Bursting oscillations induced by multiple coexisting attractors in a modified 3D van der Pol-Duffing system

This paper analytically and numerically investigates the dynamical characteristics of a fractional Duffing–van der Pol oscillator with two periodic excitations and the distributed time delay. First, we consider the pitchfork bifurcation of the system driven by both a high-frequency parametric excitation and a low-frequency external excitation. Utilizing the method of direct partition of motion, the original system is transformed into an effective integer-order slow system, and the supercritical and subcritical pitchfork bifurcations are observed in this case. Then, we study the chaotic behavior of the system when the two excitation frequencies are equal. The necessary condition for the existence of the horseshoe chaos from the homoclinic bifurcation is obtained based on the Melnikov method. Besides, the parameters effects on the routes to chaos of the system are detected by bifurcation diagrams, largest Lyapunov exponents, phase portraits, and Poincaré maps. It has been confirmed that the theoretical predictions achieve a high coincidence with the numerical results. The techniques in this paper can be applied to explore the underlying bifurcation and chaotic dynamics of fractional-order models.

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Experimental observation of distinct amplitude-modulated bursting in Liénard system

Kingston,

Vijay,

Kumarasamy

et al. 2023

Eur. Phys. J. Plus

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In this study, we explore the emergence of amplitude-modulated bursting in a multi-frequency excited Liénard system. Our investigation reveals that the system exhibits distinct patterns of amplitude-modulated bursting for a lower damping value and varying forcing frequencies of the system. Conversely, for a higher damping value with distinct system frequencies, the system exhibits intricate amplitude-modulated bursting accompanied by a variety of bursting oscillations. The discrete patterns of amplitude-modulated bursting arise as a consequence of the dynamic interplay with slowly varying multiple frequency forcing within the system. To gain a deeper understanding of these dynamics, we conduct a comprehensive stability bifurcation analysis. Furthermore, to validate our findings, we perform numerical simulations and corroborate our results through a real-time hardware circuit experiment. This interdisciplinary approach provides valuable insights into the behavior of the Liénard system under multi-frequency excitation, shedding light on its complex dynamical characteristics.

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Bursting oscillations induced by multiple coexisting attractors in a modified 3D van der Pol-Duffing system

Cited by 6 publications

References 42 publications

Comprehensive analysis of the mechanism of sensitivity to initial conditions and fractal basins of attraction in a novel variable-distance magnetic pendulum

Comprehensive analysis of the mechanism of sensitivity to initial conditions and fractal basins of attraction in a novel variable-distance magnetic pendulum

Bifurcation and chaos detection of a fractional Duffing–van der Pol oscillator with two periodic excitations and distributed time delay

Experimental observation of distinct amplitude-modulated bursting in Liénard system

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