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The dimensionality reduction modeling for a memristive circuit is carried out to realize accurate prediction, quantitative analysis, and physical control of its multistability, which has become one of the hottest research topics in the field of information science. Based on these considerations, this paper briefly reviews the specific multistability phenomenon generating from the memristive circuit in the voltage\u2010current domain and expounds the multistability control strategy. Then, this paper introduces the accurate flux\u2010charge constitutive relation of memristors. Afterwards, the dimensionality reduction modeling method of the memristive circuits, i.e., the incremental flux\u2010charge analysis method, is emphatically introduced, whose core idea is to implement the explicit expressions of the initial conditions in the flux\u2010charge model and to discuss the feasibility and effectiveness of the multistability reconstitution of the memristive circuits using their flux\u2010charge models. Furthermore, the incremental integral transformation method for modeling of the memristive system is reviewed by following the idea of the incremental flux\u2010charge analysis method. The theory and application promotion of the dimensionality reduction modeling and multistability reconstitution are proceeded, and the application prospect is prospected by taking the synchronization application of the memristor\u2010coupled system as an example.<\/jats:p>","DOI":"10.1155\/2021\/2747174","type":"journal-article","created":{"date-parts":[[2021,7,9]],"date-time":"2021-07-09T18:06:43Z","timestamp":1625854003000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["Recent Advances in Dimensionality Reduction Modeling and Multistability Reconstitution of Memristive Circuit"],"prefix":"10.1155","volume":"2021","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-1433-0487","authenticated-orcid":false,"given":"Yunzhen","family":"Zhang","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7703-4637","authenticated-orcid":false,"given":"Yuan","family":"Ping","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6709-9506","authenticated-orcid":false,"given":"Zhili","family":"Zhang","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5596-3686","authenticated-orcid":false,"given":"Guangzhe","family":"Zhao","sequence":"additional","affiliation":[]}],"member":"311","published-online":{"date-parts":[[2021,7,9]]},"reference":[{"key":"e_1_2_12_1_2","doi-asserted-by":"publisher","DOI":"10.1109\/jproc.2012.2190814"},{"key":"e_1_2_12_2_2","doi-asserted-by":"publisher","DOI":"10.1007\/s11071-017-3397-1"},{"key":"e_1_2_12_3_2","first-page":"1157","article-title":"Hidden hyperchaotic attractor in a novel simple memristive neural network","volume":"8","author":"Pham V. 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