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In this paper,the third model of four (3+1)-dimensional nonlinear evolution equations,generated by the Jaulent-Miodek hierarchy,is investigated by the bifurcation method of planar dynamical systems.The 2-parameters different bifurcation regions are obtained.According to the different phase portraits in 2-parameters different bifurcation regions,we obtain kink (anti-kink) wave solutions,solitary wave solutions and periodic wave solutions for the third of these models in the different subsets of 4-parameters space by dynamical system method.Furthermore,the explicit exact expressions of these bounded traveling waves are obtained.All these wave solutions are characterized by distinct physical structures.