Bell, JonathanHaskell, Evan C.2021-05-132021-05-132021-04-14Bell, J., Haskell, E.C. Attraction–repulsion taxis mechanisms in a predator–prey model. SN Partial Differ. Equ. Appl. 2, 34 (2021). https://doi.org/10.1007/s42985-021-00080-0https://doi.org/10.1007/s42985-021-00080-0http://hdl.handle.net/11603/21516We consider a predator–prey model where the predator population favors the prey through biased diffusion toward the prey density, while the prey population employs a chemical repulsive mechanism. This leads to a quasilinear parabolic system. We first establish the global existence of positive solutions. Thereafter we show the existence of nontrivial steady state solutions via bifurcation theory, then we discuss the stability of these branch solutions. Through numerical simulation we analyze the nature of patterns formed and interpret results in terms of the survival and distribution of the two populations.29 pagesen-USThis item is likely protected under Title 17 of the U.S. Copyright Law. Unless on a Creative Commons license, for uses protected by Copyright Law, contact the copyright holder or the author.predator prey modelpattern formationchemical repulsive mechanismbifurcation theorynumerical simulationsnontrivial steady state solutionsText