Theoretical probing, microcontroller implementation, and medical image encryption of a quadratically damped Josephson junction circuit oscillating with strictly the $$4\pi$$-periodic superconducting current

Vijeesh Vijayan; Finalise Komofor Ngopuh; Ahamat Mahamat Hassane; Hubert Boudoue Malwe; Gaetan Fautso Kuiate; Karthikeyan Rajagopal

doi:10.1007/s00339-025-09169-4

journal article·2026-02

Theoretical probing, microcontroller implementation, and medical image encryption of a quadratically damped Josephson junction circuit oscillating with strictly the $$4\pi$$-periodic superconducting current

Vijeesh Vijayan, Finalise Komofor Ngopuh, Ahamat Mahamat Hassane, Hubert Boudoue Malwe, Gaetan Fautso Kuiate, Karthikeyan Rajagopal

Applied Physics A· Volume 132· Issue 2

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OpenAlex topics: Chaos control and synchronization · Chaos-based Image/Signal Encryption · Quantum Information and Cryptography

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1. M. Kiaghadi, M. Keshvarinia, F.M. Boora, S.M. Mousavi, Machine learning applications for predicting liquid fraction in a PV system with NEPCM and fins. Case Stud. Therm. Eng. 61, 104819 (2024)10.1016/j.csite.2024.104819 ↗

2. J. Carrasquilla, R.G. Melko, Machine learning phases of matter. Nat. Phys. 13(5), 431–434 (2017)10.1038/nphys4035 ↗

3. R. Rahighi, O. Akhavan, A.S. Zeraati, S.M. Sattari-Esfahlan, All-carbon negative differential resistance nanodevice using a single flake of nanoporous graphene. ACS Appl. Electron. Mater. 3(8), 3418–3427 (2021)10.1021/acsaelm.1c00396 ↗

4. M.Z. Hasan, C.L. Kane, Colloquium: topological insulators. Rev. Mod. Phys. 82(12), 3045–3067 (2010)10.1103/RevModPhys.82.3045 ↗

5. Z. Wang, S. Wang, X. Wang, X. Luo, Permanent magnet-based superficial flow velometer with ultralow output drift. IEEE Trans. Instrum. Meas. 72, 1–12 (2023). https://doi.org/10.1109/TIM.2023.330469210.1109/TIM.2023.3304692 ↗

6. D. Jahani, O. Akhavan, A.A. Ghatar, Optical quantum hall Goos-Hänchen effect in graphene. Phys. Lett. A 465, 128700 (2023)10.1016/j.physleta.2023.128700 ↗

7. Y. Zhang, X. Xu, Machine learning f-doped Bi (Pb)–Sr–Ca–Cu–O superconducting transition temperature. J. Supercond. Nov. Magn. 34(1), 63–73 (2021)10.1007/s10948-020-05682-0 ↗

8. Y. Zhang, X. Xu, Predicting doped Fe-based superconductor critical temperature from structural and topological parameters using machine learning. Int. J. Mater. Res. 112(1), 2–9 (2021)10.1515/ijmr-2020-7986 ↗

9. Y. Zhang, X. Xu, Disordered MgB2 superconductor critical temperature modeling through regression trees. Physica C Supercond. Appl. 597, 1354062 (2022)10.1016/j.physc.2022.1354062 ↗

10. Y. Zhang, X. Xu, Predicting the superconducting transition temperature and relative resistance ratio in YBa2Cu3O7 films. Physica C Supercond. Appl. 592, 1353998 (2022)10.1016/j.physc.2021.1353998 ↗

11. B. Jin, X. Xu, Gaussian process regression based silver price forecasts. Journal of Uncertain Systems 17(03), 2450013 (2024)10.1142/S1752890924500132 ↗

12. B. Jin, X. Xu, Forecasts of thermal coal prices through Gaussian process regressions. Ironmaking Steelmaking 51(8), 819–834 (2024)10.1177/03019233241265194 ↗

13. B. Jin, X. Xu, Forecasts of China mainland new energy index prices through Gaussian process regressions. Journal of Clean Energy and Energy Storage 1, 2450006 (2024)10.1142/S2811034X24500060 ↗

14. B. Jin, X. Xu, Regional steel price index predictions for North China through machine learning. Int. J. Min. Miner. Eng. 15(3), 314–350 (2024)10.1504/IJMME.2024.140697 ↗

