{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,25]],"date-time":"2025-09-25T18:11:21Z","timestamp":1758823881856,"version":"3.37.3"},"reference-count":43,"publisher":"World Scientific Pub Co Pte Ltd","issue":"12","funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["11902108"],"award-info":[{"award-number":["11902108"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100003995","name":"Natural Science Foundation of Anhui Province","doi-asserted-by":"publisher","award":["1908085QA12"],"award-info":[{"award-number":["1908085QA12"]}],"id":[{"id":"10.13039\/501100003995","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100012226","name":"Fundamental Research Funds for the Central Universities of China","doi-asserted-by":"crossref","award":["JZ2018HGTA0200","JZ2018HGBZ0142"],"award-info":[{"award-number":["JZ2018HGTA0200","JZ2018HGBZ0142"]}],"id":[{"id":"10.13039\/501100012226","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Bifurcation Chaos"],"published-print":{"date-parts":[[2020,9,30]]},"abstract":"<jats:p> This paper is mainly devoted to the investigation of discrete-time fractional systems in three aspects. Firstly, the fractional Bogdanov map with memory effect in Riemann\u2013Liouville sense is obtained. Then, via constructing suitable controllers, the fractional Bogdanov map is shown to undergo a transition from regular state to chaotic one. Meanwhile, the positive largest Lyapunov exponent is calculated by the Jacobian matrix algorithm to distinguish the chaotic areas. Finally, the Grassberger\u2013Procaccia algorithm is employed to evaluate the correlation dimension of the controlled fractional Bogdanov system under different parameters. The main results show that the correlation dimension converges to a fixed value as the embedding dimension increases for the controlled fractional Bogdanov map in chaotic state, which also coincides with the conclusion driven by the largest Lyapunov exponent. Moreover, three-dimensional fractional Stefanski map is considered to further verify the effectiveness and generality of the obtained results. <\/jats:p>","DOI":"10.1142\/s0218127420501746","type":"journal-article","created":{"date-parts":[[2020,10,5]],"date-time":"2020-10-05T08:54:32Z","timestamp":1601888072000},"page":"2050174","source":"Crossref","is-referenced-by-count":3,"title":["On the Correlation Dimension of Discrete Fractional Chaotic Systems"],"prefix":"10.1142","volume":"30","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-1562-8541","authenticated-orcid":false,"given":"Li","family":"Ma","sequence":"first","affiliation":[{"name":"School of Mathematics, Hefei University of Technology, Hefei 230601, P. R. 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