Oscillation death in coupled counter-rotating identical nonlinear oscillators

Boosting of stable synchronization in coupled non-identical counter-rotating chaotic systems

Achieving synchronization in coupled non-identical chaotic systems has been a difficult endeavor, and improving the stability of synchronization in such systems poses additional challenges. This research work addresses these challenges by identifying stable synchronization in coupled non-identical chaotic systems and enhancing its stability. The study explores chaotic attractors that arise from various system parameters to provide generalized results. Furthermore, the impact of the transient uncoupling factor on improving synchronization stability in coupled non-identical counter-rotating chaotic oscillators is discussed. By investigating these aspects, the research aims to contribute to the understanding and advancement of synchronization in coupled non-identical chaotic systems.

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

We unravel the collective dynamics exhibited by two coupled nonlinearly damped Liénard 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.