Eliminating amplitude death by the asymmetry coupling and process delay in coupled oscillators

Coupling mode plays a key role in determining the dynamical behavior and realizing certain system's rhythm and function in the complex systems. In this work, the effects of the asymmetry and process delay in the coupling on the dynamical behavior are investigated. We find that both the asymmetry and process delay effectively reduce the region of the frequency-mismatch-induced amplitude death in the parameter space, and make the system to recover oscillation in the amplitude death regime so as to retain sustained system's rhythm function. Furthermore, we show the asymmetry and process delay can destroy synchronization. Our results suggest that the asymmetry coupling and process delay are of crucial importance in controlling amplitude death and synchronization, and hence that their considerations are vital for modeling real life problems.