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Year 2020, Volume: 8 Issue: 4, 355 - 360, 30.10.2020

Şuayb Çağrı Yener Reşat Mutlu Ertuğrul Karakulak

https://doi.org/10.17694/bajece.624645
Cited By: 1

Abstract

References

  • E. N. Lorenz and E. N. Lorenz, “Deterministic Nonperiodic Flow,” J. Atmos. Sci., vol. 20, no. 2, pp. 130–141, Mar. 1963.
  • H. Haken, “Analogy between higher instabilities in fluids and lasers,” Phys. Lett. A, vol. 53, no. 1, pp. 77–78, May 1975.
  • E. Knobloch, “CHAOS IN THE SEGMENTED DISC DYNAMO,” Phys. Lett., vol. 82A, no. 9, pp. 439–440, 1981.
  • N. Hemati, “Strange attractors in brushless DC motors,” IEEE Trans. Circuits Syst. I Fundam. Theory Appl., vol. 41, no. 1, pp. 40–45, 1994.
  • D. Poland, “Cooperative catalysis and chemical chaos: a chemical model for the Lorenz equations,” Phys. D Nonlinear Phenom., vol. 65, no. 1–2, pp. 86–99, May 1993.
  • S. I. Tzenov, “Strange Attractors Characterizing the Osmotic Instability,” Jun. 2014.
  • K. Cho and T. Miyano, “Chaotic cryptography using augmented lorenz equations aided by quantum key distribution,” IEEE Trans. Circuits Syst. I Regul. Pap., vol. 62, no. 2, pp. 478–487, Feb. 2015.
  • X. Zhang and Y. Qi, “Design of an assemble-type fractional-order unit circuit and its application in Lorenz system,” IET Circuits, Devices Syst., vol. 11, no. 5, pp. 437–445, Sep. 2017.
  • S. H. Strogatz and A. V. Oppenheim, “Synchronization of Lorenz-Based Chaotic Circuits with Applications to Communications,” IEEE Trans. Circuits Syst. II Analog Digit. Signal Process., vol. 40, no. 10, pp. 626–633, 1993.
  • M. Kaur and V. Kumar, “Efficient image encryption method based on improved Lorenz chaotic system,” Electron. Lett., vol. 54, no. 9, pp. 562–564, May 2018.
  • 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, Jul. 1993.
  • J. N. Blakely, M. B. Eskridge, and N. J. Corron, “A simple Lorenz circuit and its radio frequency implementation,” Chaos An Interdiscip. J. Nonlinear Sci., vol. 17, no. 2, p. 023112, Jun. 2007.
  • O. A. Gonzales, G. Han, J. P. de Gyvez, and E. Sanchez-Sinencio, “Lorenz-based chaotic cryptosystem: a monolithic implementation,” IEEE Trans. Circuits Syst. I Fundam. Theory Appl., vol. 47, no. 8, pp. 1243–1247, 2000.
  • A. G. Radwan, A. M. Soliman, and A. El-Sedeek, “MOS realization of the modified Lorenz chaotic system,” Chaos, Solitons & Fractals, vol. 21, no. 3, pp. 553–561, Jul. 2004.
  • S. C. Yener, R. Mutlu, T. Yener, and H. H. Kuntman, “Memristor-based timing circuit,” in 2017 Electric Electronics, Computer Science, Biomedical Engineerings’ Meeting, EBBT 2017, 2017, pp. 1–3.
  • Y. Babacan, A. Yesil, and F. Gul, “The Fabrication and MOSFET-Only Circuit Implementation of Semiconductor Memristor,” IEEE Trans. Electron Devices, vol. 65, no. 4, pp. 1625–1632, Apr. 2018.
  • C. P. Uzunoglu, Y. Babacan, F. Kacar, and M. Ugur, “Modeling and Suppression of Chaotic Ferroresonance in a Power System by Using Memristor-based System,” Electr. Power Components Syst., vol. 44, no. 6, pp. 638–645, Apr. 2016.
  • Ş. Ç. Yener and H. H. Kuntman, “Fully CMOS memristor based chaotic circuit,” Radioengineering, vol. 23, no. 4, 2014.
  • erdem uçar, ertuğrul karakulak, and reşat mutlu, “ANN Circuit Application of Complementary Resistive Switches,” Balk. J. Electr. Comput. Eng., vol. 7, no. 1, pp. 34–43, Jan. 2019.
  • A. YESIL and Y. BABACAN, “Implementation of Electronically Controllable Memristor Based Chua Circuit,” J. Inst. Sci. Technol., vol. 9, no. 1, pp. 121–129, Mar. 2019.
  • S. Arık and R. Kılıç, “RECONFIGURABLE HARDWARE PLATFORM FOR EXPERIMENTAL TESTING AND VERIFYING OF MEMRISTOR-BASED CHAOTIC SYSTEMS,” J. Circuits, Syst. Comput., vol. 23, no. 10, p. 1450145, Dec. 2014.
  • F. R. Tahir, R. Ali, and L. Fortuna, “ANALOG PROGRAMMABLE ELECTRONIC CIRCUIT-BASED CHAOTIC LORENZ SYSTEM,” Basrah J. Eng. Sci., vol. 14, no. 1, 2014.
  • S. C. Yener, C. Barbaros, R. Mutlu, and E. Karakulak, “Implementation of Microcontroller-Based Memristive Chaotic Circuit,” Acta Phys. Pol. A, vol. 132, no. 3–II, pp. 1058–1061, 2017.
  • Ş. Ç. Yener, C. Barbaros, R. MUTLU, and E. Karakulak, “Design of a Microcontroller-Based Chaotic Circuit of Lorenz Equations,” in International Conference on Science and Technology ICONST 2018 5-9 September 2018 Prizren - KOSOVO, 2018, pp. 612–615.

