Dynamical Analysis and Circuit Design for  Malasoma System

Volodymyr Rusyn; Diana Purwandari

doi:10.46336/ijqrm.v1i4.84

Dynamical Analysis and Circuit Design for Malasoma System

Volodymyr Rusyn, Diana Purwandari

Abstract

In this paper, the Malasoma system based cubic function is presented. This system contains operational amplifiers, resistors, capacitors, multipliers, and voltage sources. The first stage, we analyze the Malasoma model and execute its stability. The phase portraits and bifurcation diagram are used to analyze the dynamic behaviors of the Malasoma model. The proposed circuit was modelled by utilizing NI’s MultiSim software environment. The electronic circuit is realized by using off-the-shelf components. MATLAB and MultiSim simulation results show a good agreement.

Keywords

chaos, dynamical system, Malasoma system, circuit design

Full Text:

PDF

References

Ghezzi, L. L., and Piccardi, C. (1997). PID control of a chaotic system: An application to an epidemiological model. Automatica, 33(2), 181-191.

Haghani, A., and Safarpour, P. (2018). The Effect of System Parameters on the Chaotic Behavior of Rotor-disk-Bearing with Rubbed between the Disk and the Stator, University of Tabriz Journal of Mechanical Engineering, 81(18), 125-133.

Hu, K. Y., Ding, Y., and Wang, H. W. (2010). Chaotic roll motions of ships in regular longitudinal waves. Journal of Marine Science and Application, 9(2), 208-212.

Kumar, S., Kumar, A., Samet, B., Gómez-Aguilar, J. F., and Osman, M. S. (2020). A chaos study of tumor and effector cells in fractional tumor-immune model for cancer treatment. Chaos, Solitons & Fractals, 141, 110321.

Lai, Q., Wan, Z., Akgul, A., Boyraz, O. F., and Yildiz, M. Z. (2020). Design and implementation of a new memristive chaotic system with application in touchless fingerprint encryption. Chinese Journal of Physics, 67, 615-630.

Malasoma, J. M. (2000). What is the simplest dissipative chaotic jerk equation which is parity invariant?. Physics Letters A, 264(5), 383-389.

Mobayen, S., Vaidyanathan, S., Sambas, A., Kacar, S., and Çavuşoğlu, Ü. (2019). A novel chaotic system with boomerang-shaped equilibrium, its circuit implementation and application to sound encryption. Iranian Journal of Science and Technology, Transactions of Electrical Engineering, 43(1), 1-12.

Preishuber, M., Hütter, T., Katzenbeisser, S., and Uhl, A. (2018). Depreciating motivation and empirical security analysis of chaos-based image and video encryption. IEEE Transactions on Information Forensics and Security, 13(9), 2137-2150.

Sambas, A., Gundara, G., Sanjaya, M., and Mamat, M. (2015). Analisis dinamika kompleks sistem Malasoma dan aplikasinya pada speech encryption. ALHAZEN Journal of Physics, 2(2), 1-10.

Sambas, A., Vaidyanathan, S., Zhang, S., Zeng, Y., Mohamed, M. A., and Mamat, M. (2019). A new double-wing chaotic system with coexisting attractors and line equilibrium: bifurcation analysis and electronic circuit simulation. IEEE Access, 7, 115454-115462.

Sambas, A., Vaidyanathan, S., Tlelo-Cuautle, E., Abd-El-Atty, B., Abd El-Latif, A. A., Guillén-Fernández, O, Hidayat, Y., and Gundara, G. (2020). A 3-D multi-stable system with a peanut-shaped equilibrium curve: Circuit design, FPGA realization, and an application to image encryption. IEEE Access, 8, 137116-137132.

Sprott, J. C., and Linz, S. J. (2000). Algebraically simple chaotic flows. International Journal of Chaos Theory and Applications, 5(2), 1-20.

Sukono, Sambas, A., He, S., Liu, H., Vaidyanathan, S., Hidayat, Y., and Saputra, J. (2020). Dynamical analysis and adaptive fuzzy control for the fractional-order financial risk chaotic system. Advances in Difference Equations, 674(1), 1-12.

Vaidyanathan, S., Sambas, A., Mamat, M., and Sanjaya, M. (2017). A new three-dimensional chaotic system with a hidden attractor, circuit design and application in wireless mobile robot. Archives of Control Sciences, 27(4), 541-554.

Varan, M., Yalçın, F., and Uyaroğlu, Y. (2016). Synchronizations and secure communication applications of a third degree Malasoma system with chaotic flow. Optik, 127(23), 11086-11093.

Yin, X., She, J., Liu, Z., Wu, M., and Kaynak, O. (2020). Chaos suppression in speed control for permanent-magnet-synchronous-motor drive system. Journal of the Franklin Institute, 357(18), 13283-13303.

Zhou, S., Li, H., and Zhu, Z. (2008). Chaos control and synchronization in a fractional neuron network system. Chaos, Solitons & Fractals, 36(4), 973-984.

DOI: https://doi.org/10.46336/ijqrm.v1i4.84