15. S. Meister, M. Mecklenburg, V. Gramich, J.T. Stockburger, J. Ankerhold, B. Kubala, Resonators coupled to voltage-biased Josephson junctions: from linear response to strongly driven nonlinear oscillations. Phys. Rev. B. 92(17), 174532 (2015). https://doi.org/10.1103/PhysRevB.92.17453210.1103/PhysRevB.92.174532 ↗

16. H. Nakano, S. Saito, K. Semba, H. Takayanagi, Quantum time evolution in a qubit readout process with a Josephson bifurcation amplifier. Phys. Rev. Lett. 102(25), 257003 (2009). https://doi.org/10.1103/PhysRevLett.102.25700310.1103/PhysRevLett.102.257003 ↗

17. F. Mallet et al., Single-shot qubit readout in circuit quantum electrodynamics. Nat. Phys. 5(11), 791–795 (2009). https://doi.org/10.1038/nphys140010.1038/nphys1400 ↗

18. T. Picot, A. Lupa, S. Saito, C.J.P.M. Harmans, J.E. Mooij, Role of relaxation in the quantum measurement of a superconducting qubit using a nonlinear oscillator. Phys. Rev. B 78(13), 132508 (Oct.2008). https://doi.org/10.1103/PhysRevB.78.13250810.1103/PhysRevB.78.132508 ↗

19. Y.S. Greenberg et al., Low-frequency characterization of quantum tunneling in flux qubits. Phys. Rev. B 66(21), 214525 (2002). https://doi.org/10.1103/PhysRevB.66.21452510.1103/PhysRevB.66.214525 ↗

20. Y. Makhlin, G. Schön, A. Shnirman, Quantum-state engineering with Josephson-junction devices. Rev. Mod. Phys. 73(2), 357–400 (2001). https://doi.org/10.1103/RevModPhys.73.35710.1103/RevModPhys.73.357 ↗

21. J. Clarke, F.K. Wilhelm, Superconducting quantum bits. Nature 453, 1031–1042 (2008). https://doi.org/10.1038/nature0712810.1038/nature07128 ↗

22. K. Qian, C. Yao, Y. Wang, Q. Yang, S. Xiang, Q. Pei,... S. Dong, “Potential of Ultrashort Pulsed Electric Fields to Disrupt Dense Structure in Glioma Tumors,” IEEE Transactions on Biomedical Engineering, 1–10 2025. https://doi.org/10.1109/TBME.2025.356552010.1109/TBME.2025.3565520 ↗

23. S.T. Kingni, A. Cheukem, A.C. Chamgoué, F.T. Kamga, Analysis of Josephson junction with topologically nontrivial barrier. Eur. Phys. J. B. 93(8), 143–147 (2020). https://doi.org/10.1140/epjb/e2020-10125-310.1140/epjb/e2020-10125-3 ↗

24. L.J. Reinders, Stellar processes and quantum mechanics. In Sun in a Bottle?... Pie in the Sky! The Wishful Thinking of Nuclear Fusion Energy, in Sun in a bottle?... Pie in the sky!: The wishful thinking of nuclear fusion energy. (Springer International Publishing, Cham, 2021), pp.13–1710.1007/978-3-030-74734-3_2 ↗

25. M. Suzuki, M. Hayashi, H. Ebisawa, Nonlinear dynamics and resistive transition in intrinsic Josephson junctions. J. Phys. Chem. Solids 69(12), 3253–3256 (2008). https://doi.org/10.1016/j.jpcs.2008.06.13510.1016/j.jpcs.2008.06.135 ↗

26. M. Machida, T. Koyama, Localized rotating-modes in capacitively coupled intrinsic Josephson junctions: systematic study of branching structure and collective dynamical instability. Phys. Rev. B 70(2), 24523 (2004). https://doi.org/10.1103/PhysRevB.70.02452310.1103/PhysRevB.70.024523 ↗

27. Y.M. Shukrinov, F. Mahfouzi, P. Seidel, Equidistance of branch structure in capacitively coupled Josephson junctions model with diffusion current. Physica C Supercond. 449(1), 62–66 (2006). https://doi.org/10.1016/j.physc.2006.06.05410.1016/j.physc.2006.06.054 ↗

28. G. Cao, Y. Wang, H. Zhu, Z. Lou, L. Yu, Transferable adversarial attack on image tampering localization. J. Vis. Commun. Image Represent. 102, 104210 (2024). https://doi.org/10.1016/j.jvcir.2024.10421010.1016/j.jvcir.2024.104210 ↗

