{"abstract":[{"lang":"eng","text":"In this paper, we study the emergent behaviors of the Cucker-Smale (C-S) ensemble under the interplay of memory effect and flocking dynamics. As a mathematical model incorporating aforementioned interplay, we introduce the fractional C-S model which can be obtained by replacing the usual time derivative by the Caputo fractional time derivative. For the proposed fractional C-S model, we provide a sufficient framework which admits the emergence of anomalous flocking with the algebraic decay and an l^2-stability estimate with respect to initial data. We also provide several numerical examples and compare them with our theoretical results."}],"publication_identifier":{"issn":["1553-5231"]},"type":"journal_article","language":[{"iso":"eng"}],"intvolume":"        39","page":"5465-5489","date_updated":"2024-09-24T10:24:56Z","author":[{"first_name":"Seung-Yeal","full_name":"Ha, Seung-Yeal","last_name":"Ha"},{"first_name":"Jinwook","full_name":"Jung, Jinwook","last_name":"Jung"},{"last_name":"Kuchling","orcid_put_code_url":"https://api.orcid.org/v2.0/0000-0002-8241-4076/work/168054229","full_name":"Kuchling, Peter","id":"253182","orcid":"0000-0002-8241-4076","first_name":"Peter"}],"issue":"9","publisher":"American Institute of Mathematical Sciences (AIMS)","volume":39,"doi":"10.3934/dcds.2019223","user_id":"220548","citation":{"ama":"Ha S-Y, Jung J, Kuchling P. Emergence of anomalous flocking in the fractional Cucker-Smale model. <i>Discrete &#38; Continuous Dynamical Systems</i>. 2019;39(9):5465-5489. doi:<a href=\"https://doi.org/10.3934/dcds.2019223\">10.3934/dcds.2019223</a>","mla":"Ha, Seung-Yeal, et al. “Emergence of Anomalous Flocking in the Fractional Cucker-Smale Model.” <i>Discrete &#38; Continuous Dynamical Systems</i>, vol. 39, no. 9, American Institute of Mathematical Sciences (AIMS), 2019, pp. 5465–89, doi:<a href=\"https://doi.org/10.3934/dcds.2019223\">10.3934/dcds.2019223</a>.","bibtex":"@article{Ha_Jung_Kuchling_2019, title={Emergence of anomalous flocking in the fractional Cucker-Smale model}, volume={39}, DOI={<a href=\"https://doi.org/10.3934/dcds.2019223\">10.3934/dcds.2019223</a>}, number={9}, journal={Discrete &#38; Continuous Dynamical Systems}, publisher={American Institute of Mathematical Sciences (AIMS)}, author={Ha, Seung-Yeal and Jung, Jinwook and Kuchling, Peter}, year={2019}, pages={5465–5489} }","alphadin":"<span style=\"font-variant:small-caps;\">Ha, Seung-Yeal</span> ; <span style=\"font-variant:small-caps;\">Jung, Jinwook</span> ; <span style=\"font-variant:small-caps;\">Kuchling, Peter</span>: Emergence of anomalous flocking in the fractional Cucker-Smale model. In: <i>Discrete &#38; Continuous Dynamical Systems</i> Bd. 39, American Institute of Mathematical Sciences (AIMS) (2019), Nr. 9, S. 5465–5489","short":"S.-Y. Ha, J. Jung, P. Kuchling, Discrete &#38; Continuous Dynamical Systems 39 (2019) 5465–5489.","apa":"Ha, S.-Y., Jung, J., &#38; Kuchling, P. (2019). Emergence of anomalous flocking in the fractional Cucker-Smale model. <i>Discrete &#38; Continuous Dynamical Systems</i>, <i>39</i>(9), 5465–5489. <a href=\"https://doi.org/10.3934/dcds.2019223\">https://doi.org/10.3934/dcds.2019223</a>","chicago":"Ha, Seung-Yeal, Jinwook Jung, and Peter Kuchling. “Emergence of Anomalous Flocking in the Fractional Cucker-Smale Model.” <i>Discrete &#38; Continuous Dynamical Systems</i> 39, no. 9 (2019): 5465–89. <a href=\"https://doi.org/10.3934/dcds.2019223\">https://doi.org/10.3934/dcds.2019223</a>.","ieee":"S.-Y. Ha, J. Jung, and P. Kuchling, “Emergence of anomalous flocking in the fractional Cucker-Smale model,” <i>Discrete &#38; Continuous Dynamical Systems</i>, vol. 39, no. 9, pp. 5465–5489, 2019."},"title":"Emergence of anomalous flocking in the fractional Cucker-Smale model","publication":"Discrete & Continuous Dynamical Systems","date_created":"2024-09-20T08:35:17Z","status":"public","_id":"4958","year":"2019","publication_status":"published"}