Using coupling imperfection to control amplitude death.

Previous studies of nonlinear oscillator networks have shown that amplitude death (AD) occurs after tuning oscillator parameters and coupling properties. Here, we identify regimes where the opposite occurs and show that a local defect (or impurity) in network connectivity leads to AD suppression in situations where identically coupled oscillators cannot. The critical impurity strength value leading to oscillation restoration is an explicit function of network size and system parameters. In contrast to homogeneous coupling, network size plays a crucial role in reducing this critical value. This behavior can be traced back to the steady-state destabilization through a Hopf's bifurcation, which occurs for impurity strengths below this threshold. This effect is illustrated across different mean-field coupled networks and is supported by simulations and theoretical analysis. Since local inhomogeneities are ubiquitous and often unavoidable, such imperfections can be an unexpected source of oscillation control.