Abstract
In this study, for the first time in the literature, a Variable-Order Fractional Hopfield Neural Network Under Electromagnetic Radiation (VOFHNNUER) has been presented. Also, for the first time, Pseudo Random Number Generator (PRNG) based image encryption and data hiding application for VOFHNNUER using Least Significant Bit (LSB) method has been performed and digital circuit implementation over the sound card of a PC has been implemented. In the study, first of all, a numerical solution for VOFHNNUER, which is a four-dimensional chaotic system, has been made with Grünwald-Letnikov method. The obtained time series from the numerical solutions have been physically realized through a sound card in two channels. In addition, using the calculated state variables, a PRNG has been designed and tested with NIST-800-22 test. Finally, a PRNG-based image encryption and data hiding algorithm with the LSB method has been developed and applied for an RGB image. In this algorithm, first, a gray-scale image (message data) was encrypted and then the encrypted image was hidden into the RGB image. So, a two-level data security application has been realized.
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L. Jiancheng, K. Rajagopal, L. Tengfei, S. Kaçar, B. Arıcıoğlu, Ü. Çavuşoğlu, A.H. Kökçam, A. Karthikeyan, Math. Probl. Eng. 2020, 8083509 (2020)
S.S. Zhou, H. Jahanshahi, Q. Din, S. Bekiros, R. Alcaraz, M.O. Alassafi, F.E. Alsaadi, Y.M. Chu, Chaos Solitons Fractals 142, 110378 (2021)
S. Kacar, Z. Wei, A. Akgul, B. Aricioglu, Zeitschrift für Naturforschung A 73, 7 (2018)
Ü. Çavuşoğlu, Y. Uyaroğlu, İ Pehlivan, J. Fac. Eng. Archit. Gaz. 29, 1 (2014)
C. Li, İ Pehlivan, J.C. Sprott, Turk. J. Electr. Eng. Comput. Sci. 24, 1 (2016)
H. Jahanshahi, O. Orozco-López, J.M. Munoz-Pacheco, N.D. Alotaibi, C. Volos, Z. Wang, R. Sevilla-Escoboza, Y.M. Chu, Chaos Solitons Fractals 143, 110539 (2021)
M. Cimen, Z. Garip, M. Pala, A.F. Boz, A. Akgül, Chaos Theory Appl. 1, 1 (2019)
Ü. Çavuşoğlu, A. Zengin, İ Pehlivan, S. Kaçar, Nonlinear Dyn. 87, 1081–1094 (2017)
S. Bekiros, H. Jahanshahi, F. Bezzina, A.A. Aly, Chaos Solitons Fractals 146, 110878 (2021)
Ü. Pehlivan, E. Kurt, Q. Lai, A. Basaran, M. Kutlu, Chaos Theory Appl. 1, 1 (2019)
H. Jahanshahi, K. Rajagopal, A. Akgul, N.N. Sari, H. Namazi, S. Jafari, Int. J. Non Linear Mech. 107(110378), 126–138 (2018)
Y. Adıyaman, S. Emiroglu, M. UÇar, M. Yıldız, Chaos Theory Appl. 2, 1 (2020)
H. Jahanshahi, A. Yousefpour, Z. Wei, R. Alcaraz, S. Bekiros, Chaos Solitons Fractals 126 (2019)
S. Kaçar, Optik 127(20), 9551–9561 (2016)
