Dynamics of Trajectories and Weak Chimera Patterns in the Second-Order Kuramoto Model With Damping Effects

This study examines the second-order Kuramoto model within a specific small invariant subspace. We explore how the damping parameter influences the emergence of synchronized states and the weak chimera state in this model. In addition, we numerically investigate various behaviors in the phase space resulting from changes in the damping parameter and external force, while keeping other parameters constant. Among these behaviors, we identify equilibrium points and analyze their stability. Furthermore, this study investigates the system’s global bifurcations, both homoclinic and heteroclinic, as well as its local stability. The regions of the coherent state and the weak chimera state are also illustrated in the bifurcation diagram.