Desain dan Simulasi Numerik Sinkronisasi Unidirectional Sirkuit Jerk Serta Aplikasinya pada Sistem Keamanan Komunikasi


Aceng Sambas(1*), Mada Sanjaya WS(2), Mustafa Mamat(3)

(1) Bolabot Techno Robotic Institute, CV. Sanjaya Star Group, Bandung, INDONESIA, Indonesia
(2) Jurusan Fisika, Fakultas Sains dan Teknologi Universitas Islam Negeri Sunan Gunung Djati Bandung, INDONESIA, Indonesia
(3) Faculty of Informatic and Computing, Universiti Zaenal Abidin, Kuala Terengganu, MALAYSIA, Malaysia
(*) Corresponding Author

Abstract


Sistem chaos mempunyai karakteristik unik yang nilainya sangat sensitif terhadap perubahan parameter dan kondisi awal, mirip dengan perilaku acak namun tetap deterministik. Chaos mempunyai potensi yang baik untuk dijadikan sistem keamanan komunikasi. Dalam makalah ini, kami menunjukkan  fenomena chaos dari sirkuit Jerk dengan modulus non-linier. Perilaku chaos ini berfungsi sebagai variabel parameter kontrol. Penelitian awal dalam makalah ini adalah menganalisis diagram fase, diagram bifurkasi dan peta Poincare dari sirkuit Jerk. Analisis sinkronisasi unidirectional antara dua sistem chaos yang identik juga telah disajikan dalam makalah ini. Berdasarkan hasil sinkronisasi chaos tersebut, akhirnya efektivitas sinkronisasi unidirectional antara dua sistem Jerk yang identik dalam sistem keamanan komunikasi menunjukkan potensi untuk dijadikan sebagai masking pengiriman data. Integrasi fisika teoritis, simulasi numerik menggunakan MATLAB serta implementasi simulasi sirkuit menggunakan MultiSIM telah dilakukan dalam makalah ini.

References


H. Zhang, “Chaos Synchronization and Its Application to Secure Communication,” PhD Thesis, University of Waterloo, Canada, 2010.

H. Jaenudin., A. Sambas., Halimatussadiyah., dan M. Sanjaya W.S., “ Analisis Chaotic Sistem Dinamika Tiga Bandul dan Tiga pegas,” Prosiding Konferensi Fisika I, vol. 1, no. 1, pp. 46-48, ISSN 2301-5284, 2012.

K. Nakajima, and Y. Sawada., “ Experimental Studies on the Weak Coupling of Oscillatory Chemical Reaction Systems,” J. Chem. Phys., vol. 72, no. 4, pp. 2231–2234, 1979.

J. L. Hindmarsh, and R. M. Rose, “A Model of Neuronal Bursting Using Three Coupled First Order Differential Equations,” Proceedings of the Royal Society of London. Series B. Biological Sciences. Vol. 221, No. 1222, pp. 87-102, 1984.

Ch. K. Volos, N. G. Bardis, I. M. Kyprianidis, and I. N. Stouboulos, “ Implementation of Mobile Robot by Using Double-Scroll Chaotic Attractors,” WSEAS Recent Researches in Applications of Electrical and Computer Engineering, Vouliagmeni Beach, Athens, Greece., pp. 119–124, 2012.

Ch. K. Volos, I. M. Kyprianidis and I. N. Stouboulos., “ Motion Control of Robots Using a Chaotic Truly Random Bits Generator,” Journal of Engineering Science and Technology Review,vol. 5, no. 2, pp. 6–11, 2012.

J. C. Sprott., “ Dynamical Models of Love,” Nonlinear Dyn. Psych. Life Sci., vol. 8, pp. 303–314, 2004.

M. Sanjaya W. S., I. Mohd, M. Mamat, and Z. Salleh., “Mathematical Model of Three Species Food Chain Interaction with Mixed Functional Response,” International Journal of Modern Physics: Conference Series, vol. 9, pp. 334–340, 2012.

M. Sanjaya W. S., M. Mamat, Z. Salleh., I. Mohd, and N. M. N. Noor., “Numerical Simulation Dynamical Model of Three Species Food Chain with Holling Type-II Functional Response,” Malaysian Journal of Mathematical Sciences, vol. 5, no. 1, pp. 1–12, 2011.

Ch. K. Volos, I. M. Kyprianidis, and I. N. Stouboulos, “Synchronization Phenomena in Coupled Nonlinear Systems Applied in Economic Cycles,” WSEAS Trans. Syst., vol. 11, no. 12, pp. 681–690, 2012.

