Tipping in Stuart-Landau oscillators induced by higher-order repulsive interactions.

Abstract

Tipping phenomena in complex systems represent abrupt transitions in the system behavior due to incremental changes in parameters. Here, we report the emergence of an abrupt transition from an oscillatory to a death state in coupled limit cycle oscillators with higher-order repulsive interactions. This transition contrasts with the typical continuous transitions observed with pairwise repulsive links. It is notable that higher-order interactions introduce more complexity to the system dynamics, thereby leading to the transition to the death state at lower coupling strengths compared to pairwise coupled systems. Importantly, there exists a sudden revival of the oscillation from the death state with increasing the pairwise coupling strength despite the detrimental effect of pairwise couplings. The results are also robust for nonidentical systems. Furthermore, the analytical determination of the critical coupling strength for the tipping point aligns closely with the results obtained from numerical simulations.