A novel mega-stable system with attractors in real-life object shapes

Document Type : Research Article

Authors

1 Department of Biomedical Engineering, Amirkabir University of Technology (Tehran Polytechnic), Tehran, Iran

2 Health Technology Research Institute, Amirkabir University of Technology (Tehran Polytechnic), Tehran, Iran.

3 Department of Electrical Engineering, City University of Hong Kong, Hong Kong SAR, China.

Abstract

This paper introduces a two-dimensional autonomous mega-stable dynamical system with trigonometric nonlinearities. The nonlinearity of this system is induced by tangent hyperbolic and cosine functions. A remarkable feature of this system is the ability to generate very rich patterns of coexisting attractors via the variation of its parameters. Interestingly the shapes of its coexisting attractors resemble some real-life objects, such as Persian rugs, nuts (mainly chestnut), fruits (especially pear), and vegetables (pumpkin and onion). Simulations demonstrate the coexisting attractors, basins of attractions, and real-life object shapes. Moreover, the fixed points of the proposed system, their stability, and the energy dissipation for various pairs of parameters are investigated. Finally, the feasibility of this system is approved by analog circuit simulations. Regarding the high flexibility of this system, producing a broad range of attractor patterns, it could be applied in various fields.

Keywords

Main Subjects

References

References
1. Tél, T., de Moura, A., Grebogi, C., et al. “Chemical and biological activity in open flows: A dynamical system approach”, Physics Reports, 413(2-3), pp. 91-196 (2005). https://doi.org/10.1016/j.physrep.2005.01.005
2. Voss, H.U., Timmer, J., and Kurths, J. “Nonlinear dynamical system identification from uncertain and indirect measurements”, International Journal of Bifurcation and Chaos, 14(6), pp. 1905-1933 (2004). https://www.researchgate.net/publication/215554917
3. Kleeman, R. “Information theory and dynamical system predictability”, Entropy, 13(3), pp. 612-649 (2011). https://doi.org/10.3390/e13030612
4. Chernogor, L. and Rozumenko, V. “Earth–atmosphere–geospace as an open nonlinear dynamical system”, Radio Physics and Radio Astronomy, 13(2), p. 120 (2012).
5. Chen, Y., Georgiou, T.T., and Pavon, M. “Optimal transport over a linear dynamical system”, IEEE Transactions on Automatic Control, 62(5), pp. 2137-2152 (2016). https://doi.org/10.1109/TAC.2016.2602103
6. DeMaria, M. “A simplified dynamical system for tropical cyclone intensity prediction”, Monthly Weather Review, 137(1), pp. 68-82 (2009). https://doi.org/10.1175/2008MWR2513.1
7. Manzoni, S., Porporato, A., d'Odorico, P. et al. “Soil nutrient cycles as a nonlinear dynamical system”, Nonlinear Processes in Geophysics, 11(5/6), pp. 589-598 (2004). https://doi.org/10.5194/npg-11-589-2004
8. Dahlhaus, J., Edge, J., Tworzydło, J., et al. “Quantum Hall effect in a one-dimensional dynamical system”, Physical Review B, 84(11), 115133 (2011). https://doi.org/10.1103/PhysRevB.84.115133
9. Odintsov, S. and Oikonomou, V. “Autonomous dynamical system approach for f(R) gravity”, Physical Review D, 96, 104049 (2017). https://doi.org/10.1103/PhysRevD.96.104049
10. Kumar, S., Kumar, R., Cattani, C., et al. “Chaotic behavior of fractional predator-prey dynamical system”, Chaos, Solitons & Fractals, 135(1), 109811 (2020). https://doi.org/10.1016/j.chaos.2020.109811
