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The critical values of delay at which Hopf bifurcations occur are obtained and ordered, and it is proved that the delay can induce stability switches, which means that the delay has a significant impact on both the formation and the termination of algal blooms. During the process of stability switching, double Hopf bifurcation arises. Taking the rate of toxin liberation and time delay as the bifurcation parameters, the normal form for double Hopf bifurcation is derived, from which the classification for dynamics and bifurcation sets near double Hopf bifurcation point is obtained. It is proved that the system has complex dynamics, such as periodic oscillations, quasi-periodic oscillations on two- or three-torus and even chaos. Numerical simulations are presented to support the theoretical results. <\/jats:p>","DOI":"10.1142\/s0218127422501784","type":"journal-article","created":{"date-parts":[[2022,10,13]],"date-time":"2022-10-13T08:12:06Z","timestamp":1665648726000},"source":"Crossref","is-referenced-by-count":8,"title":["Stability Switches and Chaos in a Diffusive Toxic Phytoplankton\u2013Zooplankton Model with Delay"],"prefix":"10.1142","volume":"32","author":[{"given":"Yanfei","family":"Du","sequence":"first","affiliation":[{"name":"School of Mathematics and Data Science, Shaanxi University of Science and Technology, Xi\u2019an 710021, P. R. China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yun","family":"Yang","sequence":"additional","affiliation":[{"name":"School of Mathematics and Data Science, Shaanxi University of Science and Technology, Xi\u2019an 710021, P. R. 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