Implementation of a Microcontroller-Based Chaotic Circuit of Lorenz Equations

Year 2020, Volume: 8 Issue: 4, 355 - 360, 30.10.2020

Şuayb Çağrı Yener Reşat Mutlu Ertuğrul Karakulak

https://doi.org/10.17694/bajece.624645
Cited By: 1

Abstract

Lorenz equations are commonly used in chaos
education and studies. Simulation programs can be used to produce solutions of
Lorenz equations and to examine its chaotic waveforms. However, sometimes a
chaotic signal source can be needed. Such a circuit can be made using either
analog or digital circuit components. Recently, a microcontroller-based circuit
is suggested to obtain chaotic waveforms of Lorenz equations however only
simulations are used to show proof of concept. Such circuit needs experimental
verification. In this paper, implementation and experimental verification of
the microcontroller-based circuit which solves Lorenz equations in real time
and produces its chaotic waveforms are presented. Runge-Kutta method is used to
solve the equation system. By using Proteus, microcontroller-based chaotic
circuit is simulated and designed. Presented design has been implemented using
an Arduino Mega 2560 R3 microcontroller. The microcontroller sends the chaotic signals
to the outputs of the circuit using digital-to-analog converters. The waveforms
acquired experimentally from the implemented circuit matches well with those
obtained from Proteus simulations.

Keywords

Chaotic circuits Lorenz Equations microcontroller based circuit implementation Runge-kutta method

