A new chaotic jerk system with a sinusoidal nonlinearity, its bifurcation analysis, multistability, circuit design and complete synchronization design via backstepping control

• Autorzy: Vaidyanathan Sundarapandian , Hannachi Fareh , Moroz Irene M. , Aruna Chittineni , Mohamed Mohamad Afendee , Sambas Aceng

Identyfikatory

DOI

10.24425/acs.2024.149662

• Języki publikacji: EN

Abstrakty

EN

In this research work, we investigate a new three-dimensional jerk system with three parameters in which one of the nonlinear terms is a sinusoidal nonlinearity. We show that the new jerk system has two unstable equilibrium points on the 𝑥-axis. Numerical integrations show the existence of periodic and chaotic states, as well as unbounded solutions. Consideration of the Poincaré sphere at infinity found no periodic states. We show that the new jerk system exhibits multistability with coexisting attractors. We also present results for the offset boosting of the proposed chaotic jerk system. Using MultiSim version 14.1, we design an electronic circuit for the new jerk system with a sinusoidal nonlinearity. As a control application, we design complete synchronization for the master-slave jerk systems using backstepping control technique. Simulations are presented to illustrate the main results of this research work.

Słowa kluczowe

EN

chaos; chaotic systems; jerk systems; mechanical systems; bifurcation analysis; backstepping control; synchronization; circuit design

• Wydawca: Polish Academy of Sciences, Committee of Automatic Control and Robotics
• Czasopismo: Archives of Control Sciences
• Rocznik: 2024
• Tom: Vol. 34, No. 2
• Strony: 301--322
• Opis fizyczny: Bibliogr. 31 poz., fot., rys., wzory

Twórcy

autor

Vaidyanathan Sundarapandian

• Centre for Control Systems, Vel Tech University, 400 Feet Outer Ring Road, Avadi, Chennai-600062 Tamil Nadu, India
• Faculty of Information and Computing, Universiti Sultan Zainal Abidin Terengganu, Malaysia

• https://orcid.org/0000-0003-4696-908X

autor

Hannachi Fareh

• Larbi Tebessi University - Tebessi, route de constantine, 12022, Tebessa, Algeria

• https://orcid.org/0000-0002-8213-2757

autor

Moroz Irene M.

• Mathematical Institute, University of Oxford, Andrew Wiles Building, ROQ, Oxford Ox2 6GG, UK

• https://orcid.org/0000-0003-1503-939X

autor

Aruna Chittineni

• Department of Computer Science and Engineering, KKR & KSR Institute of Technology and Sciences, Vinjanampadu, Vatticherukuru Mandal, Guntur-522017, Andhra Pradesh, India

• https://orcid.org/0009-0005-4427-1093

autor

Mohamed Mohamad Afendee

• Faculty of Information and Computing, Universiti Sultan Zainal Abidin, Terengganu, Malaysia

• https://orcid.org/0000-0001-5985-3970

autor

Sambas Aceng

• Faculty of Informatics and Computing, Universiti Sultan Zainal Abidin, Gong Badak, 21300, Terengganu, Malaysia
• Department of Mechanical Engineering, Universitas Muhammadiyah Tasikmalaya, Jawa Barat 46196, Indonesia

