  We examine the impact of time delay on two coupled phase oscillators within
the second-order Kuramoto model, which is relevant to the operations of
real-world networks that rely on signal transmission speed constraints. Our
analytical and numerical exploration shows that time delay can cause
multi-stability within phase-locked solutions, and the stability of these
solutions decreases as inertia increases. In addition to phase-locked
solutions, we discovered non-phase-locked solutions that exhibit periodic and
chaotic behaviors, depending on the amount of inertia and time delay. Our
results suggest that this system has the potential to create patterns similar
to epileptic seizures.
