Bidirectional Coupling Scheme of Chaotic Systems and its Application in Secure Communication System

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internalnotes 1. J.L. Hindmarsh and R.M. Rose, A model of neuronal bursting using three coupled first order differential equations, Philosophical Transaction of the Royal Society of London, pp. 87-102 (1984). 2. Ch.K. Volos, N. Doukas, I.M. Kyprianidis, I.N. Stouboulus, and T.G. Kostis, Chaotic Autonomous Mobile Robot for Military Missions, In. Proc. Of the 17th Int. Conf. On Communication. WSEAS Recent Advances in Telecommunications and Circuit Design, Rhodes Island, Greece, pp. 197-202 (2013). 3. Ch. K. Volos, I. M. Kyprianidis, and I. N. Stouboulos, Α chaotic path planning generator for autonomous mobile robots, Robot. Auton. Syst., vol. 60, pp. 651-656 (2012). 4. 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(2), pp. 6-11 (2012). 5. J.C. Sprott, Dynamical models of love, Nonlinear Dyn. Psych. Life Sci., vol. 8, pp. 303-314 (2004). 6. 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). 7. 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(1), pp. 1-12 (2004). 8. 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(12) , pp. 681-690 (2012). 9. Ch.K. Volos, I.M. Kyprianidis, S.G. Stavrinides, I.N. Stouboulos, I. Magafas, and A.N. Anagnostopoulos, Nonlinear dynamics of a financial system from an engineer’s point of view, Journal of Engineering Science and Technology Review, vol. 4(3), pp.281-285 (2001). 10. J.H. García-López., R. Jaimes-Reategui., R. Chiu-Zarate., D. Lopez-Mancilla., R. Ramirez Jimenez, and A.N. Pisarchik, Secure computer communication based on chaotic Rössler oscillators, The Open Electrical and Electronic Engineering Journal, vol. 2, pp. 41-44 (2008). 11. 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(9), pp. 506-515 (2012). 12. A. Sambas, M. Sanjaya W.S., M. Mamat, and Halimatussadiyah, Design and analysis bidirectional chaotic synchronization of Rossler circuit and its application for secure communication, Applied Mathematical Sciences, vol. 7(1), pp.11-21 (2013). 13. I.M. Kyprianidis, Ch.K. Volos, I.N. Stouboulos, and J. Hadjidemetriou, Dynamics of two resistively coupled Duffing – type electrical oscillators, Int. J. Bifurc. Chaos, vol. 16, pp. 1765-1775 (2006). 14. T. Yamada and H. Fujisaka, Stability theory of synchronized motion in coup1ed oscillator systems II, Progress of Theoretical Physics, vol. 70, pp. 1240-1248 (1983). 15. V.S. Afraimovich, N.N. Verichev, and M.I. Rabinovich, Inv. Vuz, Rasiofiz, RPQAEC, vol. 29, pp. 795-803 (1986). 16. L. M. Pecora and T.L. Carroll, Synchronization in chaotic systems, Physical Review Letters, vol. 64, pp. 821-825 (1990). 17. A. Sambas., M. Sanjaya W.S., and M. Mamat, Design and numerical simulation of unidirectional chaotic synchronization and its application in secure communication system, Journal of Engineering Science and Technology Review, vol. 6(4), pp. 66- 73 (2013). 18. A. Sambas., M. Sanjaya W.S., M. Mamat, N.V. Karadimas, and O. Tacha, Numerical simulations in Jerk circuit and its application in a secure communication system, In. Proc. of the 17th Int. Conf. On Communication, WSEAS Recent Advances in Telecommunications and Circuit Design, Rhodes Island, Greece, pp. 190-196 (2013). 19. Ch.K. Volos, I.M. Kyprianidis, and I.N. Stouboulos, Experimental demonstration of a chaotic cryptographic scheme, WSEAS Trans. Circuits Syst, vol. 5, pp.1654-1661 (2006). 20. J.Z. Zhang, A.B. Wang, J.F. Wang, and Y.C. Wang, Wavelength division multiplexing of chaotic secure and fiber-optic communications, Optics Express, vol. 17(8), 6357-6367 (2009). 21. 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(1), pp. 57-68 (2012). 22. 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(19), pp. 1486-1488 (2001). 23. H.P. Ren, M.S. Baptista, and C. Grebogi, Wireless communication with chaos, Physical Review Letters, vol. 110(18), pp. 184101-184105 ( 2013). 24. J. C. Sprott, Simple Chaotic Systems and Circuits, Am. J. Phys, vol. 68, pp. 758-763 (2000). 25. A. Pandey, R.K. Baghel, and R.P. Singh. An autonomous chaotic circuit for wideband secure communication, International Journal of Engineering, Business and Enterprise Applications, vol 4(1), pp. 44-47 (2013). 26. A. Pandey, R.K. Baghel and R.P. Singh, Analysis and circuit realization of a new autonomous chaotic system, International Journal of Electronics and Communication Engineering, vol. 5(4), pp. 487-495 (2012). 27. 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). 28. A. Wolf, 1986, Quantity chaos with Lyapunov exponents, Chaos, Princeton University Press, pp. 273-290 (1986). 29. R. Gencay, and W.D. Dechert, An algoritm for The n-Lyapunov exponents of an n-dimensional unknown dynamical system, Physica D, vol. 59, pp.142-157 (1992). 30. M. Sano and Y. Sawada, Measurement of the Lyapunov spectrum from a chaotic time series. Phys. Rev. Lett, vol. 55, pp. 1082-1085 (1985). 31. X.-F. Li, K.E. Chlouverakis, and D.-L. Xu, Nonlinear dynamics and circuit realization of a new chaotic flow: A variant of Lorenz, Chen and Lü, Nonlinear Analysis: Real World Application, vol. 10, pp. 2357-2368 (2009). 32. F. Han, Multi-scroll chaos generation via linear systems and hysteresis function series, PhD thesis, Royal Melbourne Institute of Technology University, Australia, (2004). 33. V.V. Bykov, On bifurcations leading to chaos in Chua's circuit, International Journal of Bifurcation and Chaos, vol. 8(4), pp.685-699 (1998). 34. S.X. Wang, Simulation of chaos synchronization, PhD thesis, University Western Ontario, London (1998). 35. R.M. Harris, E.Marder, A.I. Selverston, and M. Moulins, The stomatogastric nervous system: A model biological neural network, Cambridge, MIT Press (1992).
