  We study analytically and numerically stability and interaction patterns of
quantized vortex lattices governed by the reduced dynamical law -- a system of
ordinary differential equations (ODEs) -- in superconductivity. By deriving
several non-autonomous first integrals of the ODEs, we obtain qualitatively
dynamical properties of a cluster of quantized vortices, including global
existence, finite time collision, equilibrium solution and invariant solution
manifolds. For a vortex lattice with 3 vortices, we establish orbital stability
when they have the same winding number and find different collision patterns
when they have different winding numbers. In addition, under several special
initial setups, we can obtain analytical solutions for the nonlinear ODEs.
