Research Article
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Year 2022, Volume 4, Issue 4, 274 - 284, 31.12.2022
https://doi.org/10.51537/chaos.1214569

Abstract

References

  • Abd, M. H., G. A. Al-Suhail, F. R. Tahir, A. M. Ali Ali, H. A. Abbood, et al., 2022 Synchronization of monostatic radar using a timedelayed chaos-based fm waveform. Remote Sensing 14: 1984.
  • Ablay, G., 2022 Lyapunov exponent enhancement in chaotic maps with uniform distribution modulo one transformation. Chaos Theory and Applications 4: 45–58.
  • Adeyemi, V.-A., E. Tlelo-Cuautle, F.-J. Perez-Pinal, and J.-C. Nuñez- Perez, 2022 Optimizing the maximum lyapunov exponent of fractional order chaotic spherical system by evolutionary algorithms. Fractal and Fractional 6: 448.
  • Alawida, M., J. S. Teh, A. Mehmood, A. Shoufan, et al., 2022 A chaos-based block cipher based on an enhanced logistic map and simultaneous confusion-diffusion operations. Journal of King Saud University-Computer and Information Sciences .
  • Algarni, A. D., N. F. Soliman, H. A. Abdallah, A. El-Samie, and E. Fathi, 2021 Encryption of ecg signals for telemedicine applications. Multimedia Tools and Applications 80: 10679–10703.
  • Alvarez, G. and S. Li, 2006 Some basic cryptographic requirements for chaos-based cryptosystems. International journal of bifurcation and chaos 16: 2129–2151.
  • Borah, M., A. Gayan, J. S. Sharma, Y. Chen, Z. Wei, et al., 2022 Is fractional-order chaos theory the new tool to model chaotic pandemics as covid-19? Nonlinear Dynamics pp. 1–29.
  • Bovy, J., 2004 Lyapunov exponents and strange attractors in discrete and continuous dynamical systems. Theoretica Phys. Project, Catholic Univ. Leuven, Flanders, Belgium, Tech. Rep 9: 1–19.
  • Chen, W., J. Zhuang, W. Yu, and Z. Wang, 2009 Measuring complexity using fuzzyen, apen, and sampen. Medical engineering & physics 31: 61–68.
  • de la Fraga, L. G., E. Tlelo-Cuautle, V. Carbajal-Gómez, and J. Munoz-Pacheco, 2012 On maximizing positive lyapunov exponents in a chaotic oscillator with heuristics. Revista mexicana de física 58: 274–281.
  • Dong, C., K. Rajagopal, S. He, S. Jafari, and K. Sun, 2021 Chaotification of sine-series maps based on the internal perturbation model. Results in Physics 31: 105010.
  • Elshamy, E. M., E.-S. M. El-Rabaie, O. S. Faragallah, O. A. Elshakankiry, A. El-Samie, et al., 2015 Efficient audio cryptosystem based on chaotic maps and double random phase encoding. International Journal of Speech Technology 18: 619–631.
  • Fadil, E., A. Abass, and S. Tahhan, 2022 Secure wdm-free space optical communication system based optical chaotic. Optical and Quantum Electronics 54: 1–14.
  • Grassi, G., 2021 Chaos in the real world: Recent applications to communications, computing, distributed sensing, robotic motion, bio-impedance modelling and encryption systems. Symmetry 13: 2151.
  • Hua, Z., B. Zhou, and Y. Zhou, 2018 Sine chaotification model for enhancing chaos and its hardware implementation. IEEE Transactions on Industrial Electronics 66: 1273–1284.
  • Li, Y., X. He, and D. Xia, 2021 A chaotification model based on sine and cosecant functions for enhancing chaos. Modern Physics Letters B 35: 2150258.
