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Next, the linear stability and Hopf bifurcations of homogeneous steady-state solutions are described in detail. In particular, the Hopf bifurcation direction and the stability of bifurcating time-periodic solutions are determined by using center manifold reduction and normal form theory. Finally, some of the main results are illustrated by an application to a predator\u2013prey model with Allee effect and one-dimensional spatial domain [Formula: see text]. <\/jats:p>","DOI":"10.1142\/s0218127417500493","type":"journal-article","created":{"date-parts":[[2017,5,8]],"date-time":"2017-05-08T05:30:57Z","timestamp":1494221457000},"page":"1750049","source":"Crossref","is-referenced-by-count":13,"title":["Bifurcation of Reaction Cross-Diffusion Systems"],"prefix":"10.1142","volume":"27","author":[{"given":"Rong","family":"Zou","sequence":"first","affiliation":[{"name":"College of Mathematics and Econometrics, Hunan University, Changsha, Hunan 410082, P. R. 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