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Abstrakty
A new 4-D dynamical system exhibiting chaos is introduced in this work. The proposed nonlinear plant with chaos has an unstable rest point and a line of rest points. Thus, the new nonlinear plant exhibits hidden attractors. A detailed dynamic analysis of the new nonlinear plant using bifurcation diagrams is described. Synchronization result of the new nonlinear plant with itself is achieved using Integral Sliding Mode Control (ISMC). Finally, a circuit modelusing MultiSim of the new 4-D nonlinear plant with chaos is carried out for practical use.
Słowa kluczowe
Czasopismo
Rocznik
Tom
Strony
485--506
Opis fizyczny
Bibliogr. 40 poz., rys., wykr., wzory
Twórcy
- School of Electrical and Computing, Vel Tech University, 400 Feet Outer Ring Road, Avadi, Chennai-600092, Tamil Nadu, India
autor
- Department of Mechanical Engineering, Universitas Muhammadiyah Tasikmalaya, Tasikmalaya 46196,West Java, Indonesia
autor
- School of Physics and Opotoelectric Engineering, Xiangtan University, Xiangtan 411105, Hunan, China
Bibliografia
- [1] A. T. Azar, A. Radwan, and S. Vaidyanthan: Mathematical Techniques of Fractional Order Systems. Amsterdam, Elsevier, 2018.
- [2] V. T. Pham, S. Vaidyanathan, C. Volos, and T. Kapitaniak: Nonlinear Dynamical Systems with Self-Excited and Hidden Attractors. Berlin, Springer, 2018.
- [3] S. Vaidyanathan: Hyperchaos, qualitative analysis, control and synchronisation of a tenterm 4-D hyperchaotic system with an exponential nonlinearity and three quadratic nonlinearities. International Journal of Modelling, Identification and Control, 23(4), (2015), 380–392.
- [4] S. Vaidyanathan: Adaptive controller and synchronizer design for the Qi Chen chaotic system. Lecture Notes of the Institute for Computer Sciences, Social-Informatics and Telecommunications Engineering, 85 (2012), 124–133.
- [5] S. Vaidyanathan: Analysis, control, and synchronization of a 3-D novel jerk chaotic system with two quadratic nonlinearities. Kyungpook Mathematical Journal, 55(3), (2015), 563–586.
- [6] S. Pakiriswamy and S. Vaidyanathan: Generalized projective synchronization of three-scroll chaotic systems via active control. Lecture Notes of the Institute for Computer Sciences, Social-Informatics and Telecommunications Engineering, 85 (2012), 146–155.
- [7] S. Vaidyanathan: Output regulation of the forced Van der Pol chaotic oscillator via adaptive control method. International Journal of PharmTech Research, 8(6), (2015), 106–116.
- [8] D. M. Wang, L. S. Wang, Y. Y. Guo, Y. C. Wang, and A. B. Wang: Key space enhancement of optical chaos secure communication: Chirped FBG feedback semiconductor laser. Optics Express, 27(3), (2019), 3065–3073.
- [9] Z. X. Liu, C. You, B. Wang, H. Xiong, and Y. Wu: Phase-mediated magnon chaos-order transition in cavity optomagnonics. Optics Letters, 44(3), (2019), 507–510.
- [10] S. Vaidyanathan: Adaptive control of the FitzHugh-Nagumo chaotic neuron model. International Journal of PharmTech Research, 8(6), (2015), 117–127.
- [11] S. Vaidyanathan: Chaos in neurons and synchronization of Birkhoff-Shaw strange chaotic attractors via adaptive control. International Journal of PharmTech Research, 8(6), (2015), 1–11.
- [12] S. Vaidyanathan: Adaptive chaotic synchronization of enzymes-substrates system with ferroelectric behaviour in brain waves. International Journal of PharmTech Research, 8(5), (2015), 964–973.
- [13] S. Dash, M. N. Das, and M. Das: Secured image transmission through region-based steganography using chaotic encryption. Advances in Intelligent Systems Computing, 711 (2019), 535–544.
- [14] R. Banupriya, J. Deepa, and S. Suganthi: Video steganography using LSB algorithm for security application. International Journal of Mechanical Engineering and Technology, 10(1), (2019), 203–211.
- [15] X. Wang, H. Zhao, and M. Wang: A new image encryption algorithm with nonlinear-diffusion based on multiple coupled map lattices. Optics and Laser Technology, 115 (2019), 42–57.
- [16] T. Sivakumar and P. Li: A secure image encryption method using scan pattern and random key stream derived from laser chaos. Optics and Laser Technology, 111 (2019), 196–204.
- [17] S. Vaidyanathan: A novel chemical chaotic reactor system and its adaptive control. International Journal of ChemTech Research, 8(7), (2015), 146–158.
- [18] S. Vaidyanathan: A novel chemical chaotic reactor system and its out-put regulation via integral sliding mode control. International Journal of ChemTech Research, 8(11), (2015), 669–683.