  • Liu, L., H. Xiang, and X. Li, 2021 A novel perturbation method to reduce the dynamical degradation of digital chaotic maps. Nonlinear Dynamics 103: 1099–1115.
  • Mammedov, Y. D., E. U. Olugu, and G. A. Farah, 2022 Weather forecasting based on data-driven and physics-informed reservoir computing models. Environmental Science and Pollution Research 29: 24131–24144.
  • Mosa, E., N.W. Messiha, O. Zahran, A. El-Samie, and E. Fathi, 2011 Chaotic encryption of speech signals. International Journal of Speech Technology 14: 285–296.
  • Moysis, L., D. N. Butusov, A. Tutueva, V. Ostrovskii, I. Kafetzis, et al., 2022a Introducing chaos and chaos based encryption applications to university students-case report of a seminar. In 2022 11th International Conference on Modern Circuits and Systems Technologies (MOCAST), pp. 1–6, IEEE.
  • Moysis, L., I. Kafetzis, M. S. Baptista, and C. Volos, 2022b Chaotification of one-dimensional maps based on remainder operator addition. Mathematics 10: 2801.
  • Nagashima, H., Y. Baba, and M. Nakahara, 2019 Introduction to chaos: physics and mathematics of chaotic phenomena. CRC Press.
  • Natiq, H., S. Banerjee, and M. Said, 2019 Cosine chaotification technique to enhance chaos and complexity of discrete systems. The European Physical Journal Special Topics 228: 185–194.
  • Petavratzis, E., C. Volos, L. Moysis, H. Nistazakis, A. Giakoumis, et al., 2022 Experimental coverage performance of a chaotic autonomous mobile robot. In 2022 11th International Conference on Modern Circuits and Systems Technologies (MOCAST), pp. 1–4, IEEE.
  • Pincus, S. M., 1991 Approximate entropy as a measure of system complexity. Proceedings of the National Academy of Sciences 88: 2297–2301.
  • Renza, D., S. Mendoza, et al., 2019 High-uncertainty audio signal encryption based on the collatz conjecture. Journal of Information Security and Applications 46: 62–69.
  • Sayed,W. S., A. G. Radwan, H. A. Fahmy, and A. El-Sedeek, 2020 Software and hardware implementation sensitivity of chaotic systems and impact on encryption applications. Circuits, Systems, and Signal Processing 39: 5638–5655.
  • Shahi, S., F. H. Fenton, and E. M. Cherry, 2022 Prediction of chaotic time series using recurrent neural networks and reservoir computing techniques: A comparative study. Machine Learning with Applications 8: 100300.
  • Teh, J. S., M. Alawida, and Y. C. Sii, 2020 Implementation and practical problems of chaos-based cryptography revisited. Journal of Information Security and Applications 50: 102421.
  • Wang, B., J. Liu, M. O. Alassafi, F. E. Alsaadi, H. Jahanshahi, et al., 2022 Intelligent parameter identification and prediction of variable time fractional derivative and application in a symmetric chaotic financial system. Chaos, Solitons & Fractals 154: 111590.
  • Wu, Q., 2021 Cascade-sine chaotification model for producing chaos. Nonlinear Dynamics 106: 2607–2620.
  • Xiu, C., J. Fang, and X. Ma, 2022 Design and circuit implementations of multimemristive hyperchaotic system. Chaos, Solitons & Fractals 161: 112409.
  • Zeraoulia, E., 2012 Robust chaos and its applications, volume 79. World Scientific.
  • Zhang, Z., H. Zhu, P. Ban, Y. Wang, and L. Y. Y. Zhang, 2022 Buffeting chaotification model for enhancing chaos and its hardware implementation. IEEE Transactions on Industrial Electronics .

