Dynamical behavior of a new jerk system inspired from chaotic memory oscillators

• Autorzy: Al-Azzawi Saad Fawzi

Identyfikatory

DOI

10.24425/acs.2024.149656

• Języki publikacji: EN

Abstrakty

EN

This paper constructs a six-term new simple 3D jerk system modeled by chaotic model memory oscillators with four parameters that control the behavior. The suitable choice of one of these parameters helps the system describe behavior and attractors. This means that the choice is a parameter of the associated behavior (dissipative or conservative) and attractors (self-excited or hidden). Some features of the equilibrium are observed that are related to the dependence on these parameters, such as saddle-foci, non-hyperbolic, and node-foci. This system is rich in dynamic features including chaotic, quasi-periodic (2-torus), and periodic via the utilization of bifurcation diagrams and Lyapunov spectrum. Finally, a new image encryption algorithm is introduced that utilizes the jerk system. The algorithm is assessed through statistical performance analysis, according to the results of the experiments and security tests, it has been verified that the suggested image encryption algorithm is highly secure and could be a viable option for real-world applications.

Słowa kluczowe

EN

chaotic memory oscillators (𝑀𝑂4); jerk system; elegant system; encryption; decryption

• Wydawca: Polish Academy of Sciences, Committee of Automatic Control and Robotics
• Czasopismo: Archives of Control Sciences
• Rocznik: 2024
• Tom: Vol. 34, No. 1
• Strony: 149--170
• Opis fizyczny: Bibliogr. 46 poz., fot., rys., tab., wzory

Twórcy

autor

Al-Azzawi Saad Fawzi

• Department of Mathematics, College of Computer Science and Mathematics, University of Mosul, Mosul, Iraq

