Experimental observation of distinct amplitude-modulated bursting in Liénard system

Abstract

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.