{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,18]],"date-time":"2025-12-18T20:04:02Z","timestamp":1766088242635,"version":"3.40.5"},"reference-count":28,"publisher":"Wiley","license":[{"start":{"date-parts":[[2024,2,28]],"date-time":"2024-02-28T00:00:00Z","timestamp":1709078400000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Research Initiation Foundation Project of Yiwu Industrial & Commercial College","award":["RCKY202309"],"award-info":[{"award-number":["RCKY202309"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Complexity"],"published-print":{"date-parts":[[2024,2,28]]},"abstract":"<jats:p>This study aims to investigate the research and development (R&amp;D) competition within the supply chain, focusing on two aspects: R&amp;D competition at the manufacturing level and competition in pricing strategies. This paper establishes a dynamic game model of R&amp;D competition, comprising two manufacturers and two retailers, with both manufacturers exhibiting bounded rationality. The key findings are as follows: (1) an increase in the adjustment speed positively affects the chaotic nature of the R&amp;D competition system, leading to a state of disorder. This chaotic state has adverse implications for manufacturing profitability. (2) The spillover effect exhibits a positive relationship with the level of chaos in the R&amp;D competition system. A greater spillover effect contributes to a more turbulent environment, which subsequently impacts the profitability of manufacturers. (3) R&amp;D cost parameters exert a positive influence on the stability of the R&amp;D competition system. When the system reaches a state of equilibrium, an escalation in the R&amp;D cost parameters poses a threat to manufacturer profitability. (4) Retailer costs play a detrimental role in the stability of the R&amp;D competition system. As retailer costs increase, there is a decline in R&amp;D levels, thereby diminishing manufacturer profitability. (5) To mitigate the chaotic state, we propose the implementation of the time-delayed feedback control (TDFC) method, which reflects a more stable state in the R&amp;D competition system.<\/jats:p>","DOI":"10.1155\/2024\/3152363","type":"journal-article","created":{"date-parts":[[2024,2,28]],"date-time":"2024-02-28T21:05:05Z","timestamp":1709154305000},"page":"1-15","source":"Crossref","is-referenced-by-count":1,"title":["The Complexities in the R&amp;D Competition Model with Spillover Effects in the Supply Chain"],"prefix":"10.1155","volume":"2024","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-3633-4913","authenticated-orcid":true,"given":"Jianli","family":"Xiao","sequence":"first","affiliation":[{"name":"School of Economics and Management, Yiwu Industrial & Commercial College, Yiwu 322000, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1314-0144","authenticated-orcid":true,"given":"Hanli","family":"Xiao","sequence":"additional","affiliation":[{"name":"School of Tourism and Resources Environment, Qiannan Normal University for Nationalities, Duyun 55900, China"}]}],"member":"311","reference":[{"issue":"4","key":"1","doi-asserted-by":"crossref","first-page":"599","DOI":"10.1111\/poms.12037","article-title":"Firms\u2019 R&D cooperation behavior in a supply chain","volume":"23","author":"Z. 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