• https://orcid.org/0000-0002-1623-0770

Bibliografia

• [1] D. Ding, W. Wang, Z. Yang, Y. Hi, J. Wang, M. Wang, Y. Niu and H. Zhu: An n-dimensional modulo chaotic system with expected Lyapunov exponents and its application in image encryption. Chaos, Solitons & Fractals, 174 (2023). DOI: 10.1016/j.chaos.2023.113841
• [2] S. Sahoo and B.K. Roy: Design of multi-wing chaotic systems with higher largest Lyapunov exponent. Chaos, Solitons & Fractals, 157 (2022). DOI: 10.1016/j.chaos.2022.111926
• [3] E. Gokcay and H. Tora: A novel data encryption method using an interlaced chaotic transform. Expert Systems with Applications, 237 (2024). DOI: 10.1016/j.eswa.2023.121494
• [4] H. Wen and Y. Lin: Cryptanalysis of an image encryption algorithm using quantum chaotic map and DNA coding. Expert Systems with Applications, 237 (2024). DOI: 10.1016/j.optlastec.2017.04.022
• [5] Q. Lai and H. Zhang: A new image encryption method based on memristive hyperchaos. Optics and Laser Technology, 166 (2023). DOI: 10.1016/j.optlastec.2023.109626
• [6] S. Yan, Y. Zhang, Y. Ren, X. Sun, Y. Cui and L. Li: A new locally active memristor and its chaotic system with infinite nested coexisting attractors. Nonlinear Dynamics, 111(18), (2023), 17547-17560. DOI: 10.1007/s11071-023-08731-0
• [7] A.L.O. Duarte and M. Eisencraft: Denoising of discrete-time chaotic signals using echo state networks. Signal Processing, 214 (2024). DOI: 10.1016/j.sigpro.2023.109252
• [8] D. Chen, S. Shi and X. Gu: Chaos detection scheme for multiple variable-frequency signals with overlapping frequencies. Eurasip Journal on Advances in Signal Processing, 2023(1), (2023). DOI: 10.1186/s13634-023-01050-x
• [9] H.E. Kiran, A. Akgul, O. Yildiz and E. Deniz: Lightweight encryption mechanism with discrete-time chaotic maps for internet of robotic things. Integration, 93 (2023). DOI: 10.1016/j.vlsi.2023.06.001
• [10] E. Petavratzis, C. Volos and I. Stouboulos: Experimental study of terrain coverage of an autonomous chaotic mobile robot. Integration, 90 (2023), 104-114. DOI: 10.1016/j.vlsi.023.01.010
• [11] S.S. Alzaid, A. Kumar, S. Kumar and B.S.T. Alkahtani: Chaotic behavior of financial dynamical system with generalized fractional operator. Fractals, 31(4), (2023). DOI: 10.1142/S0218348X2340056X
• [12] A. Azam and D.A. Sunny: Generation of multiscroll chaotic attractors of a finance system with mirror symmetry. Soft Computing, 27(6), (2023), 2769-2782. DOI: 10.1007/s00500-022-07501-1
• [13] S. Vaidyanathan and A.T. Azar: Backstepping Control of Nonlinear Dynamical Systems. Academic Press, London, U.K., 2021.
• [14] S. Vaidyanthan, A.S.T. Kammogne, E. Tlelo-Cuautle, C.N. Talonang, B. Abd-El-Atty, A.A. Abd El-Latif, E.M. Kengne, V.F. Mawamba, A. Sambas, P. Darwin and B. Ovilla-Martinez: A novel 3-D jerk system, its bifurcation analysis, electronic circuit design and a cryptographic application. Electronics, 12(13), (2023). DOI: 10.3390/electronics12132818
• [15] F. Li and J. Zeng: Multi-scroll attractor and multi-stable dynamics of a three-dimensional jerk system. Energies, 16(5), (2023). DOI: 10.3390/en16052494
• [16] Y. Xia, S. Hua and Q. Bi: Quasi-periodic structure in chaotic bursting attractor for a controlled jerk oscillator. Chaos, Solitons & Fractals, textbf174 (2023). DOI: 10.1016/j.chaos.2023.113902
• [17] S. Vaidyanathan, E. Tlelo-Cuautle, K. Benkouider, A. Sambas and B. Ovilla-Martinez: FPGA-based implementation of a new 3-D multistable chaotic jerk system with two unstable balance points. Technologies, 11(4), (2023). DOI: 10.3390/technologies11040092