A Chaotification Model Based on Modulo Operator and Secant Functions for Enhancing Chaos

Year 2022, Volume 4, Issue 4, 274 - 284, 31.12.2022
https://doi.org/10.51537/chaos.1214569

Abstract

Many drawbacks in chaos-based applications emerge from the chaotic maps' poor dynamic properties. To address this problem, in this paper a chaotification model based on modulo operator and secant functions to augment the dynamic properties of existing chaotic maps is proposed. It is demonstrated that by selecting appropriate parameters, the resulting map can achieve a higher Lyapunov exponent than its seed map. This chaotification method is applied to several well-known maps from the literature, and it produces increased chaotic behavior in all cases, as evidenced by their bifurcation and Lyapunov exponent diagrams. Furthermore, to illustrate that the proposed chaotification model can be considered in chaos-based encryption and related applications, a voice signal encryption process is considered, and different tests are being used with respect to attacks, like brute force, entropy, correlation, and histogram analysis.

References

  • Abd, M. H., G. A. Al-Suhail, F. R. Tahir, A. M. Ali Ali, H. A. Abbood, et al., 2022 Synchronization of monostatic radar using a timedelayed chaos-based fm waveform. Remote Sensing 14: 1984.
  • Ablay, G., 2022 Lyapunov exponent enhancement in chaotic maps with uniform distribution modulo one transformation. Chaos Theory and Applications 4: 45–58.
  • Adeyemi, V.-A., E. Tlelo-Cuautle, F.-J. Perez-Pinal, and J.-C. Nuñez- Perez, 2022 Optimizing the maximum lyapunov exponent of fractional order chaotic spherical system by evolutionary algorithms. Fractal and Fractional 6: 448.
  • Alawida, M., J. S. Teh, A. Mehmood, A. Shoufan, et al., 2022 A chaos-based block cipher based on an enhanced logistic map and simultaneous confusion-diffusion operations. Journal of King Saud University-Computer and Information Sciences .
  • Algarni, A. D., N. F. Soliman, H. A. Abdallah, A. El-Samie, and E. Fathi, 2021 Encryption of ecg signals for telemedicine applications. Multimedia Tools and Applications 80: 10679–10703.
  • Alvarez, G. and S. Li, 2006 Some basic cryptographic requirements for chaos-based cryptosystems. International journal of bifurcation and chaos 16: 2129–2151.
  • Borah, M., A. Gayan, J. S. Sharma, Y. Chen, Z. Wei, et al., 2022 Is fractional-order chaos theory the new tool to model chaotic pandemics as covid-19? Nonlinear Dynamics pp. 1–29.
  • Bovy, J., 2004 Lyapunov exponents and strange attractors in discrete and continuous dynamical systems. Theoretica Phys. Project, Catholic Univ. Leuven, Flanders, Belgium, Tech. Rep 9: 1–19.
  • Chen, W., J. Zhuang, W. Yu, and Z. Wang, 2009 Measuring complexity using fuzzyen, apen, and sampen. Medical engineering & physics 31: 61–68.
  • de la Fraga, L. G., E. Tlelo-Cuautle, V. Carbajal-Gómez, and J. Munoz-Pacheco, 2012 On maximizing positive lyapunov exponents in a chaotic oscillator with heuristics. Revista mexicana de física 58: 274–281.
  • Dong, C., K. Rajagopal, S. He, S. Jafari, and K. Sun, 2021 Chaotification of sine-series maps based on the internal perturbation model. Results in Physics 31: 105010.
  • Elshamy, E. M., E.-S. M. El-Rabaie, O. S. Faragallah, O. A. Elshakankiry, A. El-Samie, et al., 2015 Efficient audio cryptosystem based on chaotic maps and double random phase encoding. International Journal of Speech Technology 18: 619–631.
  • Fadil, E., A. Abass, and S. Tahhan, 2022 Secure wdm-free space optical communication system based optical chaotic. Optical and Quantum Electronics 54: 1–14.
  • Grassi, G., 2021 Chaos in the real world: Recent applications to communications, computing, distributed sensing, robotic motion, bio-impedance modelling and encryption systems. Symmetry 13: 2151.
  • Hua, Z., B. Zhou, and Y. Zhou, 2018 Sine chaotification model for enhancing chaos and its hardware implementation. IEEE Transactions on Industrial Electronics 66: 1273–1284.
  • Li, Y., X. He, and D. Xia, 2021 A chaotification model based on sine and cosecant functions for enhancing chaos. Modern Physics Letters B 35: 2150258.
