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Circuit Implementation and PRNG Applications of Time Delayed Lorenz System

Year 2022, Volume 4, Issue 1, 4 - 9, 30.03.2022
https://doi.org/10.51537/chaos.976593

Abstract

In this study, time delayed form of Lorenz system is introduced, and exemplary applications of the time delayed Lorenz system are performed. Firstly, the time delayed Lorenz system is numerically solved by considering the Lorenz system as a system of time delayed differential equations. Then, time series and phase portraits of the state variables of the time delayed system are obtained. After then, circuit implementation of the time delayed system is carried out with discrete analog components. Finally, a random number generator application is carried out by selectin different number of bits obtained from the state variables of the time delayed system. The results of all the applications are sufficiently good that the time delayed system can be used in engineering applications.

References

  • Acho, L., 2017 A continuous-time delay chaotic system obtained from a chaotic logistic map. In IASTED International Conference Modelling, Identification and Control.“Modelling, Identification and Control (MIC 2017)”, ACTA Press, Innsbruck, p. 147.
  • Adiyaman, Y., S. Emiroglu, M. K. Ucar, and M. Yildiz, 2020 Dynamical analysis, electronic circuit design and control application of a different chaotic system. Chaos Theory and Applications 2: 10–16.
  • Agarwal, S., 2021 Designing a pseudo-random bit generator using generalized cascade fractal function. Chaos Theory and Applications 3: 11–19.
  • Akgul, A., C. Arslan, and B. Aricioglu, 2019 Design of an interface for random number generators based on integer and fractional order chaotic systems. Chaos Theory and Applications 1: 1–18.
  • Alcin, M., T. Murat, P. ERDOG˘MUS¸, and I. Koyuncu, 2021 Fpgabased dual core trng design using ring and runge-kutta-butcher based on chaotic oscillator. Chaos Theory and Applications 3: 20–28.
  • Bassham, L., A. Rukhin, J. Soto, J. Nechvatal, M. Smid, et al., 2010 A statistical test suite for random and pseudorandom number generators for cryptographic applications.
  • Cheng, C.-K., H.-H. Kuo, Y.-Y. Hou, C.-C. Hwang, and T.-L. Liao, 2008 Robust chaos synchronization of noise-perturbed chaotic systems with multiple time-delays. Physica A: Statistical Mechanics and its Applications 387: 3093–3102.
  • Deng, W., Y. Wu, and C. Li, 2006 Stability analysis of differential equations with time-dependent delay. International Journal of Bifurcation and Chaos 16: 465–472.
  • Hale, J. K. and S. M. V. Lunel, 2013 Introduction to functional differential equations, volume 99. Springer Science & Business Media.
  • Jacek Kierzenka, L. F., Shampine and S. Thompson, 2021 Tutorial on solving ddes with dde23.
  • Jahanshahi, H., K. Rajagopal, A. Akgul, N. N. Sari, H. Namazi, et al., 2018 Complete analysis and engineering applications of a megastable nonlinear oscillator. International Journal of Non- Linear Mechanics 107: 126–136.
  • Kaçar, S., 2016 Analog circuit and microcontroller based rng application of a new easy realizable 4d chaotic system. Optik 127: 9551–9561.
  • Kacar, S., Z. Wei, A. Akgul, and B. Aricioglu, 2018 A novel 4d chaotic system based on two degrees of freedom nonlinear mechanical system. Zeitschrift für Naturforschung A 73: 595–607.
  • Liu, H. and J. Yang, 2015 Sliding-mode synchronization control for uncertain fractional-order chaotic systems with time delay. Entropy 17: 4202–4214.
  • Liu, J., K. Rajagopal, T. Lei, S. Kaçar, B. Arıcıo˘ glu, et al., 2020 A novel hypogenetic chaotic jerk system: Modeling, circuit implementation, and its application. Mathematical Problems in Engineering 2020.
  • Lorenz, E. N., 1963 Deterministic nonperiodic flow. Journal of atmospheric sciences 20: 130–141.
  • Moysis, L., A. Tutueva, K. Christos, and D. Butusov, 2020 A chaos based pseudo-random bit generator using multiple digits comparison. Chaos Theory and Applications 2: 58–68.
  • Pehlivan, ˙I., K. Ersin, L. Qiang, A. Basaran, and M. Kutlu, 2019 A multiscroll chaotic attractor and its electronic circuit implementation. Chaos Theory and Applications 1: 29–37.
  • Pham, V.-T., S. Vaidyanathan, C. Volos, S. Jafari, N. Kuznetsov, et al., 2016 A novel memristive time–delay chaotic system without equilibrium points. The European Physical Journal Special Topics 225: 127–136.
  • Qin-Qin, C., 2015 A method of identifying parameters of a timevarying time-delay chaotic system. Acta Phys. Sinica 64.
  • Shampine, L. F. and S. Thompson, 2001 Solving ddes in matlab. Applied Numerical Mathematics 37: 441–458.
  • Tang, J., 2014 Synchronization of different fractional order timedelay chaotic systems using active control. Mathematical problems in Engineering 2014.
  • Tang, Y., M. Cui, L. Li, H. Peng, and X. Guan, 2009 Parameter identification of time-delay chaotic system using chaotic ant swarm. Chaos, Solitons & Fractals 41: 2097–2102.
  • Vaidyanathan, S., A. Akgul, S. Kaçar, and U. Çavu¸so˘ glu, 2018 A new 4-d chaotic hyperjerk system, its synchronization, circuit design and applications in rng, image encryption and chaosbased steganography. The European Physical Journal Plus 133: 1–18.