29. J. Clarke, F.K. Wilhelm, Superconducting quantum bits. Nature 7198(4), 1031–1042 (2008)10.1038/nature07128 ↗

30. E.N. Pozzo, D. Domínguez, Fidelity and quantum chaos in the mesoscopic device for the Josephson flux qubit. Phys. Rev. Lett. 98(5), 057006 (2007)10.1103/PhysRevLett.98.057006 ↗

31. S.K. Dana, D.C. Sengupta, K.D. Edoh, Chaotic dynamics in Josephson junction. IEEE Trans. Circuits Syst. I Fundam. Theory Appl. 48(8), 990–996 (2001). https://doi.org/10.1109/81.94018910.1109/81.940189 ↗

32. S.T. Kingni, K. Rajagopal, S. Çiçek, A. Cheukem, V.K. Tamba, G.F. Kuiate, Dynamical analysis, FPGA implementation and its application to chaos based random number generator of a fractal Josephson junction with unharmonic current-phase relation. Eur. Phys. J. B. 93(3), 1–11 (2020). https://doi.org/10.1140/epjb/e2020-100562-910.1140/epjb/e2020-100562-9 ↗

33. K. K. Likharev, Dynamics of Josephson junctions and circuits (5th edition). 1986.

34. S.T. Kingni, G.F. Kuiate, R. Kengne, R. Tchitnga, P. Woafo, Analysis of a no equilibrium linear resistive-capacitive-inductance shunted junction model, dynamics, synchronization, and application to digital cryptography in its fractional-order form. Complexity 2017, 1–12 (2017). https://doi.org/10.1155/2017/4107358. (WILEY, Hindawi)10.1155/2017/4107358 ↗

35. E. Neumann, A. Pikovsky, Slow-fast dynamics in Josephson junctions. Eur. Phys. J. B. 34(8), 293–303 (2003). https://doi.org/10.1140/epjb/e2003-00225-110.1140/epjb/e2003-00225-1 ↗

36. X.S. Yang, Q. Li, A computer-assisted proof of chaos in Josephson junctions. Chaos Solitons Fractals 27(1), 25–30 (2006). https://doi.org/10.1016/j.chaos.2005.04.01710.1016/j.chaos.2005.04.017 ↗

37. W. He, J. Zhu, Y. Feng, F. Liang, K. You, H. Chai,... W. Chai, Neuromorphic-enabled video-activated cell sorting. Nature Communications, vol. 15, no. 1, 10792, 2024. https://doi.org/10.1038/s41467-024-55094-010.1038/s41467-024-55094-0 ↗

38. J. Venkatesh, A.T. Kouanou, I.K. Ngongiah, D.C. Sekhar, S.T. Kingni, Dynamical probing and suppressing chaos using genetic algorithms in a Josephson junction model with quadratic damping embedded in the microcontroller implementation. J. Vib. Eng. Technol. 13(1), 8 (2025)10.1007/s42417-024-01661-0 ↗

39. D. Davarnia and M. Kiaghadi, A graphical framework for global optimization of mixed-integer nonlinear programs, arXiv preprint arXiv:2409.19794, 2024.10.2139/ssrn.4995063 ↗

40. T. Al-Hababi, M. Cao, B. Saleh, N.F. Alkayem, H. Xu, A critical review of nonlinear damping identification in structural dynamics: methods, applications, and challenges. Sensors 20(24), 7303 (2020)10.3390/s20247303 ↗

41. J. Lidal, J. Danon, Andreev bound states and supercurrent in disordered spin-orbit-coupled nanowire superconductor-normal-superconductor junctions. Phys. Rev. B 111(6), 064516 (2025)10.1103/PhysRevB.111.064516 ↗

42. V. Eclerová, A.E. Botha, Bifurcations of the superconductor–ferromagnet–superconductor φ0 Josephson junction. C, ,.,. ommunications Nonlinear Sci. Numer. Simul. 146(07), 108777 (2025)10.1016/j.cnsns.2025.108777 ↗

43. S. Alam, M.A. Jahangir, A. Aziz, A compact model for superconductor-insulator-superconductor (SIS) Josephson junctions. IEEE Electron Device Lett. 41(8), 1249–1252 (2020)10.1109/LED.2020.3002448 ↗

44. A. Costa, J. Fabian, D. Kochan, Microscopic study of the Josephson supercurrent diode effect in Josephson junctions based on two-dimensional electron gas. Phys. Rev. B 108(5), 054522 (2023)10.1103/PhysRevB.108.054522 ↗

