{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,13]],"date-time":"2026-02-13T11:11:10Z","timestamp":1770981070436,"version":"3.50.1"},"reference-count":37,"publisher":"Wiley","issue":"1","license":[{"start":{"date-parts":[[2021,3,9]],"date-time":"2021-03-09T00:00:00Z","timestamp":1615248000000},"content-version":"vor","delay-in-days":67,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":["onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["Complexity"],"published-print":{"date-parts":[[2021,1]]},"abstract":"<jats:p>This paper presents the nonlinear dynamic analysis of energy\u2010based models arisen from the applied systems characterized by the energy transport in the presence of fractional order derivative and time delay. The studied model is the fractional version of Bianca\u2010Ferrara\u2010Dalgaard\u2010Strulik (BFDS) model of economy which is viewed as a transport network for energy in which the law of motion of capital occurs. By considering the time delay as bifurcation parameter, a proof to investigate the existence of Hopf bifurcation and the phase lock solutions using the Poincare\u2010Linstedt and the harmonic balance methods is given. At definite values of time delay, period\u2010doubling bifurcations followed up by the consequences of chaotic states are detected. Simulation results assure that the BFDS model can generate new (hyper) chaotic attractors beyond half order derivatives through the effect of the time delay on that system. In accordance with the literatures related to the problem of chaos, the concluded results confirm the proposed theorem by El\u2010Borhamy in which the time delay possesses the ability to change the dynamic state of nonlinear systems from regular to chaotic within the fractional order derivative domain.<\/jats:p>","DOI":"10.1155\/2021\/8751963","type":"journal-article","created":{"date-parts":[[2021,3,9]],"date-time":"2021-03-09T18:50:06Z","timestamp":1615315806000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Chaos Prediction in Fractional Delayed Energy\u2010Based Models of Capital Accumulation"],"prefix":"10.1155","volume":"2021","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-4557-0248","authenticated-orcid":false,"given":"Mohamed","family":"El-Borhamy","sequence":"first","affiliation":[]},{"given":"Tamer","family":"Medhat","sequence":"additional","affiliation":[]},{"given":"Manal E.","family":"Ali","sequence":"additional","affiliation":[]}],"member":"311","published-online":{"date-parts":[[2021,3,9]]},"reference":[{"key":"e_1_2_12_1_2","volume-title":"An Introduction to the Fractional Calculus and Fractional Differential Equations","author":"Miller K. 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