Some non-linear behaviors in the dynamics of complex systems using the Scale Relativity Theory in the form of Multifractal Hydrodynamic Model are analyzed. By assimilating any complex system to a mathematical multifractal-type object, it is shown that the inversion phenomenon in various mediums (temperature inversion in atmospheric structures, inversion of tension fields at Martensite-Austenite transition etc.) can be "mimed " as multifractal tunnel effects.