The behavior of hidden bifurcation in 2D scroll via saturated function series controlled by a coefficient harmonic linearization method

• Autorzy: Faiza Zaamoune , Tidjani Menacer

Identyfikatory

DOI

10.1515/dema-2022-0211

• Języki publikacji: EN

Abstrakty

EN

In this article, the behavior of hidden bifurcation in a two-dimensional (2D) scroll via saturated function series controlled by the coefficient harmonic linearization method is presented. A saturated function series approach for chaos generation. The systematic saturated function series methodicalness improved here can make multi-scroll and grid scroll chaotic attractors from a 3D linear autonomous system with a plain saturated function series supervisor. We have used a hidden bifurcation method in grid scroll., where the method of hidden bifurcation presented by Menacer, et al. in (2016) for Chua multi-scroll attractors. This additional parameter, which is absent from the initial problem, is perfectly adapted to unfold the structure of the multispiral chaotic attractor. The novelty of this article is twofold: first, the saturated function series model for hidden bifurcation in a 2 – D scroll; and second, the control of hidden bifurcation behavior by the value of the harmonic coefficient k3.

Słowa kluczowe

EN

hidden bifurcation; harmonic linearization; 2D scroll; saturated function series

PL

ukryte rozwidlenie; linearyzacja harmoniczna; szeregi funkcyjne

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2023
• Tom: Vol. 56, nr 1
• Strony: art. no. 20220211
• Opis fizyczny: Bibliogr. 16 poz., rys., tab., wykr.

Twórcy

autor

Faiza Zaamoune

• Department of Mathematics, University Mohemed Khider Biskra, Biskra, Algeria

autor

Tidjani Menacer

• Department of Mathematics, University Mohemed Khider Biskra, Biskra, Algeria

Bibliografia

• [1] J. Lü and G. Chen, Generating multiscroll chaotic attractors: Theories, methods and applications, Int J Bifurcat Chaos 16 (2006), no. 4, 775–858, DOI: https://doi.org/10.1142/S0218127406015179.
• [2] X. Zhang and Ch. Wang, A novel multi-attractor period multi-scroll chaotic integrated circuit based on CMOS wide adjustable CCCII, IEEE Access 7 (2019), no. 1, 16336–16350, DOI: https://doi.org/10.1109/ACCESS.2019.2894853.
• [3] H. Lin, Ch. Wang, Y. Sun, and T. Wang, Generating n-scroll chaotic attractors from a memristor-based magnetized Hopfield neural network, IEEE Trans. Circuits Syst II Express Briefs 70 (2023), no. 1, 311–315, DOI: https://doi.org/10.1109/TCSII.2022.3212394.
• [4] H. Lin, Ch. Wang, C. Xu, and X. Zhang, A memristive synapse control method to generate diversified multi-structure chaotic attractors, IEEE Trans Computer-aided Design Integrated Circuits Syst. 42 (2022), no. 3, 942–955, DOI: https://doi.org/10.1109/TCSII.2022.3186516.
• [5] L. Zhou, Ch. Wang, and L. Zhou, Generating hyperchaotic multi-wing attractor in a 4D memristive circuit, Nonlinear Dyn. 85 (2016), no. 4, 2653–2663, DOI: http://dx.doi.org/10.10072Fs11071-016-2852-8.
• [6] L. Zhou, Ch. Wang, and L. Zhou, A novel no-equilibrium hyperchaotic multi-wing system via introducing memristor, Int. J. Circuit Theory Appl. 46 (2018), no. 1, 84–98, DOI: https://doi.org/10.1002/cta.2339.
• [7] Q. Deng and C. Wang, Multi-scroll hidden attractors with two stable equilibrium points, Chaos 29 (2019), no. 9, 093112, DOI: https://doi.org/10.1063/1.5116732.
• [8] G. A. Leonov, N. V. Kuznetsov, and V. I. Vagaitsev, Hidden attractor in smooth Chua systems, Physica D 241 (2012), no. 18, 1482–1486, DOI: https://doi.org/10.1016/j.physd.2012.05.016.
• [9] J. Lü, G. Chen, X. Yu, and H. Leung, Design and analysis of multiscroll chaotic attractors from saturated function series, IEEE Trans. Circuits Syst. 51 (2004), no. 12, 2476–2490, DOI: https://doi.org/10.1109/TCSI.2004.838151.
• [10] G. A. Leonov, Effective methods for periodic oscillations search in dynamical systems, Appl. Math. Mech. 74 (2010), no. 1, 37–73, DOI: http://dx.doi.org/10.1016/j.jappmathmech.2010.03.004.
• [11] G. A. Leonov and N. V. Kuznetsov, Localization of hidden Chua’s attractors, Phys. Lett. A 375 (2011), no. 23, 2230–2233, DOI: https://doi.org/10.1016/j.physleta.2011.04.037.
• [12] G. A. Leonov and N. V. Kuznetsov, Analytical numerical methods for investigation of hidden oscillations in nonlinear control systems, Proc. 18th IFAC World Congress, Milano, Italy 18 (2011), no. 1, 2494–2505, DOI: http://dx.doi.org/10.3182/20110828-6-IT-1002.03315.
• [13] G. A. Leonov and N. V. Kuznetsov, Hidden attractors in dynamical systems. From hidden oscillations in Hilbert-Kolmogrov, Aizerman, and Kalman problems to hidden chaotic attractor in Chua circuits, Int. J. Bifurcat. Chaos 23 (2013), no. 1, 1330002–13300071, DOI: https://doi.org/10.1142/S0218127413300024.
• [14] T. Menacer, R. Lozi, and L. O. Chua, Hidden bifurcations in the multispiral Chua attractor, Int. J. Bifurcat. Chaos 16 (2016), no. 4, 1630039–1630065, DOI: https://dx.doi.org/10.1142/S0218127416300391.
• [15] X. Zhang and C. Wang, Multiscroll hyperchaotic system with hidden attractors and its circuit implementation, Int. J. Bifurcat. Chaos 29 (2019), no. 9, 1950117, DOI: https://doi.org/10.1142/S0218127419501177.
• [16] F. Zaamoune, T. Menacer, R. Lozi, and G. Chen, Symmetries in hidden bifurcation routes to multiscroll chaotic attractors generated by saturated function series, J. Adv. Eng. Comput. 3 (2019), no. 4, 511–522, DOI: https://doi.org/10.1142/S0218127419501177.

Uwagi

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