Arash Shabeer, Abu Babk Azad, Karim Iqbal, 2026. "Nonlinear Dynamics and Bifurcation Analysis in Power Electronic Converters under Extreme Operating Conditions" ESP International Journal of Emerging Multidisciplinary Research [ESP-IJEMR] Volume 2, Issue 1: 15-.
Power electronic converters are fundamental components in modern electrical and energy systems, supporting applications such as renewable energy integration, electric mobility, and intelligent power distribution. Despite their widespread use, the dynamic behavior of these converters under extreme operating conditions remains insufficiently understood, particularly when nonlinear effects dominate system performance. Traditional linearized models often fail to capture the complex interactions introduced by high switching frequencies, abrupt load transients, thermal stress, and input voltage disturbances. These factors give rise to nonlinear dynamics that significantly influence system stability and operational reliability.
[1] S. H. Straits, Nonlinear Dynamics and Chaos. Westview Press. (2015).
[2] Y. A. Kuznets, Elements of Applied Bifurcation Theory. Springer. (2004).
[3] J. Guckenheimer and P. Holmes, Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields. Springer. (1983).
[4] J. K. Hale and H. Koçak, Dynamics and Bifurcations. Springer. (1991).
[5] K. T. Alligood, T. D. Sauer and J. A. Yorke, Chaos: An Introduction to Dynamical Systems. Springer. (1996).
[6] S. Wiggins, Introduction to Applied Nonlinear Dynamical Systems and Chaos. Springer. (2003).
[7] D. W. Jordan and P. Smith, Nonlinear Ordinary Differential Equations. Oxford University Press. (2007).
[8] R. Seydel, Practical Bifurcation and Stability Analysis. Springer. (2010).
[9] B. D. Hassard, N. D. Kazarinoff and Y. H. Wan, Theory and Applications of Hopf Bifurcation. Cambridge University Press. (1981).
[10] A. H. Nayfeh and B. Balachandran, Applied Nonlinear Dynamics: Analytical, Computational, and Experimental Methods. Wiley. (2008).
[11] M. J. Feigenbaum, Quantitative universality for a class of nonlinear transformations. Journal of Statistical Physics. (1978).
[12] R. M. May, Simple mathematical models with very complicated dynamics. Nature. (1976).
[13] S. Banerjee and G. C. Verghese, Nonlinear Phenomena in Power Electronics. IEEE Press / Wiley. (2001).
[14] S. Banerjee, Dynamics for Engineers. Wiley. (2005).
[15] C. K. Tse, Complex Behavior of Switching Power Converters. CRC Press. (2003).
[16] R. W. Erickson and D. Maksimović, Fundamentals of Power Electronics. Springer. (2001).
[17] R. D. Middlebrook, Modeling techniques for switching regulators. IEEE Transactions. (1976).
[18] C. Fang and E. H. Abed, Bifurcation analysis of pulse-width-modulated converters. IEEE Transactions on Circuits and Systems. (2001).
[19] A. El Aroudi et al., Bifurcation analysis of DC–DC switching converters. IEEE Transactions. (2005).
[20] M. Di Bernardo, C. Budd, A. Champneys and P. Kowalczyk, Piecewise-Smooth Dynamical Systems: Theory and Applications. Springer. (2008).
[21] S. Banerjee, Border collision bifurcations in power converters. IEEE Transactions. (2006).
[22] Z. T. Zhusubaliyev and E. Mosekilde, Bifurcations and Chaos in Piecewise-Smooth Dynamical Systems. World Scientific. (2003).
[23] J. H. B. Deane, Chaos in a current-mode controlled boost DC–DC converter. IEEE Transactions. (1992).
[24] H. K. Khalil, Nonlinear Systems. Prentice Hall. (2002).
[25] R. C. Dorf and R. H. Bishop, Modern Control Systems. Pearson. (2011).
[26] K. Ogata, Modern Control Engineering. Prentice Hall. (2010).
[27] X. He et al., Nonlinear stability analysis of converter-dominated power systems. IEEE / arXiv. (2022).
[28] N. Guruwacharya et al., Dynamic modeling of power converters under low-inertia conditions. IEEE / arXiv. (2020).
[29] J. Sun, Small-signal methods for AC distributed power systems. IEEE Transactions on Power Electronics. (2009).
[30] R. W. Erickson, DC–DC power converter design principles. IEEE. (1997).
Nonlinear dynamics, bifurcation analysis, power electronic converters, extreme operating conditions, chaos theory, hybrid dynamical systems, border-collision bifurcation, Lyapunov exponent, DC-DC converters, stability analysis, switching systems, adaptive control