Collective behaviors of the Lohe Hermitian sphere model with inertia

<p style="text-indent:20px;">We present a second-order extension of the first-order Lohe Hermitian sphere (LHS) model and study its emergent asymptotic dynamics. Our proposed incorporates an inertial effect as extension. The inertia term can generate oscillatory behavior particle trajectory in small time interval(initial layer) which causes technical difficulty for application monotonicity-based arguments. For estimates, we employ two-point correlation function is defined inner product between positions particles. homogeneous ensemble with same frequency matrix, provide two sufficient frameworks terms system parameters initial data to show that functions tend unity exactly complete aggregation. In contrast, heterogeneous distinct matrices, framework data, makes be close by increasing principal coupling strength.</p>