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spelling 11930 https://intelek.unisza.edu.my/intelek/pages/view.php?ref=11930 https://intelek.unisza.edu.my/intelek/pages/search.php?search=!collection407072 Restricted Document Article Journal application/pdf Adobe Acrobat Pro DC 20 Paper Capture Plug-in with ClearScan 8 1.7 Adobe Acrobat Pro DC 20.6.20042 2024-08-26 17:46:29 6231-01-FH02-FIK-15-03330.pdf UniSZA Private Access Bidirectional Coupling Scheme of Chaotic Systems and its Application in Secure Communication System Journal of Engineering Science and Technology Review In this paper, in order to show some interesting phenomena of three dimensional autonomous ordinary differential equations, the chaotic behavior as a function of a variable control parameter, has been studied. The initial study in this paper is to analyze the phase portraits, the Lyapunov exponents, the Poincaré maps and the bifurcation diagrams. Moreover, some appropriate comparisons are made to contrast some of the existing results. Finally, the effectiveness of the bidirectional coupling scheme between two identical Jerk circuits in a secure communication system is presented in details. Finally, the simulation results are shown to demonstrate that the proposed method is correct and feasible. 8 2 89-95 1. J.L. Hindmarsh and R.M. Rose, A model of neuronal bursting using three coupled first order differential equations, Philosophical Transaction of the Royal Society of London, pp. 87-102 (1984). 2. Ch.K. Volos, N. Doukas, I.M. Kyprianidis, I.N. Stouboulus, and T.G. Kostis, Chaotic Autonomous Mobile Robot for Military Missions, In. Proc. Of the 17th Int. Conf. On Communication. WSEAS Recent Advances in Telecommunications and Circuit Design, Rhodes Island, Greece, pp. 197-202 (2013). 3. Ch. K. Volos, I. M. Kyprianidis, and I. N. Stouboulos, Α chaotic path planning generator for autonomous mobile robots, Robot. Auton. Syst., vol. 60, pp. 651-656 (2012). 4. 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(2), pp. 6-11 (2012). 5. J.C. Sprott, Dynamical models of love, Nonlinear Dyn. Psych. Life Sci., vol. 8, pp. 303-314 (2004). 6. 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). 7. 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(1), pp. 1-12 (2004). 8. 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(12) , pp. 681-690 (2012). 9. Ch.K. Volos, I.M. Kyprianidis, S.G. Stavrinides, I.N. Stouboulos, I. Magafas, and A.N. Anagnostopoulos, Nonlinear dynamics of a financial system from an engineer’s point of view, Journal of Engineering Science and Technology Review, vol. 4(3), pp.281-285 (2001). 10. J.H. García-López., R. Jaimes-Reategui., R. Chiu-Zarate., D. Lopez-Mancilla., R. Ramirez Jimenez, and A.N. Pisarchik, Secure computer communication based on chaotic Rössler oscillators, The Open Electrical and Electronic Engineering Journal, vol. 2, pp. 41-44 (2008). 11. 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(9), pp. 506-515 (2012). 12. A. Sambas, M. Sanjaya W.S., M. Mamat, and Halimatussadiyah, Design and analysis bidirectional chaotic synchronization of Rossler circuit and its application for secure communication, Applied Mathematical Sciences, vol. 7(1), pp.11-21 (2013). 13. I.M. Kyprianidis, Ch.K. Volos, I.N. Stouboulos, and J. Hadjidemetriou, Dynamics of two resistively coupled Duffing – type electrical oscillators, Int. J. Bifurc. Chaos, vol. 16, pp. 1765-1775 (2006). 14. T. Yamada and H. Fujisaka, Stability theory of synchronized motion in coup1ed oscillator systems II, Progress of Theoretical Physics, vol. 70, pp. 1240-1248 (1983). 15. V.S. Afraimovich, N.N. Verichev, and M.I. Rabinovich, Inv. Vuz, Rasiofiz, RPQAEC, vol. 29, pp. 795-803 (1986). 16. L. M. Pecora and T.L. Carroll, Synchronization in chaotic systems, Physical Review Letters, vol. 64, pp. 821-825 (1990). 17. A. Sambas., M. Sanjaya W.S., and M. Mamat, Design and numerical simulation of unidirectional chaotic synchronization and its application in secure communication system, Journal of Engineering Science and Technology Review, vol. 6(4), pp. 66- 73 (2013). 