• https://orcid.org/0000-0002-8198-8035

Bibliografia

• [1] E.N. Lorenz: Deterministic nonperiodic flow. Journal of Atmospheric Sciences, 20(2), (1963), 130-141, DOI: 10.1175/1520-0469(1963)020<0130:DNF>2.0.CO;2
• [2] S.F. Al-Azzawi, M.A. Mohamed, H. Rubiani, M. Mamat, J. Titaley and Y.A.R. Lang: Chaotic Lorenz system and it’s suppressed. Journal of Advanced Research in Dynamical and Control, 12(2), (2020), 548-555, DOI: 10.5373/JARDCS/V12I2/S20201076
• [3] J.C. Sprott: Some simple chaotic flows. Physical Review E, 50(2), (1994), R647, DOI: 10.1103/PhysRevE.50.R647
• [4] M. Molaie, S. Jafari, J.C. Sprott and S.M.R.H. Golpayegani: Simple chaotic flows with one stable equilibrium. International Journal of Bifurcation and Chaos, 23(1), (2013), 1350188, DOI: 10.1142/S0218127413501885
• [5] J.C. Sprott: Elegant chaos: algebraically simple chaotic flows. World Scientific, 2010.
• [6] F. Yu, W. Zhang, X. Xiao, W. Yao, S. Cai, J. Zhang and Y. Li: Dynamic analysis and FPGA implementation of a new, simple 5D memristive hyperchaotic Sprott-C system. Mathematics, 11(3), (2023), DOI: 701.10.3390/math11030701
• [7] S.F. Al-Azzawi and A.S. Al-Obeidi: Chaos synchronization in a new 6D hyperchaotic system with self-excited attractors and seventeen terms. Asian-European Journal of Mathematics, 14(5), (2021), 2150085, DOI: 10.1142/S1793557121500856
• [8] Q. Lai and S. Chen: Generating multiple chaotic attractors from Sprott B system. International Journal of Bifurcation and Chaos, 26(11), (2016), 1650177, DOI: 10.1142/S0218127416501777
• [9] H. Jia, W. Shi, L. Wang and G. Qi: Energy analysis of Sprott-A system and generation of a new Hamiltonian conservative chaotic system with coexisting hidden attractors. Chaos, Solitons & Fractals, 133, (2020), 109635, DOI: 10.1016/j.chaos.2020.109635
• [10] M. A. Al-hayali and F.S. Al-Azzawi: A 4D hyperchaotic Sprott S system with multi-stability and hidden attractors. Journal of Physics: Conference Series. 1879(3), (2021), 032031, DOI: 10.1088/1742-6596/1879/3/032031
• [11] S.F. Al-Azzawi and M.A. Al-Hayali: Coexisting of self-excited and hidden attractors in a new 4D hyperchaotic Sprott-S system with a single equilibrium point. Archives of Control Sciences, 32(1), (2022), 37-56, DOI: 10.24425/acs.2022.140863
• [12] O.S. Ojoniyi and A.N. Njah: A 5D hyperchaotic Sprott B system with coexisting hidden attractors. Chaos, Solitons and Fractals, 87, (2016), 172-181, DOI: 10.1016/j.chaos.2016.04.004
• [13] S.F. Al-Azzawi and M.A. Al-Hayali: Multiple attractors in a novel simple 4D hyper-chaotic system with chaotic 2-torus and its circuit implementation. Indian Journal of Physics, 97(4), (2023), 1169-1179, DOI: 10.1007/s12648-022-02483-0
• [14] Q. Yang and C. Chen: A 5D hyperchaotic system with three positive Lyapunov exponents coined. International Journal of Bifurcation and Chaos, 23(6), (2013), 1350109, DOI: 10.1142/S0218127413501095
• [15] Q. Yang, W.M. Osman and C. Chen: A new 6D hyperchaotic system with four positive Lyapunov exponents coined. International Journal of Bifurcation and Chaos, 25(4), (2015), 1550060, DOI: 10.1142/S0218127415500601
• [16] Q. Yang, D. Zhu and L.Yang: A new 7D hyperchaotic system with five positive Lyapunov exponents coined. International Journal of Bifurcation and Chaos, 28(5), (2018), 1850057, DOI: 10.1142/S0218127418500578
• [17] J.C. Sprott: A new class of chaotic circuit. Physics Letters A, 266(1), (2000), 19-23, DOI: 10.1016/S0375-9601(00)00026-8
• [18] S. Vaidyanathan, K. Benkouider, A. Sambas and S.A. Safaan: A new 4-D hyperchaotic four-wing system, its bifurcation analysis, complete synchronization and circuit simulation. Archives of Control Sciences, 32(3), (2022), 507-534, DOI: 10.24425/acs.2022.142847
• [19] S. Vaidyanathan, K. Benkouider, A. Sambas and P. Darwin: Bifurcation analysis, circuit design and sliding mode control of a new multistable chaotic population model with one prey and two predators. Archives of Control Sciences, 33(1), (2023), 127-153, DOI: 10.24425/acs.2023.145117
• [20] N. Hadj Taieb, M.A. Hammami and F. Delmotte: Stability analysis and design of state estimated controller for delay fuzzy systems with parameter. Archives of Control Sciences, 32(4), (2022), 709-731, DOI: 10.24425/acs.2022.143668
• [21] J.C. Sprott: A proposed standard for the publication of new chaotic systems. International Journal of Bifurcation and Chaos, 21(9), (2011), 2391-2394, DOI: 10.1142/S021812741103009X
• [22] S. Vaidyanathan, C.K. Volos, I.M. Kyprianidis, I.N. Stouboulos and V.T. Pham: Analysis, adaptive control and anti-synchronization of a six-term novel jerk chaotic system with two exponential nonlinearities and its circuit simulation. Journal of Engineering Science and Technology Review, 8(2), (2015), 24-36, DOI: 10.25103/jestr.082.05
• [23] S. Vaidyanathan, A. Sambas, M. Mamat and W.S. Mada Sanjaya: Analysis, synchronisation and circuit implementation of a novel jerk chaotic system and its application for voice encryption. International Journal of Modelling, Identification and Control, 28(2), (2017). 153-166, DOI: 10.1504/IJMIC.2017.10006361
• [24] S.A. Fadhel, Z.N. Al-Kateeb and M.J. Al-Shamdeen: An improved data hiding using pixel value difference method and hyperchaotic system. Journal of Physics: Conference Series. 1879(2), (2021), 022089, DOI: 10.1088/1742-6596/1879/2/022089
• [25] N.M. Mohammed and Z.N. Al-Kateeb: A new secure encryption algorithm based on RC4 cipher and 4D hyperchaotic Sprott-S system. In 2022 Fifth College of Science International Conference of Recent Trends in Information Technology (CSCTIT), 131-136, IEEE, DOI: 10.1109/CSCTIT56299.2022.10145711
