Two wavelength optical signals in the infrared regime were generated in atomic rubidium (Rb) vapor using a Ti:sapphire laser amplifier and competition between the two signals was observed. The effects of Rb number density, pump laser intensity and the chirp of laser pulses on the characteristics of the two signals were investigated. The results show that the two signals were mainly generated by two coupled difference frequency six wave mixings and, in the meantime, two coupled six wave mixing channels were identified. The competition between the two signals is dominantly governed by phase matching conditions in the two six wave mixing processes. The phase matching conditions in the two channels are primarily determined by the Rb number density and, whereas, the phase matching conditions are scarcely related to pump laser intensity and the chirp of pump laser pulses.