Emergent behaviors of discrete Lohe aggregation flows

<p style='text-indent:20px;'>The Lohe sphere model and the matrix are prototype continuous aggregation models on unit unitary group, respectively. These have been extensively investigated in recent literature. In this paper, we propose several discrete counterparts for type study their emergent behaviors using Lyapunov function method. For suitable discretization of model, employ a scheme consisting two steps. first step, solve first-order forward Euler scheme, second project intermediate state onto sphere. present sufficient framework leading to complete terms system parameters initial data. use Lie group integrator method, Lie-Trotter splitting method Strang three models. these models, also provide analytical frameworks asymptotic state-locking.</p>