Revisiting amplitude death in the presence of diffusion asymmetry

In traditional diffusive coupling, the feedback term is treated on a par with the external node signal and the coupled oscillators respond to the difference in variation of their strengths. This paper presents the study when such symmetric interaction between the feedback and the external node signal is absent and the two compete with unequal weights. It is found that this diffusion asymmetry has the potential to effectively instigate amplitude death (AD) as well as sustain oscillatory behavior in the coupled units. When the feedback is stronger than the external node signal it aids the occurrence of AD by either inducing it or enhancing the already existing AD regime. On the contrary, weak feedback resists the occurrence of AD and sustains oscillatory motion. These results are found generic to identical, conjugate, and mixed diffusive couplings. Identical diffusion has been explored for both instantaneous and delayed interactions. Results obtained numerically are found to be well in agreement with the analytical findings.