  In this work, we investigate the system of three species ecological model
involving one predator-prey subsystem coupling with a generalist predator with
negative effect on the prey. Without diffusive terms, all global dynamics of
its corresponding reaction equations are proved analytically for all classified
parameters. With diffusive terms, the transitions of different spatial
homogeneous solutions, the traveling wave solutions, are showed by higher
dimensional shooting method, the Wazewski method. Some interesting numerical
simulations are performed, and biological implications are given.
