Spatial Effects of Phase Dynamics on Oscillators Close to Bifurcation

The phase reduction approach has manifested its efficacy in investigating synchronization behaviors limit-cycle oscillators. However, spatial distributions of the value on limit cycle may lead to illusions synchronizations for oscillators close bifurcations. In this paper, we compared sensitivity function domain and time saddle-node homoclinic (SNH) bifurcation, also known as bifurcation an invariant circle. It was found that can show accumulation feature cycle, which be ignored domain. As example, uncoupled SNH driven by common independent noises were investigated, where space-dependent coupling considered noise. These results shed some light dynamics