45. M. Canturk, I.N. Askerzade, Chaotic dynamics of externally shunted Josephson junction with unharmonic CPR. J. Supercond. Nov. Magn. 26(4), 839–843 (2013)10.1007/s10948-012-2067-2 ↗

46. M. Canturk, I.N. Askerzade, Numerical study of josephson junction qubits with an unharmonic current-phase relation. IEEE Trans. Appl. Supercond. 21(5), 3541–3547 (2011). https://doi.org/10.1109/TASC.2011.215997410.1109/TASC.2011.2159974 ↗

47. Y.S. Barash, Interfacial pair breaking and planar weak links with an anharmonic current-phase relation. JETP Lett. 100(3), 205–215 (2014). https://doi.org/10.1134/S002136401415004110.1134/S0021364014150041 ↗

48. S.T. Kingni, G.F. Kuiate, V.K. Tamba, A.V. Monwanou, J. Bio, C. Orou, Analysis of a fractal Josephson junction with unharmonic current-phase relation. Supercond. Nov. Magn. 32(1), 2295–2301 (2019). https://doi.org/10.1007/s10948-018-4967-210.1007/s10948-018-4967-2 ↗

49. I.N. Askerzade, Effects of thermal fluctuations on dynamics of Josephson junction with unconventional current-phase relation. J. Supercond. Nov. Magn. 32(4), 3149–3154 (2019)10.1007/s10948-019-5112-6 ↗

50. Y.M. Shukrinov, F. Mahfouzi, Influence of coupling parameter on current–voltage characteristics of intrinsic Josephson junctions in high-Tc superconductors. Physica C: Superconductivity and its Applications 434(1), 6–12 (2006). https://doi.org/10.1016/j.physc.2005.11.00910.1016/j.physc.2005.11.009 ↗

51. K.K. Likharev, Dynamics of Josephson junctions and circuits, 5th editio (Gordon and Breach Science Publishers, New York, 1986)

52. K.K. Likharev, Superconducting weak links. Rev. Mod. Phys. 51(1), 101 (1979)10.1103/RevModPhys.51.101 ↗

53. E. Demler, A.J. Berlinsky, C. Kallin, G.B. Arnold, M.R. Beasley, Proximity effect and Josephson coupling in the SO(5) theory of high-T_C Misplaced & superconductivity. Phys. Rev. Lett. 80(13), 2917–2920 (1998). https://doi.org/10.1103/PhysRevLett.80.291710.1103/PhysRevLett.80.2917 ↗

54. S.T. Kingni, A. Cheukem, A.C. Chamgoue, F.T. Kamga, Analysis of Josephson junction with topologically nontrivial barrier. The European Physical Journal B 93(8), 1–6 (2020). https://doi.org/10.1140/epjb/e2020-10125-310.1140/epjb/e2020-10125-3 ↗

55. B. Ramakrishnan, A.A. Oumate, M. Tuna, İ Koyuncu, S.T. Kingni, K. Rajagopal, Analysis, FPGA implementation of a Josephson junction circuit with topologically nontrivial barrier and its application to ring-based dual entropy core true random number generator. Eur. Phys. J. Spec. Top. 231(5), 1049–1059 (2022)10.1140/epjs/s11734-021-00324-5 ↗

56. N. Read, D. Green, Paired states of fermions in two dimensions with breaking of parity and time-reversal symmetries and the fractional quantum hall effect. Phys. Rev. B 61(15), 10267 (2000)10.1103/PhysRevB.61.10267 ↗

57. D.A. Ivanov, Non-abelian statistics of half-quantum vortices in p -wave superconductors. Phys. Rev. Lett. 86(1), 1–4 (2001)

58. X.L. Qi, S.C. Zhang, Topological insulators and superconductors. Rev. Mod. Phys. 83(10), 1–54 (2011). https://doi.org/10.1103/RevModPhys.83.105710.1103/RevModPhys.83.1057 ↗

59. L. Fu, C.L. Kane, Superconducting proximity effect and Majorana fermions at the surface of a topological insulator. Phys. Rev. Lett. 100(9), 096407 (2008). https://doi.org/10.1103/PhysRevLett.100.09640710.1103/PhysRevLett.100.096407 ↗

60. L. Yu, Y. Li, S. Weng, H. Tian, J. Liu, Adaptive multi-teacher softened relational knowledge distillation framework for payload mismatch in image steganalysis. J. Vis. Commun. Image Represent. 95, 103900 (2023). https://doi.org/10.1016/j.jvcir.2023.10390010.1016/j.jvcir.2023.103900 ↗