• [18] K. Zourmba, C. Fischer, B. Gambo, J.Y. Effa and A. Mohamadou: Chaotic oscillator with diode-inductor nonlinear bipole-based jerk circuit: Dynamical study and synchronization. Journal of Circuits, Systems and Computers, 32(12), (2023). DOI: 10.1142/S0218126623502146
• [19] J. Li and N. Cui: Dynamical analysis of a new 5D hyperchaotic system. Physica Scripta, 98(10), (2023). DOI: 10.1088/1402-4896/acf41a
• [20] H. Wang, G. Ke, J. Pan and Q. Su: Modeling, dynamical analysis and numerical simulation of a new 3D cubic Lorenz-like system. Scientific Reports, 13(1), (2023). DOI: 10.1038/s41598-023-33826-4
• [21] L. Laskaridis, C. Volos, H. Nistazakis and E. Meletlidou: Exploring the dynamics of a multistable general model of discrete memristor-based map featuring an exponentially varying memristance. Integration, 95 (2024). DOI: 10.1016/j.vlsi.2023.102131
• [22] F. Yu, Y. Yuan, C. Wu, W. Yao, C. Xu, S. Cai and C. Wang: Modeling and hardware implementation of a class of Hamiltonian conservative chaotic systems with transient quasi-period and multistability. Nonlinear Dynamics, 112(3), (2024), 2331-2347. DOI: 10.1007/s11071-023-09148-5
• [23] C. Li, Y. Jiang and X. Ma: On offset boosting in chaotic system. Chaos, 3(2), (2021), 47-54. DOI: 10.51537/chaos.959841
• [24] X. Zhang, J. Xu and A.J. Moshayedi: Design and FPGA implementation of a hyperchaotic conservative circuit with initial offset-boosting and transient transition behavior based on memcapacitor. Chaos, Solitons and Fractals, 179 (2024). DOI: 10.1016/j.chaos.2024.114460
• [25] J. Zhang, Y. Guo and J. Cuo: Design of memristor hyperchaotic circuit with burst oscillation and infinite attractor coexistence and its application. Microelectronic Engineering, 282 (2023). DOI: 10.1016/j.mee.2023.112099
• [26] A. Dlamini and E.F. Doungmo Goufo: Generation of self-similarity in a chaotic system of attractors with many scrolls and their circuit’s implementation. Chaos, Solitons & Fractals, 176 (2023). DOI: 10.1016/j.chaos.2023.114084
• [27] T. Bonny, W.A. Nassan, S. Vaidyanathan and A. Sambas: Highly-secured chaos-based communication system using cascaded masking technique and adaptive synchronization. Multimedia Tools and Applications, 82(22), (2023). DOI: 10.1007/s11042-023-14643-3
• [28] S. Vaidyanathan and A.T. Azar: Adaptive control and synchronization of Halvorsen circulant chaotic systems. Studies in Fuzziness and Soft Computing, 337 (2016), 225-247. DOI: 10.1007/978-3-319-30340-6_10
• [29] N. Debdouche, L. Zarour, H. Benhouhenni, F. Mehazzem and B. Deffaf: Robust integral backstepping control microgrid connected photovoltaic System with battery Energy storage through multi-functional voltage source inverter using direct power control SVM strategies. Energy Reports, 10 (2023), 565-580. DOI: 10.1016/j.egyr.2023.07.012
• [30] J.D. Barros, L. Rocha and J.F. Silva: Backstepping control of NPC multilevel converter interfacing AC and DC microgrids. Energies, 16(14), (2023). DOI: 10.3390/en16145515
• [31] E. Özalp, G. Margazoglou and L. Magri: Reconstruction, forecasting, and stability of chaotic dynamics from partial data. Chaos, 33(9), (2023). DOI: 10.1063/5.0159479

Uwagi

Opracowanie rekordu ze środków MNiSW, umowa nr POPUL/SP/0154/2024/02 w ramach programu "Społeczna odpowiedzialność nauki II" - moduł: Popularyzacja nauki (2025)