T. L. Caroll, “ A Simple circuit demonstrating regular and synchronized chaos,” Am J Phys. vol. 63, no.4, pp. 377-379, 1995.

C.K. Volos, I.M. Kyprianidis, and I.N. Stouboulos, “Synchronization of two Mutually Coupled Duffing – type Circuits,” International Journal of Circuit, Systems and Signal processing. vol.1, no. 3, pp. 274-281, 2007.

M. Mamat, M. Sanjaya W.S, and D. S. Maulana, “Numerical Simulation Chaotic Synchronization of Chua Circuit and Its Application for Secure Communication,” Applied Mathematical Sciences, vol. 7, no. 1, pp. 1 – 10, 2013.

M. Mamat, M. Sanjaya.W.S, Z. Salleh, N.M Mohamad Noor, and M. F.Ahmad, “Numerical Simulation of Unidirectional Chaotic Synchronization of Non-Autonomous Circuit and Its Application for Secure Communication,” Adv. Studies Theor. Phys., vol. 6, no. 10, pp. 497 – 509, 2012.

M. Mamat, M., Z. Salleh., M. Sanjaya W. S., and I. Mohd, “The Dynamics of Chaotic FitzHugh-Nagumo Neuronal Systems,” Applied Mathematical Sciences, vol 6. no. 38, pp. 1863 – 1876, 2012.

M. Sanjaya, W. S., M. Mamat, Z. Salleh, and I Mohd., “Bidirectional Chaotic Synchronization of Hindmarsh-Rose Neuron Model,” Applied Mathematical Sciences, vol. 5, no. 54, pp. 2685 – 2695, 2011.

A. Sambas, M. Sanjaya W.S, and Halimatussadiyah, “Unidirectional Chaotic Synchronization of Rossler Circuit and Its Application for Secure Communication,” WSEAS Trans. Syst., vol. 11, no. 9, pp. 506-515, 2012.

L. M. Pecora, and T. L. Carroll, “Synchronization in Chaotic Systems,” Physical Review Letters, vol. 64, pp. 821–825, 1990.

K. M. Cuomo, and A. V. Oppenheim, “Circuit implementation of synchronized chaos with applications to communications,” Phys. Rev Lett., vol. 71, no. 1, pp. 65-68, 1993.

J. Z. Zhang, A. B. Wang, J. F. Wang, and Y. C. Wang, “Wavelength division multiplexing of chaotic secure and fiber-optic communications, Opt. Express. vol. 17, no. 8, pp. 6357–6367, 2009.

M.J. Rodriguez, R.J. Reategui, and A.N. Pisarchik., “Secure Communication Based on Chaotic Cipher and Chaos Synchronization,” Discontinuity, Nonlinearity and Complexity, vol. 1, pp. 57-68, 2012.

F. Rogister, A. Locquet, D. Pieroux, M. Sciamanna, O. Deparis, P. Mégret, and M. Blondel., “Secure communication scheme using chaotic laser diodes subject to incoherent optical feedback and incoherent optical injection,” Optics Letters. vol. 26, no. 19, pp. 1486-1488, 2001.

J. C. Sprott, “Simple Chaotic Systems and Circuits,” Am. J. Phys., vol. 68, pp. 758–763, 2000.

Q. H. Alsafasfeh, and M. S. Al-Arni., A New Chaotic Behavior from Lorenz and Rossler Systems and Its Electronic Circuit Implementation., Circuits and Systems, vol. 2, pp. 101–105, 2011.

A. Wolf., “ Quantity Chaos with Lyapunov Exponents,” Chaos, Princeton University Press, pp. 273-290, 1986.

R. Gencay, and Dechert W.D., “ An Algoritm For The n-Lyapunov Exponents Of An n-Dimensional Unknown Dynamical System,” Physica D, vol. 59, pp.142-157, 1992.

M. Sano, and Y. Sawada., “ Measurement of the Lyapunov Spectrum From a Chaotic Time Series,” Phys. Rev. Lett., vol. 55, pp. 1082 – 1085, 1985.

Z. Jing, D. Xu, Y. Chang, L. Chen, “ Bifurcations, Chaos, and System Collapse in a Three Node Power System, International Journal of Electrical Power & Energy Systems,” vol.25, no.6, pp. 443-461, 2003.

V. V. Bykov, “ On bifurcations Leading to Chaos in Chua's Circuit,” International Journal of Bifurcation and Chaos. vol 8, no. 4, pp. 685-699, 1998.


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