{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,9]],"date-time":"2025-12-09T11:33:27Z","timestamp":1765280007295,"version":"3.37.3"},"reference-count":40,"publisher":"World Scientific Pub Co Pte Ltd","issue":"08","funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["11571016"],"award-info":[{"award-number":["11571016"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["61403115"],"award-info":[{"award-number":["61403115"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"specialized research fund for the doctoral program of higher dducation of China","award":["20093401120001"],"award-info":[{"award-number":["20093401120001"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Bifurcation Chaos"],"published-print":{"date-parts":[[2017,7]]},"abstract":"<jats:p>Turing instability and pattern formation in the Lengyel\u2013Epstein (L\u2013E) model with superdiffusion are investigated in this paper. The effects of superdiffusion on the stability of the homogeneous steady state are studied in detail. In the presence of superdiffusion, instability will occur in the stable homogeneous steady state and more complex dynamics will exist. As a result of Turing instability, some patterns are formed. Through stability analysis of the system at the equilibrium point, conditions ensuring Turing and Hopf bifurcations are obtained. To further explore pattern selection, the weakly nonlinear analysis and multiple scale analysis are employed to derive amplitude equations of the stationary patterns. Then complex dynamics of amplitude equations, such as the existence of homogeneous solutions, stripe and hexagon patterns, mixed structure patterns, their stability, interaction and transition between them, are analyzed. Then different patterns occur immediately. Finally, the numerical simulations are presented to show the effectiveness of theoretical analysis and patterns are identified numerically. Whereas in the existing results of such model with normal diffusion, no amplitude equations are derived and patterns are only identified through numerical simulations.<\/jats:p>","DOI":"10.1142\/s0218127417300269","type":"journal-article","created":{"date-parts":[[2017,8,10]],"date-time":"2017-08-10T03:54:31Z","timestamp":1502337271000},"page":"1730026","source":"Crossref","is-referenced-by-count":35,"title":["Turing Patterns in the Lengyel\u2013Epstein System with Superdiffusion"],"prefix":"10.1142","volume":"27","author":[{"given":"Biao","family":"Liu","sequence":"first","affiliation":[{"name":"School of Mathematical Sciences, Anhui University, Hefei 230601, P. R. China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7780-0861","authenticated-orcid":false,"given":"Ranchao","family":"Wu","sequence":"additional","affiliation":[{"name":"School of Mathematical Sciences, Anhui University, Hefei 230601, P. R. China"}]},{"given":"Naveed","family":"Iqbal","sequence":"additional","affiliation":[{"name":"School of Mathematical Sciences, Anhui University, Hefei 230601, P. R. China"}]},{"given":"Liping","family":"Chen","sequence":"additional","affiliation":[{"name":"School of Electrical Engineering and Automation, Hefei University of Technology, Hefei 230009, P. R. 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