A. Akgül, S. Kaçar, B. Aricioğlu, İ. Pehlivan, in Proceedings of IEEE 8th international conference on electrical and electronics engineering [ELECO], Bursa/ TURKEY, 2013
Ü. Çavuşoğlu, A. Akgul, A. Zengin, İ Pehlivan, Chaos Solitons Fractals 104, 655–667 (2017)
B. Gürevin, M. Yıldız, E. Güleryüz, M. Kutlu, Ö. Sorgun, Chaos Theory Appl. 2, 2 (2020)
A. Akgul, M.Z. Yildiz, O.F. Boyraz, E. Guleryuz, S. Kacar, B. Gurevin, J. Fac. Eng. Archit. Gaz. 35, 3 (2020)
L. Moysis, A. Tutueva, C. Volos, D. Butusov, Chaos Theory Appl. 2, 2 (2020)
S. Vaidyanathan, A. Akgul, S. Kaçar, U. Cavusoğlu, Eur. Phys. J. Plus 133, 46 (2018)
A. Arshad, S. Shaukat, A. Ali, A. Eleyan, S. Shah, J. Ahmad, Chaos Theory Appl. 2, 1 (2020)
A. Akgul, S. Kacar, B. Aricioglu, Nonlinear Dyn 90, 1123–1140 (2017)
M. Alçın, Chaos Theory Appl. 2, 1 (2020)
C. Bayilmis, Ü. Çavuşoğlu, A. Akgul, S. Kacar, A. Sevin, Tehnicki Vjesnik. 24, 1065–1069 (2017)
Ö. Boyraz, M. Çimen, E. Güleryüz, M. Yıldız, Chaos Theory Appl. 3, 1 (2021)
C. Bayilmis,Ü. Çavuşoğlu, A. Akgul, A. Sevin, S. Kacar, in Proceedings of International Conference on Computer Science and Information Systems, Dubai, (2014), p. 89
S. Agarwal, Chaos Theory Appl. 3, 1 (2021)
Ü. Çavuşoğlu, S. Kaçar, I. Pehlivan, A. Zengin, Chaos Solitons Fractals 95, (2017)
M. Alçın, M. Tuna, P. Erdoğmuş, İ Koyuncu, Chaos Theory Appl. 3, 1 (2021)
Ü. Çavuşoğlu, A. Akgül, S. Kaçar, İ. Pehlivan, A. Zengin, Security Comm. Networks 9, (2016)
S.B. Chen, H. Jahanshahi, O.A. Abba, J.E. Solís-Pérez, S. Bekiros, J.F. Gómez-Aguilar, A. Yousefpour, Y.M. Chu, Chaos Solitons Fractals 140, 110223 (2020)
K. Rajagopal, A. Akgul, S. Jafari, B. Aricioglu, Nonlinear Dyn. 91, 957 (2018)
H. Jahanshahi, A. Yousefpour, J.M. Munoz-Pacheco, S. Kacar, V.T. Pham, F.E. Alsaadi, Appl. Math. Comput. 383, 125310 (2020)
J. Wang, L. Xiao, K. Rajagopal, A. Akgul, S. Cicek, B. Aricioglu, Symmetry 13, 340 (2021)
H. Jahanshahi, J.M. Munoz-Pacheco, S. Bekiros, N.D. Alotaibi, Chaos Solitons Fractals 143, 110632 (2021)
M. Çimen, Z. Garip, Ö. Boyraz, İ Pehlivan, M. Yıldız, A.F. Boz, Chaos Theory Appl. 2, 1 (2020)
H. Jahanshahi, S. Bekiros, H. Gritli, Y.M. Chu, J.F. Gomez-Aguilar, A.A. Aly, Fractals. https://doi.org/10.1142/S0218348X21501553 (2021) (to be published)
A. Akgül, C. Arslan, B. Arıcıoğlu, Chaos Theory Appl. 1, 1 (2019)
H. Jahanshahi, A. Yousefpour, J.M. Munoz-Pacheco, I. Moroz, Z. Wei, O. Castillo, Appl. Soft Comput. 87, 105943 (2020)
M.A. Platas-Garza, E. Zambrano-Serrano, J.R. Rodríguez-Cruz, C. Posadas-Castillo, Chin. J. Phys. 71, 22–37 (2021)
E. Zambrano-Serrano, S. Bekiros, M.A. Platas-Garza, C. Posadas-Castillo, P. Agarwal, H. Jahanshahi, A.A. Aly, Physica A Stat. Mech. Appl. 578, (2021)