18. A. Sambas., M. Sanjaya W.S., M. Mamat, N.V. Karadimas, and O. Tacha, Numerical simulations in Jerk circuit and its application in a secure communication system, In. Proc. of the 17th Int. Conf. On Communication, WSEAS Recent Advances in Telecommunications and Circuit Design, Rhodes Island, Greece, pp. 190-196 (2013). 19. Ch.K. Volos, I.M. Kyprianidis, and I.N. Stouboulos, Experimental demonstration of a chaotic cryptographic scheme, WSEAS Trans. Circuits Syst, vol. 5, pp.1654-1661 (2006). 20. J.Z. Zhang, A.B. Wang, J.F. Wang, and Y.C. Wang, Wavelength division multiplexing of chaotic secure and fiber-optic communications, Optics Express, vol. 17(8), 6357-6367 (2009). 21. 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(1), pp. 57-68 (2012). 22. 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(19), pp. 1486-1488 (2001). 23. H.P. Ren, M.S. Baptista, and C. Grebogi, Wireless communication with chaos, Physical Review Letters, vol. 110(18), pp. 184101-184105 ( 2013). 24. J. C. Sprott, Simple Chaotic Systems and Circuits, Am. J. Phys, vol. 68, pp. 758-763 (2000). 25. A. Pandey, R.K. Baghel, and R.P. Singh. An autonomous chaotic circuit for wideband secure communication, International Journal of Engineering, Business and Enterprise Applications, vol 4(1), pp. 44-47 (2013). 26. A. Pandey, R.K. Baghel and R.P. Singh, Analysis and circuit realization of a new autonomous chaotic system, International Journal of Electronics and Communication Engineering, vol. 5(4), pp. 487-495 (2012). 27. 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). 28. A. Wolf, 1986, Quantity chaos with Lyapunov exponents, Chaos, Princeton University Press, pp. 273-290 (1986). 29. R. Gencay, and W.D. Dechert, An algoritm for The n-Lyapunov exponents of an n-dimensional unknown dynamical system, Physica D, vol. 59, pp.142-157 (1992). 30. M. Sano and Y. Sawada, Measurement of the Lyapunov spectrum from a chaotic time series. Phys. Rev. Lett, vol. 55, pp. 1082-1085 (1985). 31. X.-F. Li, K.E. Chlouverakis, and D.-L. Xu, Nonlinear dynamics and circuit realization of a new chaotic flow: A variant of Lorenz, Chen and Lü, Nonlinear Analysis: Real World Application, vol. 10, pp. 2357-2368 (2009). 32. F. Han, Multi-scroll chaos generation via linear systems and hysteresis function series, PhD thesis, Royal Melbourne Institute of Technology University, Australia, (2004). 33. V.V. Bykov, On bifurcations leading to chaos in Chua's circuit, International Journal of Bifurcation and Chaos, vol. 8(4), pp.685-699 (1998). 34. S.X. Wang, Simulation of chaos synchronization, PhD thesis, University Western Ontario, London (1998). 35. R.M. Harris, E.Marder, A.I. Selverston, and M. Moulins, The stomatogastric nervous system: A model biological neural network, Cambridge, MIT Press (1992).
spellingShingle Bidirectional Coupling Scheme of Chaotic Systems and its Application in Secure Communication System
summary In this paper, in order to show some interesting phenomena of three dimensional autonomous ordinary differential equations, the chaotic behavior as a function of a variable control parameter, has been studied. The initial study in this paper is to analyze the phase portraits, the Lyapunov exponents, the Poincaré maps and the bifurcation diagrams. Moreover, some appropriate comparisons are made to contrast some of the existing results. Finally, the effectiveness of the bidirectional coupling scheme between two identical Jerk circuits in a secure communication system is presented in details. Finally, the simulation results are shown to demonstrate that the proposed method is correct and feasible.
title Bidirectional Coupling Scheme of Chaotic Systems and its Application in Secure Communication System
title_full Bidirectional Coupling Scheme of Chaotic Systems and its Application in Secure Communication System
title_fullStr Bidirectional Coupling Scheme of Chaotic Systems and its Application in Secure Communication System
title_full_unstemmed Bidirectional Coupling Scheme of Chaotic Systems and its Application in Secure Communication System
title_short Bidirectional Coupling Scheme of Chaotic Systems and its Application in Secure Communication System
title_sort bidirectional coupling scheme of chaotic systems and its application in secure communication system