We investigate the time dependent Ginzburg-Landau (TDGL) system that models a thin superconducting wire subjected to a constant voltage difference across its ends using bridge geometry boundary conditions. Using a combination of computational methods, formal asymptotic expansions, and rigorous analysis, we analyze the behavior of solutions as the physical parameters of wire length, voltage and temperature are varied. In addition to numerical experiments that reveal a rich array of phase slip center (PSC) behavior, period-doubling, period tripling, period four, period eight, etc. as well as highly oscillatory solution for which periodicity is lost, we show that the parameter L–V plane, where L is the half length of the wire and V is the voltage, is partitioned into regimes where the solutions exhibit different periodicity. In particular, we present the analytical results to reveal those regions in the L–V parameter space where the basic 2π/V-time periodic solution dominates the dynamics.