Amplitude modulation control method for bursting dynamics under time-delayed feedback

Abstract

Time-delayed feedback control is one of the important active control methods for complex dynamical behaviors in nonlinear systems. Yet its relationship and effectiveness on multiple time scale dynamics need to be further explored. As a purpose to gain insight into such complexity, we investigate the effectiveness of amplitude modulation in controlling (suppressing or enhancing) bursting oscillations in a classical mechanical oscillator with time-delayed feedback. It is shown how the presence of delay can change the amplitude of the singular cycle oscillations, or suppress them altogether. The results are compared to the conventional periodic perturbation method. In many cases, the amplitudes of periodic solutions under delayed feedback are easier to satisfy the technical requirements. If the delayed feedback is added, stable periodic bursting can be easily accomplished. Therefore, we demonstrate that an effective vibration modulation for bursting dynamics is possible if appropriate time delay and feedback gains are chosen.

Orbits and chaos of a two‐fluid magnetized plasma oscillator subjected to parametric excitation with square delayed feedback

“…Goryunov and Preobrazhenskaya [27] considered the problem of the coexistence of quasistable attractors of a neurodynamic model with delay and developed an algorithm for estimating Lyapunov exponents for the system. Yu et al [28] investigated the effectiveness of amplitude modulation in controlling bursting oscillations in a classical mechanical oscillator with time-delayed feedback, then demonstrated that an effective vibration modulation for bursting dynamics is possible if appropriate time delay and feedback gains are chosen. Li et al [29] studied a delayed rumor spreading model with discontinuous threshold control.…”

“…Yu et al. [28] investigated the effectiveness of amplitude modulation in controlling bursting oscillations in a classical mechanical oscillator with time‐delayed feedback, then demonstrated that an effective vibration modulation for bursting dynamics is possible if appropriate time delay and feedback gains are chosen. Li et al.…”

Bursting dynamics and the bifurcation mechanism of a modified Rayleigh-van der Pol-Duffing oscillator

“…Multi-timescale dynamics exist in various research fields [1][2][3][4][5]. The common characteristics of multi-timescale dynamic systems are that state variables interact on different time scales, leading to complex bursting oscillation patterns.…”