  • Liu, L., H. Xiang, and X. Li, 2021 A novel perturbation method to reduce the dynamical degradation of digital chaotic maps. Nonlinear Dynamics 103: 1099–1115.
  • Mammedov, Y. D., E. U. Olugu, and G. A. Farah, 2022 Weather forecasting based on data-driven and physics-informed reservoir computing models. Environmental Science and Pollution Research 29: 24131–24144.
  • Mosa, E., N.W. Messiha, O. Zahran, A. El-Samie, and E. Fathi, 2011 Chaotic encryption of speech signals. International Journal of Speech Technology 14: 285–296.
  • Moysis, L., D. N. Butusov, A. Tutueva, V. Ostrovskii, I. Kafetzis, et al., 2022a Introducing chaos and chaos based encryption applications to university students-case report of a seminar. In 2022 11th International Conference on Modern Circuits and Systems Technologies (MOCAST), pp. 1–6, IEEE.
  • Moysis, L., I. Kafetzis, M. S. Baptista, and C. Volos, 2022b Chaotification of one-dimensional maps based on remainder operator addition. Mathematics 10: 2801.
  • Nagashima, H., Y. Baba, and M. Nakahara, 2019 Introduction to chaos: physics and mathematics of chaotic phenomena. CRC Press.
  • Natiq, H., S. Banerjee, and M. Said, 2019 Cosine chaotification technique to enhance chaos and complexity of discrete systems. The European Physical Journal Special Topics 228: 185–194.
  • Petavratzis, E., C. Volos, L. Moysis, H. Nistazakis, A. Giakoumis, et al., 2022 Experimental coverage performance of a chaotic autonomous mobile robot. In 2022 11th International Conference on Modern Circuits and Systems Technologies (MOCAST), pp. 1–4, IEEE.
  • Pincus, S. M., 1991 Approximate entropy as a measure of system complexity. Proceedings of the National Academy of Sciences 88: 2297–2301.
  • Renza, D., S. Mendoza, et al., 2019 High-uncertainty audio signal encryption based on the collatz conjecture. Journal of Information Security and Applications 46: 62–69.
  • Sayed,W. S., A. G. Radwan, H. A. Fahmy, and A. El-Sedeek, 2020 Software and hardware implementation sensitivity of chaotic systems and impact on encryption applications. Circuits, Systems, and Signal Processing 39: 5638–5655.
  • Shahi, S., F. H. Fenton, and E. M. Cherry, 2022 Prediction of chaotic time series using recurrent neural networks and reservoir computing techniques: A comparative study. Machine Learning with Applications 8: 100300.
  • Teh, J. S., M. Alawida, and Y. C. Sii, 2020 Implementation and practical problems of chaos-based cryptography revisited. Journal of Information Security and Applications 50: 102421.
  • Wang, B., J. Liu, M. O. Alassafi, F. E. Alsaadi, H. Jahanshahi, et al., 2022 Intelligent parameter identification and prediction of variable time fractional derivative and application in a symmetric chaotic financial system. Chaos, Solitons & Fractals 154: 111590.
  • Wu, Q., 2021 Cascade-sine chaotification model for producing chaos. Nonlinear Dynamics 106: 2607–2620.
  • Xiu, C., J. Fang, and X. Ma, 2022 Design and circuit implementations of multimemristive hyperchaotic system. Chaos, Solitons & Fractals 161: 112409.
  • Zeraoulia, E., 2012 Robust chaos and its applications, volume 79. World Scientific.
  • Zhang, Z., H. Zhu, P. Ban, Y. Wang, and L. Y. Y. Zhang, 2022 Buffeting chaotification model for enhancing chaos and its hardware implementation. IEEE Transactions on Industrial Electronics .

Details

Primary Language English
Subjects Physics, Applied
Journal Section Research Articles
Authors

Nikolaos CHARALAMPİDİS> (Primary Author)
Aristotle University of Thessaloniki
0000-0003-0531-7720
Greece


Christos K. VOLOS>
Aristotle University of Thessaloniki
0000-0001-8763-7255
Greece


Lazaros MOYSIS>
Universiity of Western Macedonia
0000-0002-5652-2532
Greece


Ioannis STOUBOULOS>
Aristotle University of Thessaloniki
0000-0003-1942-8413
Greece

Publication Date December 31, 2022
Published in Issue Year 2022, Volume 4, Issue 4

Cite

APA Charalampidis, N. , Volos, C. K. , Moysıs, L. & Stouboulos, I. (2022). A Chaotification Model Based on Modulo Operator and Secant Functions for Enhancing Chaos . Chaos Theory and Applications , Dissemination and Research in the Study of Complex Systems and Their Applications (EDIESCA 2022) , 274-284 . DOI: 10.51537/chaos.1214569

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