Year 2022, Volume 4, Issue 1, 4 - 9, 30.03.2022
https://doi.org/10.51537/chaos.976593

Abstract

References

  • Acho, L., 2017 A continuous-time delay chaotic system obtained from a chaotic logistic map. In IASTED International Conference Modelling, Identification and Control.“Modelling, Identification and Control (MIC 2017)”, ACTA Press, Innsbruck, p. 147.
  • Adiyaman, Y., S. Emiroglu, M. K. Ucar, and M. Yildiz, 2020 Dynamical analysis, electronic circuit design and control application of a different chaotic system. Chaos Theory and Applications 2: 10–16.
  • Agarwal, S., 2021 Designing a pseudo-random bit generator using generalized cascade fractal function. Chaos Theory and Applications 3: 11–19.
  • Akgul, A., C. Arslan, and B. Aricioglu, 2019 Design of an interface for random number generators based on integer and fractional order chaotic systems. Chaos Theory and Applications 1: 1–18.
  • Alcin, M., T. Murat, P. ERDOG˘MUS¸, and I. Koyuncu, 2021 Fpgabased dual core trng design using ring and runge-kutta-butcher based on chaotic oscillator. Chaos Theory and Applications 3: 20–28.
  • Bassham, L., A. Rukhin, J. Soto, J. Nechvatal, M. Smid, et al., 2010 A statistical test suite for random and pseudorandom number generators for cryptographic applications.
  • Cheng, C.-K., H.-H. Kuo, Y.-Y. Hou, C.-C. Hwang, and T.-L. Liao, 2008 Robust chaos synchronization of noise-perturbed chaotic systems with multiple time-delays. Physica A: Statistical Mechanics and its Applications 387: 3093–3102.
  • Deng, W., Y. Wu, and C. Li, 2006 Stability analysis of differential equations with time-dependent delay. International Journal of Bifurcation and Chaos 16: 465–472.
  • Hale, J. K. and S. M. V. Lunel, 2013 Introduction to functional differential equations, volume 99. Springer Science & Business Media.
  • Jacek Kierzenka, L. F., Shampine and S. Thompson, 2021 Tutorial on solving ddes with dde23.
  • Jahanshahi, H., K. Rajagopal, A. Akgul, N. N. Sari, H. Namazi, et al., 2018 Complete analysis and engineering applications of a megastable nonlinear oscillator. International Journal of Non- Linear Mechanics 107: 126–136.
  • Kaçar, S., 2016 Analog circuit and microcontroller based rng application of a new easy realizable 4d chaotic system. Optik 127: 9551–9561.
  • Kacar, S., Z. Wei, A. Akgul, and B. Aricioglu, 2018 A novel 4d chaotic system based on two degrees of freedom nonlinear mechanical system. Zeitschrift für Naturforschung A 73: 595–607.
  • Liu, H. and J. Yang, 2015 Sliding-mode synchronization control for uncertain fractional-order chaotic systems with time delay. Entropy 17: 4202–4214.
  • Liu, J., K. Rajagopal, T. Lei, S. Kaçar, B. Arıcıo˘ glu, et al., 2020 A novel hypogenetic chaotic jerk system: Modeling, circuit implementation, and its application. Mathematical Problems in Engineering 2020.
  • Lorenz, E. N., 1963 Deterministic nonperiodic flow. Journal of atmospheric sciences 20: 130–141.
  • Moysis, L., A. Tutueva, K. Christos, and D. Butusov, 2020 A chaos based pseudo-random bit generator using multiple digits comparison. Chaos Theory and Applications 2: 58–68.
  • Pehlivan, ˙I., K. Ersin, L. Qiang, A. Basaran, and M. Kutlu, 2019 A multiscroll chaotic attractor and its electronic circuit implementation. Chaos Theory and Applications 1: 29–37.
  • Pham, V.-T., S. Vaidyanathan, C. Volos, S. Jafari, N. Kuznetsov, et al., 2016 A novel memristive time–delay chaotic system without equilibrium points. The European Physical Journal Special Topics 225: 127–136.
  • Qin-Qin, C., 2015 A method of identifying parameters of a timevarying time-delay chaotic system. Acta Phys. Sinica 64.
  • Shampine, L. F. and S. Thompson, 2001 Solving ddes in matlab. Applied Numerical Mathematics 37: 441–458.
  • Tang, J., 2014 Synchronization of different fractional order timedelay chaotic systems using active control. Mathematical problems in Engineering 2014.
  • Tang, Y., M. Cui, L. Li, H. Peng, and X. Guan, 2009 Parameter identification of time-delay chaotic system using chaotic ant swarm. Chaos, Solitons & Fractals 41: 2097–2102.
  • Vaidyanathan, S., A. Akgul, S. Kaçar, and U. Çavu¸so˘ glu, 2018 A new 4-d chaotic hyperjerk system, its synchronization, circuit design and applications in rng, image encryption and chaosbased steganography. The European Physical Journal Plus 133: 1–18.

Details

Primary Language English
Subjects Engineering, Electrical and Electronic
Journal Section Research Articles
Authors

Burak ARICIOĞLU (Primary Author)
SAKARYA UYGULAMALI BİLİMLER ÜNİVERSİTESİ
0000-0001-9526-7629
Türkiye


Sezgin KAÇAR
Sakarya Uygulamalı Bilimler Üniversitesi
0000-0002-5171-237X
Türkiye

Publication Date March 30, 2022
Published in Issue Year 2022, Volume 4, Issue 1

Cite

APA Arıcıoğlu, B. & Kaçar, S. (2022). Circuit Implementation and PRNG Applications of Time Delayed Lorenz System . Chaos Theory and Applications , 4 (1) , 4-9 . DOI: 10.51537/chaos.976593

Chaos Theory and Applications in Applied Sciences and Engineering: An interdisciplinary journal of nonlinear science 23830