of Applied Research and Technology, vol. 2, no. 2, pp. 127157, (2002). [ Links ]
[20] A.Y. AguilarBustos, C. CruzHernández, R.M. LópezGutiérrez, E. TleloCuautle, C. Posadas Castillo, Hyperchaotic Encryption for Secure EMail Communication, Book Chapter in Emergent Web Intelligence, Richard Chbeir (Eds.), in press (2009). [ Links ]
[21] G.Y. Qi, G.R. Chen, Y.H. Zhang, On a new asymmetric chaotic system. Chaos, Solitons and Fractals, vol. 37, no. 2, pp. 409423, (2008). [ Links ]
[22] C. SánchezLópez, A. CastroHernández, A. PérezTrejo, Experimental Verification of the Chua's Circuit Designed with UGCs. IEICE Electron. Express vol. 5, no. 17, pp. 657661, (2008). [ Links ]
[23] E. TleloCuautle, A. GaonaHernández, J. GarcíaDelgado, Implementation of a chaotic oscillator by designing Chua's diode with CMOS CFOAs. Analog Integrated Circuits and Signal Processing, vol. 48, no. 2, pp. 159162, (2006). [ Links ]
[24] J.H. Zhang, W. Zhang, M.H. Yao, X.Y. Guo MultiPulse Shilnikov Chaotic Dynamics for a NonAutonomous Buckled Thin Plate under Parametric Excitation, International Journal of Nonlinear Sciences and Numerical Simulation, vol. 9, no. 4, 381394, (2008). [ Links ]
[25] J.M. MuñozPacheco, E. TleloCuautle, Synthesis of n Scroll Attractors using Saturated Functions from HighLevel Simulation, Journal of PhysicsConference series, vol. 96, no. 1, February (2008). DOI: 10.1088/17426596/96/1/012050. [ Links ]
[26] Behnam Ghavami, Hossein Pedram, Mehrdad Najibi, An EDA tool for implementation of low power and secure cryptochips Computers & Electrical Engineering, In Press, Corrected Proof, Available online 11 October (2008) [ Links ]
[27] K. S. Kundert and O. Zinke, The designer's guide to Verilog AMS Kluwer Academic Publishers, (2004). [ Links ]
[28] R.A. Rutenbar, G. Gielen, J. Roychowdhury, Hierarchical Modeling, Optimization, and Synthesis for SystemLevel Analog and RF Designs, Proceedings of the IEEE, vol. 95, no. 3, pp. 640669, (2007). [ Links ]
[29] E. TleloCuautle, M.A. DuarteVillaseñor, J.M. GarcíaOrtega, C. SánchezLópez, Designing SRCOs by combining SPICE and VerilogA, International Journal of Electronics, vol. 94, no. 4, pp. 373379, April (2007). [ Links ]
[30] E. TleloCuautle, J.M. Muñozpacheco, Automatic simulation of 1D and 2D chaotic oscillators, Journal of Physics: Conference Series, vol. 96, no. 1, February (2008). DOI: 10.1088/17426596/96/1/012059. [ Links ]
[31] E. TleloCuautle, J.M. MuñozPacheco, J. MartínezCarballido, Frequencyscaling simulation of Chua's circuit by automatic determination and control of stepsize, Applied Mathematics and Computation, vol. 194, no. 2, pp. 486491, (2007). [ Links ]
[32] J.M. MuñozPacheco, E. TleloCuautle, R. TrejoGuerra, C. CruzHernández; Synchronization of nScrolls Chaotic Systems Synthesized from HighLevel Behavioral Modeling, Proceedings of the 7th International Caribbean Conference on Devices, Circuits and Systems, Mexico, Apr. 2830, (2008). [ Links ]
[33] http://focus.ti.com/docs/prod/folders/print/tlc2262.html [ Links ]