Effect of coupling strength and phase lag asymmetries in two-populations with higher-order interaction

We consider a network of globally coupled two-populations of identical phase oscillators with both pairwise and higher-order (triad) interactions. We introduce asymmetry coupling strength parameters that quantify the degree of asymmetry between the intra- and inter-populations coupling strengths in both pairwise and higher-order interactions. In addition, we also introduce phase lag asymmetry parameters in both pairwise and higher-order interactions to investigate the tradeoff between the coupling strength asymmetry parameters and the phase lag asymmetry parameters on the observed dynamical states. Stable and breathing chimera states coexist with global synchronized state. Stable chimera manifests via a saddle-node bifurcation, while breathing chimera manifests via a Hopf bifurcation and finally, the latter loses its stability via a homoclinic bifurcation leading to global synchronization. Increase in the asymmetry between the intra- and inter-populations coupling strengths of higher-order (pairwise) interaction always promotes (suppresses) the stable regions of the chimera states in the phase diagrams even in the presence of strong asymmetry (homogeneous or heterogeneous) parameters in pairwise and higher-order interactions, which always destabilizes the chimera states. We also deduce the low-dimensional evolution equations for the macroscopic order parameters using the Ott-Antonsen ansatz. The analytical saddle-node and Hopf bifurcation curves deduced from the evolution equation for the macroscopic order parameters agree very well with the simulation results and XPPAUT bifurcation curves.