References

  • E. N. Lorenz and E. N. Lorenz, “Deterministic Nonperiodic Flow,” J. Atmos. Sci., vol. 20, no. 2, pp. 130–141, Mar. 1963.
  • H. Haken, “Analogy between higher instabilities in fluids and lasers,” Phys. Lett. A, vol. 53, no. 1, pp. 77–78, May 1975.
  • E. Knobloch, “CHAOS IN THE SEGMENTED DISC DYNAMO,” Phys. Lett., vol. 82A, no. 9, pp. 439–440, 1981.
  • N. Hemati, “Strange attractors in brushless DC motors,” IEEE Trans. Circuits Syst. I Fundam. Theory Appl., vol. 41, no. 1, pp. 40–45, 1994.
  • D. Poland, “Cooperative catalysis and chemical chaos: a chemical model for the Lorenz equations,” Phys. D Nonlinear Phenom., vol. 65, no. 1–2, pp. 86–99, May 1993.
  • S. I. Tzenov, “Strange Attractors Characterizing the Osmotic Instability,” Jun. 2014.
  • K. Cho and T. Miyano, “Chaotic cryptography using augmented lorenz equations aided by quantum key distribution,” IEEE Trans. Circuits Syst. I Regul. Pap., vol. 62, no. 2, pp. 478–487, Feb. 2015.
  • X. Zhang and Y. Qi, “Design of an assemble-type fractional-order unit circuit and its application in Lorenz system,” IET Circuits, Devices Syst., vol. 11, no. 5, pp. 437–445, Sep. 2017.
  • S. H. Strogatz and A. V. Oppenheim, “Synchronization of Lorenz-Based Chaotic Circuits with Applications to Communications,” IEEE Trans. Circuits Syst. II Analog Digit. Signal Process., vol. 40, no. 10, pp. 626–633, 1993.
  • M. Kaur and V. Kumar, “Efficient image encryption method based on improved Lorenz chaotic system,” Electron. Lett., vol. 54, no. 9, pp. 562–564, May 2018.
  • 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, Jul. 1993.
  • J. N. Blakely, M. B. Eskridge, and N. J. Corron, “A simple Lorenz circuit and its radio frequency implementation,” Chaos An Interdiscip. J. Nonlinear Sci., vol. 17, no. 2, p. 023112, Jun. 2007.
  • O. A. Gonzales, G. Han, J. P. de Gyvez, and E. Sanchez-Sinencio, “Lorenz-based chaotic cryptosystem: a monolithic implementation,” IEEE Trans. Circuits Syst. I Fundam. Theory Appl., vol. 47, no. 8, pp. 1243–1247, 2000.
  • A. G. Radwan, A. M. Soliman, and A. El-Sedeek, “MOS realization of the modified Lorenz chaotic system,” Chaos, Solitons & Fractals, vol. 21, no. 3, pp. 553–561, Jul. 2004.
  • S. C. Yener, R. Mutlu, T. Yener, and H. H. Kuntman, “Memristor-based timing circuit,” in 2017 Electric Electronics, Computer Science, Biomedical Engineerings’ Meeting, EBBT 2017, 2017, pp. 1–3.
  • Y. Babacan, A. Yesil, and F. Gul, “The Fabrication and MOSFET-Only Circuit Implementation of Semiconductor Memristor,” IEEE Trans. Electron Devices, vol. 65, no. 4, pp. 1625–1632, Apr. 2018.
  • C. P. Uzunoglu, Y. Babacan, F. Kacar, and M. Ugur, “Modeling and Suppression of Chaotic Ferroresonance in a Power System by Using Memristor-based System,” Electr. Power Components Syst., vol. 44, no. 6, pp. 638–645, Apr. 2016.
  • Ş. Ç. Yener and H. H. Kuntman, “Fully CMOS memristor based chaotic circuit,” Radioengineering, vol. 23, no. 4, 2014.
  • erdem uçar, ertuğrul karakulak, and reşat mutlu, “ANN Circuit Application of Complementary Resistive Switches,” Balk. J. Electr. Comput. Eng., vol. 7, no. 1, pp. 34–43, Jan. 2019.
  • A. YESIL and Y. BABACAN, “Implementation of Electronically Controllable Memristor Based Chua Circuit,” J. Inst. Sci. Technol., vol. 9, no. 1, pp. 121–129, Mar. 2019.
  • S. Arık and R. Kılıç, “RECONFIGURABLE HARDWARE PLATFORM FOR EXPERIMENTAL TESTING AND VERIFYING OF MEMRISTOR-BASED CHAOTIC SYSTEMS,” J. Circuits, Syst. Comput., vol. 23, no. 10, p. 1450145, Dec. 2014.
  • F. R. Tahir, R. Ali, and L. Fortuna, “ANALOG PROGRAMMABLE ELECTRONIC CIRCUIT-BASED CHAOTIC LORENZ SYSTEM,” Basrah J. Eng. Sci., vol. 14, no. 1, 2014.
  • S. C. Yener, C. Barbaros, R. Mutlu, and E. Karakulak, “Implementation of Microcontroller-Based Memristive Chaotic Circuit,” Acta Phys. Pol. A, vol. 132, no. 3–II, pp. 1058–1061, 2017.
  • Ş. Ç. Yener, C. Barbaros, R. MUTLU, and E. Karakulak, “Design of a Microcontroller-Based Chaotic Circuit of Lorenz Equations,” in International Conference on Science and Technology ICONST 2018 5-9 September 2018 Prizren - KOSOVO, 2018, pp. 612–615.
There are 24 citations in total.

Details

Primary Language English
Subjects Electrical Engineering
Journal Section Araştırma Articlessi
Authors

Şuayb Çağrı Yener 0000-0002-6211-3751

Reşat Mutlu 0000-0003-0030-7136

Ertuğrul Karakulak 0000-0001-5937-2114

Publication Date October 30, 2020
Published in Issue Year 2020 Volume: 8 Issue: 4

Cite

APA Yener, Ş. Ç., Mutlu, R., & Karakulak, E. (2020). Implementation of a Microcontroller-Based Chaotic Circuit of Lorenz Equations. Balkan Journal of Electrical and Computer Engineering, 8(4), 355-360. https://doi.org/10.17694/bajece.624645

Cited By

A Microcontroller based Liénard Oscillator
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https://doi.org/10.55581/ejeas.1194452
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