J.M. Munoz-Pacheco, C. Posadas-Castillo, E. Zambrano-Serrano, Symmetry 12, 9 (2020)
E. Zambrano-Serrano, J.M. Munoz-Pacheco, L.C. Gómez-Pavón, A. Luis-Ramos, G. Chen, Eur. Phys. J. Spec. Top. 227, 907–919 (2018)
J.F. Li, H. Jahanshahi, S. Kacar, Y.M. Chu, J.F. Gómez-Aguilar, N.D. Alotaibi, K.H. Alharbi, Chaos Solitons Fractals 145, 110681 (2021)
H. Jahanshahi, S.S. Sajjadi, S. Bekiros, A.A. Aly, Chaos Solitons Fractals 144, 110698 (2021)
T. Li, A.G. Song, S.M. Fei, Y.Q. Guo, Nonlinear Anal. Theory Method. Appl. 71, 2372 (2009)
H. Jahanshahi, M. Shahriari-Kahkeshi, R. Alcaraz, X. Wang, V.P. Singh, V.-T. Pham, Entropy 21, 156 (2019)
Q.T. Gan, R.X. Hu, Y.H. Liang, Commun. Nonlinear Sci. Numer. Simul. 17, 3708–3718 (2012)
H. Lin, C. Wang, W. Yao, Y. Tan, Commun. Nonlinear Sci. Numer. Simul. 90, 105390 (2020)
P. Arena, L. Fortuna, D. Porto, Phys. Rev. E 61, 776–781 (2000)
P. Arena, R. Caponetto, L. Fortuna, D. Porto, Int. J. Bifurc. Chaos 8(7), 1527–1539 (1998)
L.-L. Huang, J.H. Park, G.-C. Wu, Z.-W. Mo, J. Comput. Appl. Math. 370, 112633 (2020)
X. Huang, Z. Zhao, Z. Wang, Y.X. Lia, Neurocomputing 94, 13–21 (2012)
K. Moaddy, A.G. Radwan, K.N. Salama, S. Momani, I. Hashim, Comput. Math. Appl. 64, 3329–3339 (2012)
Y.-L. Wang, H. Jahanshahi, S. Bekiros, F. Bezzina, Y.-M. Chu, A.A. Aly, Chaos Solitons Fractals 146, 110881 (2021)
S. Zhou, H. Li, Z. Zhu, Chaos Solitons Fractals 36(4), 973–984 (2008)
J. Yu, C. Hu, H. Jiang, Neural Netw. 35, 82–87 (2012)
C.J.Z. Aguilar, J.F. Gomez-Aguilar, V.M. Alvarado-Martineza, H.M. Romero-Ugalde, Chaos Solitons Fractals 130, 109444 (2020)
C.J. Zuniga-Aguilar, A. Coronel-Escamilla, J.F. Gomez-Aguilar, V.M. Alvarado-Martinez, H.M. Romero-Ugalde, Eur. Phys. J. Plus 133, 2 (2018)
C.J. Zuniga-Aguilar, H.M. Romero-Ugalde, J.F. Gomez-Aguilar, R.F. Escobar-Jimenez, M. Valtierra-Rodriguez, Chaos Solitons Fractals 103, 382–403 (2017)
Z. Sabir, M.A.Z. Raja, M. Shoaib, J.F. Gomez-Aguilar, Comput. Appl. Math. 39, 4 (2020)
Z. Sabir, M.A.Z. Raja, H.A. Wahab, M. Shoaib, J.F. Gomez-Aguilar, Numer. Methods Part D. E. (2020). https://doi.org/10.1002/num.22692
J. Yang, L. Wang, Y. Wang, T. Guo, Neurocomputing 227, 142–148 (2017)
M.-F. Danca, N. Kuznetsov, Chaos Solitons Fractals 103, 144–150 (2017)
K. Rajagopal, J.M. Munoz-Pacheco, V.T. Pham, D.V. Hoang, F.E. Alsaadi, F.E. Alsaadi, Eur. Phys. J. Spec. Top. 227, 811 (2018)
F.M. Allehiany, E.E. Mahmoud, L.S. Jahanzaib, P. Trikha, H. Alotaibi, Results Phys. 21, 103786 (2021)
A. Boroomand, M. Menhaj, in Proceedings of international conference on neural information processing ICONIP 2008: advances in neuro-information processing, Auckland, 2009, p. 883