61. M. Veldhorst, C.G. Molenaar, C.J.M. Verwijs, H. Hilgenkamp, A. Brinkman, Optimizing the Majorana character of SQUIDs with topologically nontrivial barriers. Phys. Rev. B 86(2), 024509 (2012)10.1103/PhysRevB.86.024509 ↗

62. X. Wang et al., “Controllable creation of topological boundary states in topological insulator based Josephson corner junctions Share,” Phys. Rev. B, vol. 112, no. 7, pp. 045430 –, 2025.10.1103/m49c-7vqh ↗

63. J. Park, Y.B. Choi, G.H. Lee, H.J. Lee, Characterization of Shapiro steps in the presence of a 4π-periodic Josephson current. Phys. Rev. B 103(23), 235428 (2021)10.1103/PhysRevB.103.235428 ↗

64. Y. Jang, Y. Joo, Optimal conditions for observing fractional Josephson effect in topological Josephson junctions. J. Korean Phys. Soc. 78(11), 58–63 (2020). https://doi.org/10.1007/s40042-020-00035-510.1007/s40042-020-00035-5 ↗

65. F. Domínguez et al., Josephson junction dynamics in the presence of 2 π - and 4 π -periodic supercurrents. Phys. Rev. B 195430(05), 1–9 (2017). https://doi.org/10.1103/PhysRevB.95.19543010.1103/PhysRevB.95.195430 ↗

66. H.L. Ndassi, R. Kengne, A.G. Gakam Tegue, M.T. Motchongom, R. Tchitnga, M. Tchoffo, A robust image encryption scheme based on compressed sensing and novel 7D oscillato with complex dynamics. Heliyon 9(6), e16514 (2023). https://doi.org/10.1016/j.heliyon.2023.e1651410.1016/j.heliyon.2023.e16514 ↗

67. J. Ramadoss, V.K. Tamba, C. Ainamon, K. Rajagopal, S.T. Kingni, Medical image encryption based on RNG with an autonomous piecewise damping Josephson junction jerk oscillator embedded in FPGA. Phys. Scr. 98(5), 055212 (2023)10.1088/1402-4896/acc89b ↗

68. N.F. Pedersen, K. Saermark, Analytical solution for a Josephson-junction model with capacitance. Physica 69(2), 572–578 (1973). https://doi.org/10.1016/0031-8914(73)90089-X10.1016/0031-8914(73)90089-X ↗

69. Y. Tanaka, T. Yokoyama, N. Nagaosa, Manipulation of the Majorana Fermion, Andreev Reflection, and Josephson Current on Topological Insulators. Phys. Rev. Lett. 103, 107002–107005 (2009)10.1103/PhysRevLett.103.107002 ↗

70. I.R. Rahmonov, Y.M. Shukrinov, Determination of Cooper pairs and Majorana fermions currents ratio in dc SQUID with topologically nontrivial barriers. Low Temp. Phys. 43(7), 824–828 (2017). https://doi.org/10.1063/1.499563110.1063/1.4995631 ↗

71. I.N. Askerzade, A. Bozbey, M. Canturk, Modern aspects of Josephson dynamics and superconductivity electronics (Springer, Berlin, 2017)10.1007/978-3-319-48433-4 ↗

72. C. Li, Y. Jiang, X. Ma, On offset boosting in chaotic system. Chaos Theory Appl. 3(2), 47–54 (2021). https://doi.org/10.51537/chaos.95984110.51537/chaos.959841 ↗

73. B. Sriram, D.M. Godonou, C. Ainamon, I.K. Ngongiah, K. Rajagopal, Dynamical probing and multiple actions of linear offset boosting of constants in Josephson junction instigated by Wien bridge oscillator embedded in the microcontroller. Pramana 98, 138–211 (2024). https://doi.org/10.1007/s12043-024-02816-010.1007/s12043-024-02816-0 ↗

74. K. Zhan, D. Wei, J. Shi, J. Yu, Cross-utilizing hyperchaotic and DNA sequences for image encryption. J. Electron. Imaging 26, 013021 (2017). https://doi.org/10.1117/1.JEI.26.1.01302110.1117/1.JEI.26.1.013021 ↗

75. Y.P.K. Nkandeu, A. Tiedeu, An image encryption algorithm based on substitution technique and chaos mixing. Multimedia Tools Appl. 78, 10013–10034 (2019). https://doi.org/10.1007/s11042-018-6612-210.1007/s11042-018-6612-2 ↗

76. M. Madani and Y. Bentoutou, “Cryptage d'images médicales à la base des cartes chaotiques, ” International Conference Colloque Tassili SCCIBOV, 2015.

