Nonlinear Vibrations by Periodic Perturbation in a Murali–Lakshmanan–Chua Electronic Circuit Combined with Multiple Frequency Signal

Bursting Oscillations and Sliding Motion in Permanent Magnet Synchronous Motor Systems with Friction Factor

“…When condition a 1 a 2 > a 3 degenerates to a 1 a 2 � a 3 , a pair of pure imaginary roots appear in the solution of characteristic polynomial (14) indicating the occurrence of Hopf bifurcation. erefore, the conditions of Hopf bifurcation are as follows:…”

“…e two-parameter bifurcation diagram, Poincaré map, and Lyapunov exponent spectrum are employed to analyze the inherent properties of autonomous PMSM system. Meanwhile, the nonsmooth bursting oscillations of nonautonomous PMSM system with friction factor are studied through equilibrium curves and transformation phase portraits (TPP) [14,15]. In addition, the mechanism of sliding motion is discussed separately, and the theoretical results obtained from attractor and vector field structure analysis [16,17] are also verified by the calculation of frequency and sliding time length.…”

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

“…Although the van der Pol equation has been studied over wide parameter regimes, from perturbations of harmonic motion to relaxation oscillations, bifurcations, and combination resonance condition, the effectiveness of periodic amplitude modulation in controlling bursting dynamics of the system has been discussed little. Common control methods mainly include feedback and nonfeedback control (Hu et al, 2017; Mao et al, 2020). One of the classical nonfeedback methods is periodic perturbation (Yang, 2021a; Yu et al, 2020), which can suppress nonlinear dynamics into a periodic orbit.…”