Y. Pu, Z. Yi, J. Zhou, IEEE Trans. Neural Netw. Learn. Syst. 28, 10 (2017)
C. Ma, J. Mou, F. Yang, H. Yan, Eur. Phys. J. Plus 135, 100 (2020)
L. Chen, J. Qu, Y. Chai, R. Wu, G. Qi, Entropy 15(8), 3265–3276 (2013)
K.B. Oldham, J. Spanier, The Fractional Calculus: Theory and Applications of Differentiation and Integration to Arbitrary Order (Academic, New York, 1974)
I. Podlubny, Fractional Differential Equations: An Introduction to Fractional Derivatives, Fractional Differential Equations, to Methods of Their Solution and Some of Their Applications (Academic, San Diego, 1998)
A.C. McBride, G.F. Roach, Fractional Calculus (Halsted, New York, 1986)
S.G. Samko, A.A. Kilbas, O.I. Marichev, Fractional Integrals and Derivatives: Theory and Applications (Gordon and Breach, Yverdon-les-Bains, 1993)
K. Nishimoto, Fractional Calculus: Integrations and Differentiations of Arbitrary Order (University of New Haven Press, New Haven, 1989)
C.L. MacDonald, N. Bhattacharya, B.P. Sprouse, G.A. Silva, J. Comput. Phys. 297, 231–236 (2015)
C. Chi, F. Gao, J. Softw. 8, 3 (2013)
N. Bhattacharya, G.A. Silva, arXiv:200708660v1, (2020)
X. Zhang, L. Wang, Z. Zhou, Y. Niu, IEEE Access 7, 74734–74746 (2019)
H. Li, Y. Wang , Z. Zuo, Opt Lasers Eng. 115, (2019)
X. Wang, A. Akgul, S. Kaçar, V.-T. Pham, Complexity 2017, 8412093 (2017)
Z. Li, C. Peng, W. Tan, L. Li, Complexity 2021, 8824915 (2021)
F. Musanna, S. Kumar, Multimed. Tools Appl. 78, 14867–14895 (2019)
H. Liua, Y. Xu, C. Ma, Optik 216, 164925 (2020)
G. Kaur, R. Agarwal, V. Patidar, Eng. Sci. Technol. 23(5), 998–1014 (2020)
M.T. Elkandoz, W. Alexan, H.H. Hussein, in Proceeding of 2019 international conference on electrical and computing technologies and applications (ICECTA), Ras Al Khaimah, United Arab Emirates, 2019, p. 1
M.Y. Valandar, M.J. Barani, P. Ayubi, M. Aghazadeh, , Multimed. Tools Appl. 78, (2019)
H. Ogras, Int. J. Comput. Netw. Inf. Secur. 2, (2019)
A. Alabaichi, M.A.A.K. Al-Dabbas, A. Salih, Int. J. Electr. Comput. Eng. 10, 1 (2020)
A. Jaradat, E. Taqieddin, M. Mowafi, Secur. Commun. Netw. 2021, 6679284 (2021)
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Kaçar, S. Digital circuit implementation and PRNG-based data security application of variable-order fractional Hopfield neural network under electromagnetic radiation using Grünwald-Letnikov method. Eur. Phys. J. Spec. Top. 231, 1969–1981 (2022). https://doi.org/10.1140/epjs/s11734-022-00451-7
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DOI: https://doi.org/10.1140/epjs/s11734-022-00451-7