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.

Automated summary

Previous studies have shown that amplitude death (AD) occurs in nonlinear oscillator networks after tuning parameters and coupling properties. However, we have found that the presence of a local defect or impurity in network connectivity can suppress AD, which is not observed in identically coupled oscillators. The critical impurity strength value leading to oscillation restoration is determined by the network size and system parameters. This behavior is attributed to the steady-state destabilization caused by a Hopf's bifurcation occurring for impurity strengths below the threshold value. The effect is demonstrated in various mean-field coupled networks through simulations and theoretical analysis, highlighting the unexpected role of local inhomogeneities in oscillation control.