- [19] S. Vaidyanathan: Global chaos synchronization of chemical chaotic reactors via novel sliding mode control method. International Journal of ChemTech Research, 8(7), (2015), 209–221.
- [20] S. Vaidyanathan: Lotka-Volterra population biology models with negative feedback and their ecological monitoring. International Journal of PharmTech Research, 8(5), (2015), 974–981.
- [21] O. I. Tacha, C. K. Volos, I. M. Kyprianidis, I. N. Stouboulos, S. Vaidyanathan, and V. T. Pham: Analysis, adaptive control and circuit simulation of a novel nonlinear finance system. Applied Mathematics and Computation, 276 (2016), 200–217.
- [22] F. Liu: Unconventional direct acquisition method for chaotic DSSS signals. AEU – International Journal of Electronics and Communications, 99 (2019), 293–298.
- [23] X. Y. Wang and Z. M. Li: A color image encryption algorithm based on Hopfield chaotic neural network. Optics and Lasers in Engineering, 115 (2019), 107–118.
- [24] Z. Hua, Y. Zhou, and H. Huang: Cosine-transform-based chaotic system for image encryption. Information Sciences, 480 (2019), 403–419.
- [25] P. S. Gohari, H. Mohammadi, and S. Taghvaei: Using chaotic maps for 3D boundary surveillance by quadrotor robot. Applied Soft Computing, 76 (2019), 68–77.
- [26] Y. Naseer, D. Shah, and T. Shah: A novel approach to improve multimedia security utilizing 3D mixed chaotic map. Microprocessors and Microsystems, 65 (2019), 1–6.
- [27] B. Karakaya, A. Gulten, and M. Frasca: A true random bit generator based on a memristive chaotic circuit: Analysis, design and FPGA implementation. Chaos, Solitons and Fractals, 119 (2019), 143–149.
- [28] H. Wang and G. Dong: New dynamics coined in a 4-D quadratic autonomous hyper-chaotic system. Applied Mathematics and Computation, 346 (2019), 272–286.
- [29] S. Vaidyanathan: Analysis and synchronization of the hyperchaotic Yujun systems via sliding mode control. Advances in Intelligent Systems and Computing, 176 (2012), 329–337.
- [30] S. Vaidyanathan, C. Volos, and V. T. Pham: Global chaos control of a novel nine-term chaotic system via sliding mode control. Studies in Computational Intelligence, 576 (2015), 571–590.
- [31] S. Zhang, Y. C. Zeng, and Z. J. Li: Chaos in a novel fractional order system without a linear term. International Journal of Non-Linear Mechanics, 106 (2018), 1–12.
- [32] S. Zhang, Y. C. Zeng, Z. J. Li, M .J. Wang, X. Zhang, and D. Chang: A novel simple no-equilibrium chaotic system with complex hidden dynamics. International Journal of Dynamics and Control, 23 (2018), 1–12.
- [33] S. Zhang,Y. C. Zeng, and Z. J. Li: One to four-wing chaotic attractors coined from a novel 3D fractional-order chaotic system with complex dynamic. Chinese Journal of Physics, 56 (2018), 793–806.
- [34] L. Wang, S. Zhang, Y. C. Zeng, and Z. J. Li: Generating hidden extreme multistability in memristive chaotic oscillator via micro-perturbation. Electron letters, 52 (2018), 1008–1010.
- [35] S. Zhang and Y. C. 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.
- [36] S. Vaidyanthan and C. H. Lien: Applications of Sliding Mode Control in Science and Engineering. Berlin, Springer, 2017.
- [37] W. M. Haddad and V. S. Chellaboina: Nonlinear Dynamical Systems and Control: A Lyapunov-Based Approach. Princeton University Press, Princeton, 2008.
- [38] A. Sambas, S. Vaidyanathan, M. Mamat,W. S. M. Sanjaya, and D. S. Rahayu: A 3-D novel jerk chaotic system and its application in secure communication system and mobile robot navigation. Studies in Computational Intelligence, 636 (2016), 283–310.
- [39] S. Vaidyanathan, A. Sambas, M. Mamat, and W. S. M. Sanjaya: A new three-dimensional chaotic system with a hidden attractor, circuit design and application in wireless mobile robot. Archives of Control Sciences, 27 (2017), 541–554.
- [40] A. S. Elwakil and M. P. Kennedy: High frequency Wien-type chaotic oscillator. Electronics Letters, 34 (1998), 1161–1162.
Uwagi
EN
1. This is an open-access article distributed under the terms of the Creative CommonsAttribution-NonCommercial-NoDerivatives License (CC BY-NC-ND 3.0 https://creativecommons.org/licenses/by-nc-nd/3.0/), which permits use, distribution, and reproduction in any medium, provided that the article is properly cited, theuse is non-commercial, and no modifications or adaptations are made
PL
2. Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2019).
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-114ce8ec-3044-45db-a8bb-b5f8155dde10