Bifurcation Analysis and Electronic Circuit for Sprott Jerk System

R Apip Miptahudin

doi:10.46336/ijqrm.v2i2.145

Bifurcation Analysis and Electronic Circuit for Sprott Jerk System

R Apip Miptahudin

Abstract

In this paper, the Sprott jerk system based quadratic function is presented. The dynamics of this system is revealed through equilibrium analysis, phase portrait, bifurcation diagram and Lyapunov exponents. The Sprott system can exhibit a chaotic attractor, which has complex dynamic behavior. Finally, the circuit implementation is carried out to verify the Sprott Jerk system. The comparison between the MATLAB and MultiSIM simulation results demonstrate the effectiveness of the Sprott system.

Keywords

chaos, dynamical system, Sprott system, circuit design

Full Text:

PDF

References

Anter, A. M., & Ali, M. (2020). Feature selection strategy based on hybrid crow search optimization algorithm integrated with chaos theory and fuzzy c-means algorithm for medical diagnosis problems. Soft Computing, 24(3), 1565-1584.

Baladron, J., Fasoli, D., Faugeras, O., & Touboul, J. (2012). Mean-field description and propagation of chaos in networks of Hodgkin-Huxley and FitzHugh-Nagumo neurons. The Journal of Mathematical Neuroscience, 2(1), 1-50.

Belazi, A., Talha, M., Kharbech, S., & Xiang, W. (2019). Novel medical image encryption scheme based on chaos and DNA encoding. IEEE access, 7, 36667-36681.

Devolder, T., Rontani, D., Petit-Watelot, S., Bouzehouane, K., Andrieu, S., Létang, J., ... & Kim, J. V. (2019). Chaos in magnetic nanocontact vortex oscillators. Physical review letters, 123(14), 147701.

Kengne, J., Negou, A. N., & Njitacke, Z. T. (2017). Antimonotonicity, chaos and multiple attractors in a novel autonomous jerk circuit. International Journal of Bifurcation and Chaos, 27(07), 1750100.

Kumar, A., & Sahu, P. R. (2016). Performance analysis of differential chaos shift keying modulation with transmit antenna selection. IET Communications, 10(3), 327-335.

Li, C., Sprott, J. C., & Xing, H. (2016). Hypogenetic chaotic jerk flows. Physics Letters A, 380(11-12), 1172-1177.

Luo, X. S., Zhang, B., & Qin, Y. H. (2010). Controlling chaos in space-clamped FitzHugh–Nagumo neuron by adaptive passive method. Nonlinear Analysis: Real World Applications, 11(3), 1752-1759.

Mboupda Pone, J. R., Kingni, S. T., Kol, G. R., & Pham, V. T. (2019). Hopf bifurcation, antimonotonicity and amplitude controls in the chaotic Toda jerk oscillator: analysis, circuit realization and combination synchronization in its fractional-order form. Automatika, 60(2), 149-161.

Mobayen, S., Vaidyanathan, S., Sambas, A., Kacar, S., & 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.

Mobayen, S., Fekih, A., Vaidyanathan, S., & Sambas, A. (2021). Chameleon Chaotic Systems with Quadratic Nonlinearities: An Adaptive Finite-Time Sliding Mode Control Approach and Circuit Simulation. IEEE Access, 9, 64558-64573.

Moon, K. W., Chun, B. S., Kim, W., Qiu, Z. Q., & Hwang, C. (2014). Duffing oscillation-induced reversal of magnetic vortex core by a resonant perpendicular magnetic field. Scientific reports, 4(1), 1-5.

Oliveira, J., Oliveira, P. M., Boaventura-Cunha, J., & Pinho, T. (2017). Chaos-based grey wolf optimizer for higher order sliding mode position control of a robotic manipulator. Nonlinear Dynamics, 90(2), 1353-1362.

Petit-Watelot, S., Kim, J. V., Ruotolo, A., Otxoa, R. M., Bouzehouane, K., Grollier, J., ... & Devolder, T. (2012). Commensurability and chaos in magnetic vortex oscillations. Nature Physics, 8(9), 682-687.

Rajagopal, K., Pham, V. T., Tahir, F. R., Akgul, A., Abdolmohammadi, H. R., & Jafari, S. (2018). A chaotic jerk system with non-hyperbolic equilibrium: Dynamics, effect of time delay and circuit realisation. Pramana, 90(4), 1-8.

Sambas, A., Vaidyanathan, S., Zhang, S., Zeng, Y., Mohamed, M. A., & 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., ... & 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.

Sambas, A., Vaidyanathan, S., Bonny, T., Zhang, S., Hidayat, Y., Gundara, G., & Mamat, M. (2021a). Mathematical Model and FPGA Realization of a Multi-Stable Chaotic Dynamical System with a Closed Butterfly-Like Curve of Equilibrium Points. Applied Sciences, 11(2), 788.

Sambas, A., Vaidyanathan, S., Moroz, I. M., Idowu, B., Mohamed, M. A., Mamat, M., & Sanjaya, W. S. (2021b). A simple multi-stable chaotic jerk system with two saddle-foci equilibrium points: Analysis, synchronization via backstepping technique and MultiSim circuit design. International Journal of Electrical & Computer Engineering, 11(4), 2941-2952.

Sprott, J. C. (1997). Some simple chaotic jerk functions. American Journal of Physics, 65(6), 537-543.

Stollenwerk, N., Sommer, P. F., Kooi, B., Mateus, L., Ghaffari, P., & Aguiar, M. (2017). Hopf and torus bifurcations, torus destruction and chaos in population biology. Ecological Complexity, 30, 91-99.

Sukono, Sambas, A., He, S., Liu, H., Vaidyanathan, S., Hidayat, Y., & 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.

Vaidyanathan, S., Feki, M., Sambas, A., & Lien, C. H. (2018). A new biological snap oscillator: its modelling, analysis, simulations and circuit design. International Journal of Simulation and Process Modelling, 13(5), 419-432.

Vaidyanathan, S., Sambas, A., Abd-El-Atty, B., Abd El-Latif, A. A., Tlelo-Cuautle, E., Guillén-Fernández, O., ... & Ibrahim, M. A. H. (2021). A 5-D multi-stable hyperchaotic two-disk dynamo system with no equilibrium point: Circuit design, FPGA realization and applications to TRNGs and image encryption. IEEE Access, 9, 81352-81369.

Wolf, A., Swift, J. B., Swinney, H. L., & Vastano, J. A. (1985). Determining Lyapunov exponents from a time series. Physica D: nonlinear phenomena, 16(3), 285-317.

Wei, Z., Zhang, W., & Yao, M. (2015). On the periodic orbit bifurcating from one single non-hyperbolic equilibrium in a chaotic jerk system. Nonlinear dynamics, 82(3), 1251-1258.

Xiao-Dan, Z., Xiang-Dong, L., Yuan, Z., & Cheng, L. (2013). Chaotic dynamic behavior analysis and control for a financial risk system. Chinese Physics B, 22(3), 030509.

Zhang, M., Ji, Y., Zhang, Y., Wu, Y., Xu, H., & Xu, W. (2014). Remote radar based on chaos generation and radio over fiber. IEEE Photonics journal, 6(5), 1-12.

Zhang, J., & Liao, X. (2017). Synchronization and chaos in coupled memristor-based FitzHugh-Nagumo circuits with memristor synapse. Aeu-international journal of electronics and communications, 75, 82-90.

DOI: https://doi.org/10.46336/ijqrm.v2i2.145