{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T13:27:00Z","timestamp":1753882020982,"version":"3.41.2"},"reference-count":36,"publisher":"World Scientific Pub Co Pte Ltd","issue":"02","funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["12162032"],"award-info":[{"award-number":["12162032"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["12062027"],"award-info":[{"award-number":["12062027"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Cross-integration Innovation team of modern Applied Mathematics and Life Sciences in Yunnan Province","award":["202405AS350003"],"award-info":[{"award-number":["202405AS350003"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. Bioinform. Comput. Biol."],"published-print":{"date-parts":[[2025,4]]},"abstract":"<jats:p> Bacillus subtilis (B.\u00a0subtilis), a bacterium known to enter a competent state spontaneously, has garnered significant attention due to its intricate internal regulatory mechanisms. This study proposes a six-dimensional continuous delay differential equation (DDE) model incorporating two-time delays and a stochastic model that accounts for noise, aimed at delving deeper into the dynamic behaviors of the B.\u00a0subtilis competence gene regulation circuit. Our investigation reveals that time delays play a crucial role in inducing oscillatory behavior within the continuous DDE model. Analyzing the dynamics of multiple time delays proves to be more intricate than studying a single delay. Furthermore, certain parameter adjustments significantly influence the system\u2019s dynamic characteristics. The introduction of noise also triggers oscillations, with the irregular oscillation patterns closely aligning with real-world observations. Intriguingly, the effects of parameters and noise regulation undergo significant changes when time delays are jointly considered. This analysis offers a fresh perspective on understanding B.\u00a0subtilis competence and provides essential theoretical support for subsequent experimental endeavors in this domain of biomathematics. <\/jats:p>","DOI":"10.1142\/s0219720025500052","type":"journal-article","created":{"date-parts":[[2025,5,9]],"date-time":"2025-05-09T09:24:42Z","timestamp":1746782682000},"source":"Crossref","is-referenced-by-count":0,"title":["Computational modeling and dynamical analysis for B.\u00a0subtilis competence genic regulation circuit with multiple time delays and external noisy regulation"],"prefix":"10.1142","volume":"23","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-7775-1599","authenticated-orcid":false,"given":"Na","family":"Zhao","sequence":"first","affiliation":[{"name":"Department of Mathematics, South China University of Technology, Guangzhou 510641, P. R. China"},{"name":"Department of Mathematics, Yunnan Normal University, Kunming 650500, P. R. 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