By operating with the Scale Relativity Theory in the dynamics of complex systems, we can achieve a description of these complex systems through a holographic-type perspective. Then, gauge invariances of a Riccati-type become functional in complex system dynamics, which implies several consequences: conservation laws (in particular, for classical dynamics, the kinetic momentum conservation law), simultaneity and synchronization between the structural units (of a complex system) dynamics, and temporal patterns through harmonic mappings.