We study pacemaker rhythms generated by two nonoscillatory model cells that are coupled by inhibitory synapses. A minimal ionic model that exhibits postinhibitory rebound (PIR) is presented. When the post-synaptic conductance depends instantaneously on presynaptic potential the classical alternating rhythm is obtained. Using phase-plane analysis we identify two underlying mechanisms, “release” and “escape,” for the out-of-phase oscillation. When the postsynaptic conductance is not instantaneous but decays slowly, the two cells can oscillate synchronously with no phase difference. In each case, different stable activity patterns can coexist over a substantial parameter range.
*Present address of Xiao-Jing Wang: Department of Mathematics, University of Chicago, 5734 University Avenue, Chicago, IL 60637 USA.