11. Lin, H., Wang, C., Yu, F., et al. “An extremely simple multiwing chaotic system: Dynamics analysis, encryption application, and hardware implementation”, IEEE Transactions on Industrial Electronics, 68(12), pp. 12708-12719 (2021). https://doi.org/10.1109/TIE.2020.3047012
12. Deng, J., Zhou, M., Wang, C., et al. “Image segmentation encryption algorithm with chaotic sequence generation participated by cipher and multi-feedback loops”, Multimedia Tools and Applications, 80, pp. 13821-13840 (2021). https://doi.org/10.1007/s11042-020-10429-z
13. Leonov, G., Kuznetsov, N., and Vagaitsev, V. “Hidden attractor in smooth Chua systems”, Physica D: Nonlinear Phenomena, 241(18), pp. 1482-1486 (2012). https://doi.org/10.1016/j.physd.2012.05.016
14. Pehlivan, I., Moroz, I.M., and Vaidyanathan, S. “Analysis, synchronization and circuit design of a novel butterfly attractor”, Journal of Sound and Vibration, 333(20), pp. 5077-5096 (2014). https://doi.org/10.1016/j.jsv.2014.05.025
15. Munmuangsaen, B. and Srisuchinwong, B. “A new five-term simple chaotic attractor”, Physics Letters A, 373(44), pp. 4038-4043 (2009). https://doi.org/10.1016/j.physleta.2009.08.068
16. Kallosh, R., Linde, A., and Roest, D. “Universal attractor for inflation at strong coupling”, Physical Review Letters, 112, 011303 (2014). https://doi.org/10.1103/PhysRevLett.112.011303
17. Carrilho, P., Mulryne, D., Ronayne, J., et al. “Attractor behavior in multifield inflation”, Journal of Cosmology and Astroparticle Physics, 2018(06), 32 (2018). https://doi.org/10.1088/1475-7516/2018/06/032
18. Wang, Z., Moroz, I., Wei, Z., et al. “Dynamics at infinity and a Hopf bifurcation arising in a quadratic system with coexisting attractors”, Pramana, 90(1), article number 12 (2018). https://doi.org/10.1007/s12043-017-1505-x
19. Gong, L., Wu, R., and Zhou, N. “A new 4D chaotic system with coexisting hidden chaotic attractors”, International Journal of Bifurcation and Chaos, 30(10), 2050142 (2020). https://doi.org/10.1142/S0218127420501424
20. Lin, H., Wang, C., Hong, Q., et al. “A multi-stable memristor and its application in a neural network”, IEEE Transactions on Circuits and Systems II: Express Briefs, 67(12), pp. 3472-3476 (2020). https://doi.org/10.1109/TCSII.2020.3000492
21. Xu, Q., Cheng, S., Ju, Z., et al. “Asymmetric coexisting bifurcations and multi-stability in an asymmetric memristive diode-bridge-based jerk circuit”, Chinese Journal of Physics, 70, pp. 69-81 (2021). https://doi.org/10.1016/j.cjph.2020.11.007
22. Tang, Y., Abdolmohammadi, H.R., Khalaf, A.J.M., et al. “Carpet oscillator: A new megastable nonlinear oscillator with infinite islands of self-excited and hidden attractors”, Pramana, 91, article number 11 (2018). https://doi.org/10.1007/s12043-018-1581-6
23. Vo, T.P., Shaverdi, Y., Khalaf, A.J.M., et al. “A giga-stable oscillator with hidden and self-excited attractors: A megastable oscillator forced by his twin”, Entropy, 21(5), 535 (2019). https://doi.org/10.3390/e21050535
24. Bao, B.C., Xu, Q., Bao, H., et al. “Extreme multistability in a memristive circuit”, Electronics Letters, 52(12), pp. 1008-1010 (2016). https://doi.org/10.1049/el.2016.0563
25. Xu, Q., Liu, T., Feng, C.T., et al. “Continuous non-autonomous memristive Rulkov model with extreme multistability”, Chinese Physics B, 30(12), 128702 (2021). https://doi.org/10.1088/1674-1056/ac2f30
