{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T19:41:04Z","timestamp":1760125264540,"version":"build-2065373602"},"reference-count":34,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2023,3,27]],"date-time":"2023-03-27T00:00:00Z","timestamp":1679875200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Algorithms"],"abstract":"<jats:p>Synchronization of food chain models is an intensely investigated area in dynamical systems. Two pioneering models in three species food chain systems exhibiting chaotic dynamics are the Hastings and Powell (HP) model and the Upadhyay and Rai (UR) model. These are known to synchronize, even though the top predators in the two models behave differently. In the current manuscript, we show that although the HP and UR models synchronize for certain initial conditions, they do not synchronize for arbitrarily large initial conditions due to the blow-up dynamics present in the UR model. Thus, the synchronization of these model systems is purely a local (in initial data) phenomenon. Interestingly, we find that a similar result holds for the modified UR model as well, which has global in-time solutions for any positive initial condition. Thus, the lack of synchrony could also be attributed to the difference in the top predator\u2019s feeding preferences in the model systems. Our results have large-scale applications to population synchrony in tri-trophic food chains.<\/jats:p>","DOI":"10.3390\/a16040180","type":"journal-article","created":{"date-parts":[[2023,3,27]],"date-time":"2023-03-27T03:31:48Z","timestamp":1679887908000},"page":"180","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Blow-Up Dynamics and Synchronization in Tri-Trophic Food Chain Models"],"prefix":"10.3390","volume":"16","author":[{"given":"Eric M.","family":"Takyi","sequence":"first","affiliation":[{"name":"Department of Mathematics and Computer Science, Ursinus College, Collegeville, PA 19426, USA"}]},{"given":"Rana D.","family":"Parshad","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Iowa State University, Ames, IA 50011, USA"}]},{"given":"Ranjit Kumar","family":"Upadhyay","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Computing, Indian Institute of Technology (ISM), Dhanbad 826004, India"}]},{"given":"Vikas","family":"Rai","sequence":"additional","affiliation":[{"name":"School of Computational and Integrative Sciences, Jawaharlal Nehru University, New Delhi 110067, India"}]}],"member":"1968","published-online":{"date-parts":[[2023,3,27]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"2361","DOI":"10.1142\/S0218127400001511","article-title":"Chaos and phase synchronization in ecological systems","volume":"10","author":"Blasius","year":"2000","journal-title":"Int. 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