{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,21]],"date-time":"2026-01-21T12:50:51Z","timestamp":1768999851561,"version":"3.49.0"},"reference-count":53,"publisher":"MDPI AG","issue":"10","license":[{"start":{"date-parts":[[2022,9,24]],"date-time":"2022-09-24T00:00:00Z","timestamp":1663977600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Deutsche Forschungsgemeinschaft (DFG)","award":["235221301"],"award-info":[{"award-number":["235221301"]}]},{"name":"Deutsche Forschungsgemeinschaft (DFG)","award":["390685689"],"award-info":[{"award-number":["390685689"]}]},{"name":"Germany\u2019s Excellence Strategy\u2014The Berlin Mathematics Research Center MATH+","award":["235221301"],"award-info":[{"award-number":["235221301"]}]},{"name":"Germany\u2019s Excellence Strategy\u2014The Berlin Mathematics Research Center MATH+","award":["390685689"],"award-info":[{"award-number":["390685689"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>We introduce an agent-based model for co-evolving opinions and social dynamics, under the influence of multiplicative noise. In this model, every agent is characterized by a position in a social space and a continuous opinion state variable. Agents\u2019 movements are governed by the positions and opinions of other agents and similarly, the opinion dynamics are influenced by agents\u2019 spatial proximity and their opinion similarity. Using numerical simulations and formal analyses, we study this feedback loop between opinion dynamics and the mobility of agents in a social space. We investigate the behaviour of this ABM in different regimes and explore the influence of various factors on the appearance of emerging phenomena such as group formation and opinion consensus. We study the empirical distribution, and, in the limit of infinite number of agents, we derive a corresponding reduced model given by a partial differential equation (PDE). Finally, using numerical examples, we show that a resulting PDE model is a good approximation of the original ABM.<\/jats:p>","DOI":"10.3390\/e24101352","type":"journal-article","created":{"date-parts":[[2022,9,25]],"date-time":"2022-09-25T23:13:27Z","timestamp":1664147607000},"page":"1352","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":13,"title":["Feedback Loops in Opinion Dynamics of Agent-Based Models with Multiplicative Noise"],"prefix":"10.3390","volume":"24","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-8422-4930","authenticated-orcid":false,"given":"Nata\u0161a","family":"Djurdjevac Conrad","sequence":"first","affiliation":[{"name":"Zuse Institute Berlin, 14195 Berlin, Germany"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jonas","family":"K\u00f6ppl","sequence":"additional","affiliation":[{"name":"Zuse Institute Berlin, 14195 Berlin, Germany"},{"name":"Weierstrass Institute for Applied Analysis and Stochastics, 10117 Berlin, Germany"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8122-7164","authenticated-orcid":false,"given":"Ana","family":"Djurdjevac","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Computer Science, Freie Universit\u00e4t Berlin, 14195 Berlin, Germany"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2022,9,24]]},"reference":[{"key":"ref_1","unstructured":"Lewandowsky, S., Smillie, L., Garcia, D., Hertwig, R., Weatherall, J., Egidy, S., Robertson, R.E., O\u2019Connor, C., Kozyreva, A., and Lorenz-Spreen, P. 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