Phase slip centers in a two-band superconducting filament: Application to MgB2

► Numerical solution of two-band Ginzburg-Landau equations for MgB2 parameters. ► Strongly pronounced S-shaped forms of current-voltage characteristics. ► Three regimes on the current-voltage characteristics of two-band MgB2 filaments. ► One of the regime represents fluctuations of the current-density. ► For some parameters these fluctuations gradually disappear and become flattened.