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We study analytically and numerically stability and interaction patterns ofquantized vortex lattices governed by the reduced dynamical law -- a system ofordinary differential equations (ODEs) -- in superconductivity. By derivingseveral non-autonomous first integrals of the ODEs, we obtain qualitativelydynamical properties of a cluster of quantized vortices, including globalexistence, finite time collision, equilibrium solution and invariant solutionmanifolds. For a vortex lattice with 3 vortices, we establish orbital stabilitywhen they have the same winding number and find different collision patternswhen they have different winding numbers. In addition, under several specialinitial setups, we can obtain analytical solutions for the nonlinear ODEs.

Quantized vortex dynamics and interaction patterns in superconductivity based on the reduced dynamical law