Studying the Effect of Initial Conditions and System Parameters on the Behavior of a Chaotic Duffing System
Main Article Content
Abstract
This work presents a five-period chaotic system called the Duffing system, in which the effect of changing the initial conditions and system parameters d, g and w, on the behavior of the chaotic system, is studied. This work provides a complete analysis of system properties such as time series, attractors, and Fast Fourier Transformation Spectrum (FFT). The system shows periodic behavior when the initial conditions xi and yi equal 0.8 and 0, respectively, then the system becomes quasi-chaotic when the initial conditions xi and yi equal 0 and 0, and when the system parameters d, g and w equal 0.02, 8 and 0.09. Finally, the system exhibits hyperchaotic behavior at the first two conditions, 0 and 0, and the bandwidth of the chaotic signal becomes wider (2 a.u.) than in the first case. So, this system can be used in many physical applications, such as encrypting confidential information.
Received: Apr. 03, 2023
Accepted: May 14, 2023
Article Details
This work is licensed under a Creative Commons Attribution 4.0 International License.
Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution (CC-BY) 4.0 License that allows others to share the work with an acknowledgement of the work’s authorship and initial publication in this journal.
How to Cite
References
P. Kattan, Petra Books, 1 (2012).
K. M. Ibrahim and R. K. Jamal, Aust. J. Bas. Appl. Sci. 10, 8 (2016).
R. K. Jamal and D. A. Kafi, Iraqi J. Phys. 14, 51 (2016).
D. A. Kafi, R. K. Jamal, and K. A. Al-Naimee, Iraqi J. Phys. 14, 51 (2016).
R. K. Jamal and D. A. Kafi, IOP Conference Series: Mater. Sci. Eng. (IOP Publishing, 2019). p. 012119.
R. K. Jamal and D. A. Kafi, Nonlin. Optic. Quant. Optic.: Con. Mod. Optic. 51, 79 (2019).
R. K. Jamal, F. H. Ali, and F. A. Mutlak, Iraqi J. Sci. 62, 2213 (2021).
R. S. Abdulaali, R. K. Jamal, and S. K. Mousa, Optic. Quant. Elect. 53, 1 (2021).
D. A. Kafi, S. K. Mousa, and R. K. Jamal, Optic. Quant. Elect. 54, 502 (2022).
S. K. Mousa and R. K. Jamal, Optic. Quant. Elect. 53, 1 (2021).
I. A. Hamadi, R. K. Jamal, and S. K. Mousa, Optic. Quant. Elect. 54, 33 (2022).
N. Hiroyuki, Introduction to Chaos. (Bristol, Philadelphia, IOP Publishing, 1999).
L. F. Olsen and H. Degn, Quart. Rev. Biophys. 18, 165 (1985).
E. R. Weibel, Americ. J. Physiology-Lung Cell. Molec. Physio. 261, L361 (1991).
E. N. Lorenz, J. Atmosph. Sci. 20, 130 (1963).
M. Lakshmanan and K. Murali, Chaos in Nonlinear Oscillators: Controlling and Synchronization. Vol. 13. (USA, World scientific, 1996).
L. O. Chua and T. Lin, Inter. J. Cir. Theo. Appl. 18, 541 (1990).
C. K. Tse, IEEE Trans. Cir. Syst. I: Fund. Theo. Appl. 41, 16 (1994).
G. Poddar, K. Chakrabarty, and S. Banerjee, Elect. lett. 31, 841 (1995).
M. J. Ogorzalek, IEEE Trans. Cir. Syst. 36, 1221 (1989).
H. Kawakami, IEEE Trans. Cir. Syst. 31, 248 (1984).
C. Li, I. Pehlivan, J. C. Sprott, and A. Akgul, IEICE Elect. Exp. 12, 20141116 (2015).
A. Akgul, I. Moroz, I. Pehlivan, and S. Vaidyanathan, Optik 127, 5491 (2016).
Z. Hou, N. Kang, X. Kong, G. Chen, and G. Yan, Inter. J. Bifur. Chaos 20, 557 (2010).
A. A. Abdallah and A. K. Farhan, Iraqi J. Sci. 36, 324 (2022).
R. S. Abdulaali and R. K. Jamal, Iraqi J. Sci. 63, 556 (2022).
M. K. Ibraheem and R. K. Jamal, Optic. Quant. Elect. 54, 614 (2022).
N. M. Ali and R. K. Jamal, Optic. Quant. Elect. 54, 641 (2022).
M. W. Kadhim, D. A. Kafi, E. A. Abed, and R. K. Jamal, J. Optic., 1 (2023).
N. H. Aljahdaly and M. A. Alharbi, J. Low Freq. Noise, Vibrat. Acti. Cont. 41, 1454 (2022).
Y. O. El-Dib, Math. Comp. Simul. 194, 552 (2022).
Y. O. El-Dib, Inter. J. Dynam. Cont. 10, 1148 (2022).
J. M. Thompson and H. B. Stewart, Non-Linear Dynamics and Chaos. 2nd Ed. (Chichester, John Wiley & Sons, 1986).
W. Van Drongelen, Signal Processing for Neuroscientists. 2nd Ed. (UK. USA, Elesevier, Academic press, 2018).