A generalization of the Harris [1962] model has recently been proposed to explain the multi-spacecraft Cluster observations of thin bifurcated current sheets. It utilizes features of the ion motion in thin sheets and assumes anisotropy of the ion species. We report the results of 2D PIC simulations based on this model. Simulations confirm its self-consistency. They also reveal the lower-hybrid drift instability at the edges of the thinned sheet and a transition to a new quasi-equilibrium state with a considerable contribution of electrons to the bifurcated current. This can be explained using a modification of the original equilibrium model that assumes a small electron anisotropy. At later time instabilities of both parities are detected inside the sheet. They have much larger wavelengths and end up with the kink-type flapping motions of the bifurcated sheet as a whole.