In this paper, we study the bifurcations and exact traveling wave solutions of a new two-component system from the perspective of the theory of dynamical systems. We obtain all possible bifurcations of phase portraits of the system under various conditions about the parameters associated with the planar dynamical system. Then, we show the existence of traveling wave solutions including solitary waves, periodic waves and periodic blow-up waves, and give their exact expressions. These results can help understand the dynamical behavior of the traveling wave solutions of the system.
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