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There are three elemental components in a Leech heartbeat computational model: neuron,graded synapse and spike-mediated synapse.We attain some bifurcation structure in its ISI(s) for a single neuron in previous.And we notice,graded synaptic transmission and spike-mediated synaptic transmission play different role in Leech elemental oscillator.We reveal bifurcation physical characteristic of an isolated heart interneuron in a HH model,and in order to explore the relation between synaptic transmission and its primitive property,we focus on this bifurcation diagram all the way.At first,we construct a simplified oscillator only with grade synapse between two neurons,called L3 and R3.Each parameter changes from its canonical value respectively for functional analysis.In all the experiment,we fix on the injection current for L3 neuron but vary it for R3 neuron,just like a single neuron.These settings help us recognize the functional deviation of transmission under an asymmetry injection into leech heartbeat elemental oscillator.As we plug in spike-mediate synapse one by one,some ISI(s) diagram changes greatly and the other shows little.That means,spike-mediate synapse which belongs to different grade take part in different activity,even it is not clear yet.The computation shows that graded synaptic transmission helps the physical activity steady,while spike-mediated synaptic transmission disturbs the situation.But spike-mediated synaptic transmission between different grades keeps the bifurcation of ISI(s) as well.That means,if the oscillator is running wrong,spike-mediated synaptic transmission between the same graded neurons should be pay more attention firstly.