Effect of propagation delays on the steady state behavior in ALOHA systems is investigated. The basic model of ALOHA systems with propagation delays is introduced and analyzed in line with the catastrophe theory. The bifurcation set, which shows the necessary and sufficient condition that the system is either monostable or bistable, is given explicitly in terms of a few system and user parameters including propagation delays. The global behavior of the system is determined by the cusp catastrophe. Analysis of bifurcation sets shows that propagation delays stabilize the system.
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