Nontrivial amplitude death in coupled parity-time-symmetric Lienard oscillators

We unravel the collective dynamics exhibited by two coupled nonlinearly damped Lienard oscillators exhibiting parity and time symmetry, which is a classical example of the position-dependent damped systems. The coupled system facilitates the onset of limit-cycle and aperiodic oscillations in addition to large-amplitude oscillations. In particular, a nontrivial amplitude death state emerges as a consequence of balanced linear loss and gain of the coupled PT-symmetric systems, where gain in the amplitude of oscillation in one oscillator is exactly balanced by the loss in the other. Further, quasiperiodic attractors exist in the parameter space of a neutrally stable trivial steady state. We deduce analytical critical curves enclosing the stable regions of a nontrivial fixed point, leading to the manifestation of nontrivial amplitude death state, and neutrally stable trivial steady state. The latter loses its stability leading to the emergence of the former. The analytical critical curves exactly match with the simulation boundaries. There is also a reemergence of dynamical states as a function of the coupling strength and multistability among the observed dynamical states. The basin of attraction provides an explanation for the observed probability of dynamical states.

Automated summary

This study uncovers the collective dynamics of two coupled nonlinearly damped Lienard oscillators, focusing on the emergence of a nontrivial amplitude death state and quasiperiodic attractors. Analytical critical curves are deduced to explain the stability regions of the nontrivial fixed point and the neutrally stable trivial steady state, matching simulation boundaries. The dynamics also show multistability and a reemergence of states with changes in coupling strength, with the basin of attraction providing insight into the probability of observed dynamical states.