i-manager Publications

Dynamical Behavior of a Van der Pol Oscillator Circuit with Internal Delay

Saumen Chakraborty*, Saumendra Sankar De Sarkar **

* Department of Physics, Bidhan Chandra College, Asansol, West Bengal, India.

** Department of Physics, Raniganj Girls' College, Raniganj, West Bengal, India.

Periodicity:July - December'2020
DOI : https://doi.org/10.26634/jcir.8.2.18161

Abstract

The qualitative dynamical behavior of an electronic oscillator based on Van der Pol equation is studied with an inherent delay attributed due to finite propagation time and processing time of signal. The stability governing equations have been obtained analytically. In addition to this, the dynamics of the system has been simulated numerically. Though the inherent delay is generally small, the study has been extended for higher values of delay also. Numerical simulation results are found to be consistent with the analytical predictions. The behavior of the modified system beyond the stable region has also been explored using nonlinear tool like bifurcation diagram and chaotic behavior has been found with proper parameter values.

Keywords

Van Der Pol Oscillator, Delay, Stability, Bifurcation Diagram.

How to Cite this Article?

Chakraborty, S., and Sarkar, S. S. D. (2020). Dynamical Behavior of a Van der Pol Oscillator Circuit with Internal Delay. i-manager's Journal on Circuits and Systems, 8(2), 16-21. https://doi.org/10.26634/jcir.8.2.18161

References

[1]. Atay, F. M. (1998). Van der Pol's oscillator under delayed feedback. Journal of Sound and Vibration, 218(2), 333- 339.

[2]. Calzolari, P. U., Franchi, E., & Soncini, G. (1992). An analytical investigation on the propagation delay in ring oscillators. Integration, 13(2), 129-152. https://doi.org/10. 1016/0167-9260(92)90002-G

[3]. Franklin, G. F., Powell, J. D., & Emami-Naeini, A. (1994). Feedback control of dynamic systems (3rd ed.). MA: Addison Wiley.

[4]. Harb, B. (2014). Effect of time delay on the pull-in range of phase locked loops. Journal of Vibroengineering, 16(1), 369-377.

[5]. Hunt, D., Korniss, G., & Szymanski, B. K. (2011). The impact of competing time delays in coupled stochastic systems. Physics Letters A, 375(5), 880-885.

[6]. Kiss, G., & Lessard, J. P. (2017). Rapidly and slowly oscillating periodic solutions of a delayed van der Pol oscillator. Journal of Dynamics and Differential Equations, 29(4), 1233-1257. https://doi.org/10.1007/s10884-017-95 99-x

[7]. Peng, M., Zhang, Z., Qu, Z., & Bi, Q. (2019). Qualitative analysis in a delayed Van del Pol oscillator. Physica A: Statistical Mechanics and its Applications, 544, 1-22. https://doi.org/10.1016/j.physa.2019.123482

[8]. Premraj, D., Suresh, K., & Thamilmaran, K. (2019). Effect of processing delay on bifurcation delay in a network of slow-fast oscillators. Chaos: An Interdisciplinary Journal of Nonlinear Science, 29(12). https://doi.org/10.1063/1.512 3417

[9]. Xu, J., & Chung, K. W. (2003). Effects of time delayed position feedback on a van der Pol–Duffing oscillator. Physica D: Nonlinear Phenomena, 180(1-2), 17-39. https:// doi.org/10.1016/S0167-2789(03)00049-6

[10]. Yao, C., He, Z., & Zou, W. (2020). Oscillation behavior driven by processing delay in diffusively coupled inactive systems: Cluster synchronization and multistability. Chaos: An Interdisciplinary Journal of Nonlinear Science, 30(12). https://doi.org/10.1063/5.0025958

[11]. Zduniak, B., Bodnar, M., & Forys, U. (2014). A modified van der Pol equation with delay in a description of the heart action. International Journal of Applied Mathematics and Computer Science, 24(4), 853-863.

If you have access to this article please login to view the article or kindly login to purchase the article

Single Article

	North Americas,UK, Middle East,Europe		India	Rest of world
	USD	EUR	INR	USD-ROW
Online	15	15

ADD TO CART

Options for accessing this content:

If you would like institutional access to this content, please recommend the title to your librarian.
If you already have i-manager's user account: Login above and proceed to purchase the article.
New Users: Please register, then proceed to purchase the article.