{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T15:01:26Z","timestamp":1753887686788,"version":"3.41.2"},"reference-count":38,"publisher":"Wiley","issue":"1","license":[{"start":{"date-parts":[[2021,3,22]],"date-time":"2021-03-22T00:00:00Z","timestamp":1616371200000},"content-version":"vor","delay-in-days":80,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100002383","name":"King Saud University","doi-asserted-by":"publisher","award":["RSP-2020\/167"],"award-info":[{"award-number":["RSP-2020\/167"]}],"id":[{"id":"10.13039\/501100002383","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["Complexity"],"published-print":{"date-parts":[[2021,1]]},"abstract":"<jats:p>Based on a nonlinear demand function and a market\u2010clearing price, a cobweb model is introduced in this paper. A gradient mechanism that depends on the marginal profit is adopted to form the 1D discrete dynamic cobweb map. Analytical studies show that the map possesses four fixed points and only one attains the profit maximization. The stability\/instability conditions for this fixed point are calculated and numerically studied. The numerical studies provide some insights about the cobweb map and confirm that this fixed point can be destabilized due to period\u2010doubling bifurcation. The second part of the paper discusses the memory factor on the stabilization of the map\u2019s equilibrium point. A gradient mechanism that depends on the marginal profit in the past two time steps is adopted to incorporate memory in the model. Hence, a 2D discrete dynamic map is constructed. Through theoretical and numerical investigations, we show that the equilibrium point of the 2D map becomes unstable due to two types of bifurcations that are Neimark\u2013Sacker and flip bifurcations. Furthermore, the influence of the speed of adjustment parameter on the map\u2019s equilibrium is analyzed via numerical experiments.<\/jats:p>","DOI":"10.1155\/2021\/6642706","type":"journal-article","created":{"date-parts":[[2021,3,22]],"date-time":"2021-03-22T21:20:08Z","timestamp":1616448008000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Further Investigations on the Dynamics and Multistability Coexisted in a Memory\u2010Based Cobweb Model"],"prefix":"10.1155","volume":"2021","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-1167-2430","authenticated-orcid":false,"given":"S. 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