• [26] A. Raslan and A. Entesar: Enhancing Banach’s contraction method using the particle swarm optimization to solve the system Drinfeld-Sokolov-Wilson. Journal of Physics: Conference Series, 2322(1), (2022), 012031, DOI: 10.1088/1742-6596/2322/1/012031
• [27] A.N. Negou and J. Kengne: Dynamic analysis of a unique jerk system with a smoothly adjustable symmetry and nonlinearity: Reversals of period doubling, offset boosting and coexisting bifurcations. AEU-International Journal of Electronics and Communications, 90, (2018), 1-19, DOI: 10.1016/j.aeue.2018.04.003
• [28] K. Rajagopal, V.T. Pham, F.R. Tahir, A. Akgul, H.R. Abdolmohammadi and S. Jafari: A chaotic jerk system with non-hyperbolic equilibrium: Dynamics, effect of time delay and circuit realisation. Pramana, 90(52), (2018), 1-8, DOI: 10.1007/s12043-018-1545-x
• [29] W. Feng, Y.G. He, C.L. Li, X.M. Su and X.Q. Chen: Dynamical behavior of a 3D jerk system with a generalized Memristive device. Complexity, 2018, (2018), DOI: 10.1155/2018/5620956
• [30] J.R.M. Pone, S.T. Kingni, G.R. Kol and V.T. Pham: Hopf bifurcation, antimonotonicity and amplitude controls in the chaotic Toda jerk oscillator: analysis, circuit realization and combination synchronization in its fractional-order form. Journal for Control, Measurement, Electronics, Computing and Communications, 60(2), (2019), 149-161, DOI: 10.1080/00051144.2019.1600109
• [31] S. Zhang and Y. Zeng: A simple jerk-like system without equilibrium: Asymmetric coexisting hidden attractors, bursting oscillation and double full Feigenbaum remerging trees. Chaos, Solitons and Fractals, 120, (2019), 25-40, DOI: 10.1016/j.chaos.2018.12.036
• [32] K. Lamamra, S. Vaidyanathan, W.T. Putra, E. Darnila and A. Sambas: A new 3-D chaotic jerk system with four nonlinear terms, its backstepping synchronization and circuit simulation. Journal of Physics: Conference Series, 1477(2), (2020), 022017, DOI: 10.1088/1742-6596/1477/2/022017
• [33] L.K. Kengne, H.K. Tagne, J.M. Pone and J. Kengne: Dynamics, control and symmetry-breaking aspects of a new chaotic jerk system and its circuit implementation. The European Physical Journal Plus, 135(3), (2020), 340, DOI: 10.1140/epjp/s13360-020-00338-3
• [34] M. Joshi and A. Ranjan: An autonomous simple chaotic jerk system with stable and unstable equilibria using reverse sine hyperbolic functions. International Journal of Bifurcation and Chaos, 30(5), (2020), 2050070, DOI: 10.1142/S0218127420500704
• [35] K. Rajagopal, S.T. Kingni, G.H. Kom, V.T. Pham, A. Karthikeyan and S. Jafari: Self-excited and hidden attractors in a simple chaotic jerk system and in its time-delayed form: analysis, electronic implementation, and synchronization. Journal of the Korean Physical Society, 77(2), (2020), 145-152, DOI: 10.3938/jkps.77.145
• [36] C. Li, J.C. Sprott, W. Joo-Chen Thio and Z. Gu: A simple memristive jerk system. IET Circuits, Devices & Systems, 15(4), (2021), 388-392, DOI: 10.1049/cds2.12035
• [37] M.H. Arshad, M. Kassas, A.E. Hussein and M.A. Abido: A simple technique for studying chaos using jerk equation with discrete time sine map. Applied Sciences, 11(1), (2021), 437, DOI: 10.3390/app11010437
• [38] M. Liu, B. Sang, N. Wang and I. Ahmad: Chaotic dynamics by some quadratic jerk systems. Axioms, 10(3), (2021), 227, DOI: 10.3390/axioms10030227
• [39] A. Sambas, S. Vaidyanathan, I. Moroz, B. Idowu, M.A. Mohamed, M. Mamat and W.M. Sanjaya: A simple multi-stable chaotic jerk system with two saddle-foci equilibrium points: analysis, synchronization via active backstepping control and electronic circuit design. International Journal of Electrical and Computer Engineering, 11(4), (2021), 2941-2952, DOI: 10.11591/ijece.v11i4.pp2941-2952
• [40] P.P. Singh and B.K. Roy: Pliers shaped coexisting bifurcation behaviors in a simple jerk chaotic system in comparison with 21 reported systems. IFAC-PapersOnLine, 55(1), (2022), 920-926, DOI: 10.1016/j.ifacol.2022.04.151
• [41] X. Hu, B. Sang and N. Wang: The chaotic mechanisms in some jerk systems. AIMS Mathematics, 7(9), (2022), 15714-15740, DOI: 10.3934/math.2022861
• [42] P.C. Rech: Self-excited and hidden attractors in a multistable jerk system. Chaos, Solitons and Fractals, 164, (2022), 112614, DOI: 10.1016/j.chaos.2022.112614
• [43] S. Vaidyanathan, K. Benkouider and A. Sambas: A new multistable jerk chaotic system, its bifurcation analysis, backstepping control-based synchronization design and circuit simulation. Archives of Control Sciences, 32(1), (2022), 123-152, DOI: 10.24425/acs.2022.140868
• [44] R. Suresh, K. Sathish Kumar, M. Regan, K.A. Niranjan Kumar, R. Narmada Devi and A.J. Obaid: Dynamical properties of a modified chaotic Colpitts oscillator with triangular wave non-linearity. Archives of Control Sciences, 33(1), (2023), 25-53, DOI: 10.24425/acs.2023.145112
• [45] N. Khan, M.A. Qureshi, S. Akbar and A. Ara: Probing 3D chaotic Thomas’ cyclically attractor with multimedia encryption and electronic circuitry. Archives of Control Sciences, 33(1), (2023) 239-271, DOI: 10.24425/acs.2023145120
• [46] M.A. Mohamed, T. Bonny, A. Sambas, S. Vaidyanathan, W. Al Nassan, S. Zhang, K. Obaideen, M. Mamat and Mohd K.M. Nawawi: A speech cryptosystem using the new chaotic system with a capsule-shaped equilibrium curve. Computers, Materials and Continua, 75(3), (2023), 5987-6006, DOI: 10.32604/cmc.2023.035668