  We study the dynamics of a collection of nonlinearly coupled limit cycle
oscillators, relevant to systems ranging from neuronal populations to
electrical circuits, under coupling topologies varying from a regular ring to a
random network. We find that the trajectories of this system escape to infinity
under regular coupling, for sufficiently strong coupling strengths. However,
when some fraction of the regular connections are dynamically randomized, the
unbounded growth is suppressed and the system always remains bounded. Further
we determine the critical fraction of random links necessary for successful
prevention of explosive behaviour, for different network rewiring time-scales.
These results suggest a mechanism by which blow-ups may be controlled in
extended oscillator systems.
