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This paper studies nonlinear instability and bifurcations in a packet reservation multiple access (PRMA) protocol for communication of voice and data terminals. This protocol has been widely considered for providing speech and data communications in a terrestrial microcell system. Recently modified versions of the PRMA protocol have been the subject of extensive research, with the goal of application to low earth orbit mobile satellite systems. These systems are expected to play a significant role in providing communication services to users around the world. A bistable behavior of the PRMA protocol for traffic with both voice and data sources is investigated, and bifurcations of equilibrium points when system parameters change are determined. A price based bifurcation control scheme is proposed to increase capacity of the PRMA protocol, defined as the number of simultaneous users within the system. Markov analysis show that the adaptively controlled system has a unique probability distribution function. Also, equilibrium point analysis (EPA) shows that the system possesses a unique equilibrium point. Finally, a brief discussion concerning the extension of the proposed bifurcation control scheme to the PRMA protocol over a random packet error channel is also provided.