Eliminating delay-induced oscillation death by gradient coupling

In this work, we investigate gradient coupling effect on oscillation death in a ring of N delay-coupled oscillators. We find that the gradient coupling monotonically reduces the domain of death island in the parameter space of the diffusive coupling and time delay, and thus the death island can be completely eliminated once the gradient coupling strength exceeds a certain threshold, whose value is found to be a constant if N is sufficiently large. For two special cases, a ring with zero gradient coupling and a one-way ring for identical diffusive and gradient couplings, all previous results in the literature are recovered. In particular, for the one-way ring, a size effect of N is discovered, which indicates that under this situation the death can always be eliminated if N is above a critical N-max. All the described results are proved to hold generally in coupled oscillator systems.