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It is proved that for an arbitrary spatial dimension, the corresponding initial boundary value problem possesses a unique global bounded classical solution when the prey-taxis is restricted to a small range. Moreover, the local stabilities of constant steady states (including trivial, semi-trivial and positive constant steady states) are investigated. A further study on the coexistence steady state implies that the prey-taxis term suppresses the global asymptotical stability and influences the steady-state\/Hopf bifurcations (if they exist). Analyses of steady-state bifurcation, Hopf bifurcation, and even Hopf\/steady-state mode interaction are carried out in detail by means of the Lyapunov\u2013Schmidt procedure. In particular, we obtain stable or unstable steady states, time-periodic solutions, quasi-periodic solutions, and sphere-like surfaces of solutions. These results provide theoretical evidences to the complex spatiotemporal dynamics found in numerical simulations.<\/jats:p>","DOI":"10.1142\/s0218127420500224","type":"journal-article","created":{"date-parts":[[2020,3,10]],"date-time":"2020-03-10T09:56:49Z","timestamp":1583834209000},"page":"2050022","source":"Crossref","is-referenced-by-count":42,"title":["Stability and Bifurcation in a Predator\u2013Prey System with Prey-Taxis"],"prefix":"10.1142","volume":"30","author":[{"given":"Huanhuan","family":"Qiu","sequence":"first","affiliation":[{"name":"School of Mathematics and Statistics, Chongqing Jiaotong University, Chongqing 400074, P. R. China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9114-5269","authenticated-orcid":false,"given":"Shangjiang","family":"Guo","sequence":"additional","affiliation":[{"name":"School of Mathematics and Physics, China University of Geosciences, Wuhan, Hubei 430074, P. R. 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