26. Akgul, A., Boyraz, O.F., Rajagopal, K., et al. “An unforced megastable chaotic oscillator and its application on protecting electrophysiological signals”, Zeitschrift für Naturforschung A, 75(12), pp. 1025-1037 (2020). https://doi.org/10.1515/zna-2020-0222
27. Chen, B., Rajagopal, K., Hamarash, I.I., et al. “Simple megastable oscillators with different types of attractors; tori, chaotic and hyperchaotic ones”, The European Physical Journal Special Topics, 229(6), pp. 1155-1161 (2020). https://doi.org/10.1140/epjst/e2020-900240-1
28. Chen, M., Sun, M., Bao, B., et al. “Controlling extreme multistability of memristor emulator-based dynamical circuit in flux–charge domain”, Nonlinear Dynamics, 91(2), pp. 1395-1412 (2018). https://doi.org/10.1007/s11071-017-3952-9
29. Chen, M., Sun, M., Bao, H., et al. “Flux–charge analysis of two-memristor-based Chua's circuit: Dimensionality decreasing model for detecting extreme multistability”, IEEE Transactions on Industrial Electronics, 67(3), pp. 2197-2206 (2019). https://doi.org/10.1109/TIE.2019.2907444
30. Rajagopal, K., Singh, J.P., Akgul, A., et al. “A novel dissipative and conservative megastable oscillator with engineering applications”, Modern Physics Letters B, 34(1), 2150007 (2020). https://doi.org/10.1142/S021798492150007X
31. Li, H., Bao, H., Zhu, L., et al. “Extreme multistability in simple area-preserving map”, IEEE Access, 8, pp. 175972-175980 (2020). https://doi.org/10.1109/ACCESS.2020.3026676
32. Gong, L.-H., Luo, H.-X., Wu, R.-Q., et al. “New 4D chaotic system with hidden attractors and self-excited attractors and its application in image encryption based on RNG”, Physica A: Statistical Mechanics and its Applications, 591, 126793 (2022). https://doi.org/10.1016/j.physa.2021.126793
33. Tuna, M., Karthikeyan, A., Rajagopal, K., et al. “Hyperjerk multiscroll oscillators with megastability: Analysis, FPGA implementation and a novel ANN-ring-based true random number generator”, AEU-International Journal of Electronics and Communications, 112, 152941 (2019). https://doi.org/10.1016/j.aeue.2019.152941
34. Karami, M., Ramamoorthy, R., Ali, A.M.A., et al. “Jagged-shape chaotic attractors of a megastable oscillator with spatially square-wave damping”, The European Physical Journal Special Topics, 231, pp. 2445-2454 (2022). https://doi.org/10.1140/epjs/s11734-021-00373-w
35. Karami, M., Ramakrishnan, B., Hamarash, I.I., et al. “Investigation of the simplest megastable chaotic oscillator with spatially triangular wave damping”, International Journal of Bifurcation and Chaos, 32(07), 2230016 (2022). https://doi.org/10.1142/S0218127422300166
36. Li, R., Dong, E., Tong, J., et al. “A new autonomous memristive megastable oscillator and its hamiltonian-energy-dependent megastability”, Chaos: An Interdisciplinary Journal of Nonlinear Science, 32(1), 013127 (2022). https://doi.org/10.1063/5.0066951
37. Vijayakumar, M., Natiq, H., Meli, M.I.T., et al. “Hamiltonian energy computation of a novel memristive mega-stable oscillator (MMO) with dissipative, conservative and repelled dynamics”, Chaos, Solitons & Fractals, 155(1), 111765 (2022). https://doi.org/10.1016/j.chaos.2021.111765
Scientia Iranica
Volume 32, Issue 10
Transactions on Computer Science & Engineering and Electrical Engineering
May and June 2026 Article ID:7030

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History

  • Receive Date: 30 July 2022
  • Revise Date: 09 January 2023
  • Accept Date: 16 April 2023

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