Stability and Bifurcation Analysis in a Maglev System with Multiple Delays

Abstract

This paper considers the time-delayed feedback control for Maglev system with two discrete time delays. We determine constraints on the feedback time delays which ensure the stability of the Maglev system. An algorithm is developed for drawing a two-parametric bifurcation diagram with respect to two delays τ 1 and τ 2 . Direction and stability of periodic solutions are also determined using the normal form method and center manifold theory by Hassard. The complex dynamical behavior of the Maglev system near the domain of stability is confirmed by exhaustive numerical simulation.

A Robust Levitation Control of Maglev Vehicles Subject to Time Delay and Disturbances: Design and Hardware Experimentation

“…Remark 4. In the actual system, signal transmission in the maglev control system would be delayed, which may cause serious safety accidents [12][13][14]. In this paper, time delay was introduced into the dynamic modeling.…”

“…Nevertheless, the levitation system must have time delay due to the existence of signal transmission, inductance delay, and controller calculation. Time delay leads to more complex dynamic characteristics, including homogeneous bifurcation, Hopf bifurcation, and limit cycle oscillation [14,15]. The maglev train CMS04 presented by the National University of Defense Technology experienced severe rail-vehicle resonance caused by excessive time delay during testing [16,17].…”

Dynamic behaviors of a non-selective harvesting Lotka–Volterra amensalism model incorporating partial closure for the populations

“…Amensalism is one of the basic interactions between the species, where a species inflicts harm on the other species without any costs or benefits received by the other. During the last decade, many scholars [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15] investigated the dynamic behaviors of the amensalism model. Such topics as the local stability of the equilibrium [1,5,12,14], the existence of the positive periodic solution [2,11,13], extinction of the species [3], bifurcation of the system with delay [7] and the influence of the refuge [10,14] have been studied and many excellent results have been obtained.…”

Dynamic behaviors of a nonlinear amensalism model

“…During the last decade, many scholars [1][2][3][4][5][6][7][8][9][10][11][12] investigated the dynamic behaviors of the amensalism model; here, amensalism means that a species inflicts harm to other species without any costs or benefits received by the other. Such topics as the stability of the equilibrium [1,[3][4][5][6][7][8], the existence of the positive periodic solution [2,9,11], the extinction of the species [8,10], the influence of the cover [8,12], the influence of the functional response [10], etc. have been extensively studied.…”