New test-particle simulations have been performed to study the secular
evolution of the gaseous distribution in NGC 4736. We find that the d
istribution of gas clouds can be understood in the frame of perturbati
on induced by a nuclear oval potential, in addition to a spiral-like p
otential. Our experiments show that both inner and outer rings are sta
ble structures located at the inner Lindblad resonance (ILR) and the o
uter Lindblad resonance(OLR), respectively, in agreement with the obse
rvations of NGC 4736. One of our-simplified simulations indicates that
both nuclear starburst and orbital resonance might be needed for keep
ing the inner ring stable for a long period. We have introduced a symp
lectic algorithm in the orbit integration. Its stronger stability allo
ws us to adopt a rather large time step to save computational time. Su
bstitution of a viscous force for cloud-cloud interactions proves adeq
uate in the case of NGC 4736.