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We analyze the local stability of the positive constant steady state and prove the global attractivity by means of the LaSalle\u2019s invariance principle. Additionally, we derive the parameter region that makes the positive constant steady state stable, and conclude that the boundary of this region contains a Hopf bifurcation curve and countable Turing curves. Thus, we get the existence of Turing\u2013Hopf bifurcation and Turing\u2013Turing bifurcation. Moreover, we calculate the normal form of the Turing\u2013Hopf singularity on the center manifold. Our theoretical analysis shows that the system may produce a pair of spatially inhomogeneous steady states, spatially homogeneous periodic solutions, transient spatially inhomogeneous periodic solutions or even other solutions near the Turing\u2013Hopf singularity. Finally, we carry out some numerical simulations for illustrating the analytical results.<\/jats:p>","DOI":"10.1142\/s0218127420501692","type":"journal-article","created":{"date-parts":[[2020,10,5]],"date-time":"2020-10-05T08:54:32Z","timestamp":1601888072000},"page":"2050169","source":"Crossref","is-referenced-by-count":10,"title":["Spatiotemporal Dynamics of a Modified Leslie\u2013Gower Model with Weak Allee Effect"],"prefix":"10.1142","volume":"30","author":[{"given":"Yuying","family":"Liu","sequence":"first","affiliation":[{"name":"School of Mathematics, Harbin Institute of Technology, Harbin, Heilongjiang, 150001, P. R. China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/2.zoppoz.workers.dev:443\/https\/orcid.org\/0000-0001-5753-2946","authenticated-orcid":false,"given":"Junjie","family":"Wei","sequence":"additional","affiliation":[{"name":"School of Mathematics, Harbin Institute of Technology, Harbin, Heilongjiang, 150001, P. R. 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