77. R. Gupta, R. Pachauri, A.K. Singh, An effective approach of secured medical image transmission using encryption method. Mol. Cell. Biomech. 15, 63 (2018). https://doi.org/10.3970/mcb.2018.0011410.3970/mcb.2018.00114 ↗

78. Y. Abanda, A. Tiedeu, Image encryption by chaos mixing. IET Image Process. 10, 742–750 (2016). https://doi.org/10.1049/iet-ipr.2015.024410.1049/iet-ipr.2015.0244 ↗

79. G. Jeatsa Kitio, A. Djomo Fanda, I.R. Kemlenack Feulefack, J.R. Mboupda Pone, R. Kengne, A. Tiedeu, Biomedical image encryption with a novel memristive Chua oscillator embedded in a microcontroller. Braz. J. Phys. 53, 56 (2023). https://doi.org/10.1007/s13538-023-01268-y10.1007/s13538-023-01268-y ↗

80. Y.P.K. Nkandeu, J.R. Mboupda Pone, A. Tiedeu, Image encryption algorithm based on synchronized parallel diffusion and new combinations of 1D discrete maps. Sensing and Imaging 21, 1–36 (2020). https://doi.org/10.1007/s11220-020-00318-y10.1007/s11220-020-00318-y ↗

81. F. Hadji, “Conception et réalisation d'un système de cryptage pour les images médicales,” Université Mohamed Boudiaf-M’Sila, Faculté des Mathématiques et de l’Infromatique, Département d’Informatique, 2018.

82. M. Kiaghadi, M. Keshvarinia, M. Sheikholeslami, Modeling, simulation, and artificial intelligence: a convergence in heat transfer systems, in Revolutionizing Heat Transfer. (Elsevier, 2025), pp.201–22210.1016/B978-0-443-31530-5.00014-6 ↗

83. A. Tolk, P. Barry, S.C. Doskey, Using modeling and simulation and artificial intelligence to improve complex adaptive systems engineering. Int. J. Model. Simul. Sci. Comput. 13(02), 2241004 (2022)10.1142/S1793962322410045 ↗

84. M. Khorashadizade, S. Hosseini, M. Jouyban, An improved binary slime mold algorithm for intrusion detection systems. Concurrency Comput. Pract. Exp. 37(15–17), e70127 (2025)10.1002/cpe.70127 ↗

85. M. Hafezan, R. Jahadi, and E. Atoofian, PCTC: Hardware and Software Co-design for P runed C apsule Networks on T ensor C ores. In European Conference on Parallel Processing, pp. 196–210, 2024. Cham: Springer Nature Switzerland.10.1007/978-3-031-69766-1_14 ↗

86. S. Mansouri, V. Samatova, N. Korchiev, and K. Anyanwu, DeMaTO: an ontology for modeling transactional behavior in decentralized marketplaces. In 2023 IEEE/WIC International Conference on Web Intelligence and Intelligent Agent Technology (WI-IAT), pp. 171–180, 2023. IEEE.10.1109/WI-IAT59888.2023.00029 ↗

87. H. Zhu, Y. Zhao, Y. Song, 2D logistic-modulated-sine-coupling-logistic chaotic map for image encryption. IEEE Access 7, 14081–14098 (2019)10.1109/ACCESS.2019.2893538 ↗

88. X. Chai, Z. Gan, K. Yang, Y.R. Chen, X. Liu, A novel color image encryption algorithm based on genetic recombination and the four-dimensional memristive hyperchaotic system. Chin. Phys. B. 25(10), 100503 (2016)10.1088/1674-1056/25/10/100503 ↗

89. K. Zhan, D. Wei, J. Shi, J. Yu, Cross-utilizing hyperchaotic and DNA sequences for image encryption. J. Electron. Imaging 26(1), 013021–013021 (2017). https://doi.org/10.1117/1.JEI.26.1.01302110.1117/1.JEI.26.1.013021 ↗

90. H. Zhu, Y. Zhao, Y. Song, 2D logistic–modulated–sine–coupling–logistic chaotic map for image encryption. IEEE Access 7, 14081–14098 (2019). https://doi.org/10.1109/ACCESS.2019.289353810.1109/ACCESS.2019.2893538 ↗