{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,12]],"date-time":"2025-11-12T14:21:38Z","timestamp":1762957298542,"version":"build-2065373602"},"reference-count":35,"publisher":"MDPI AG","issue":"11","license":[{"start":{"date-parts":[[2023,11,17]],"date-time":"2023-11-17T00:00:00Z","timestamp":1700179200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"National Social Fund","award":["22&ZD122","71871115","22GLB032","22YJC790128","BR2022057","22SYA-010","2022SJYB0215"],"award-info":[{"award-number":["22&ZD122","71871115","22GLB032","22YJC790128","BR2022057","22SYA-010","2022SJYB0215"]}]},{"name":"National Natural Science Foundation of China","award":["22&ZD122","71871115","22GLB032","22YJC790128","BR2022057","22SYA-010","2022SJYB0215"],"award-info":[{"award-number":["22&ZD122","71871115","22GLB032","22YJC790128","BR2022057","22SYA-010","2022SJYB0215"]}]},{"name":"General Project of the Social Science Foundation of Jiangsu Province","award":["22&ZD122","71871115","22GLB032","22YJC790128","BR2022057","22SYA-010","2022SJYB0215"],"award-info":[{"award-number":["22&ZD122","71871115","22GLB032","22YJC790128","BR2022057","22SYA-010","2022SJYB0215"]}]},{"name":"Humanities and Social Science Planning Foundation of the Ministry of Education of China","award":["22&ZD122","71871115","22GLB032","22YJC790128","BR2022057","22SYA-010","2022SJYB0215"],"award-info":[{"award-number":["22&ZD122","71871115","22GLB032","22YJC790128","BR2022057","22SYA-010","2022SJYB0215"]}]},{"name":"Soft Science Research Program General Project of Jiangsu Province","award":["22&ZD122","71871115","22GLB032","22YJC790128","BR2022057","22SYA-010","2022SJYB0215"],"award-info":[{"award-number":["22&ZD122","71871115","22GLB032","22YJC790128","BR2022057","22SYA-010","2022SJYB0215"]}]},{"name":"Key Supporting Project of the Social Science Application Research Excellent Program of Jiangsu Province","award":["22&ZD122","71871115","22GLB032","22YJC790128","BR2022057","22SYA-010","2022SJYB0215"],"award-info":[{"award-number":["22&ZD122","71871115","22GLB032","22YJC790128","BR2022057","22SYA-010","2022SJYB0215"]}]},{"name":"General Project of Philosophy and Social Science Research in Colleges and Universities of Jiangsu Province","award":["22&ZD122","71871115","22GLB032","22YJC790128","BR2022057","22SYA-010","2022SJYB0215"],"award-info":[{"award-number":["22&ZD122","71871115","22GLB032","22YJC790128","BR2022057","22SYA-010","2022SJYB0215"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>The innovation of private enterprises plays a crucial role. This study focuses on the impacts of market information asymmetry, the technology spillover effect, and the order of innovation research and development (R&amp;D) decisions on the evolution of private enterprises\u2019 innovation. This study constructs a dynamic model to analyze how the innovation decision-making order of private enterprises influences their profits and intertemporal innovation decision making. First, we derive the equilibrium point under sequential decisions and the stability of the system at the equilibrium point. Second, we investigate the impact of sequential and simultaneous innovation decisions on the evolution of the dynamic system and its economic implications. Finally, we study the evolutionary dynamics of the attractor with the rate of innovation adjustment and point to the existence of multiple equilibria. The results suggest that the speed of the innovation R&amp;D cost change should be moderate, and the asynchronous updating of the innovation R&amp;D strategy can prevent the system evolution from turning into chaos. These conclusions guide innovation policies.<\/jats:p>","DOI":"10.3390\/e25111553","type":"journal-article","created":{"date-parts":[[2023,11,17]],"date-time":"2023-11-17T09:10:38Z","timestamp":1700212238000},"page":"1553","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Evolution Dynamics Model of Private Enterprises under Simultaneous and Sequential Innovation Decisions"],"prefix":"10.3390","volume":"25","author":[{"given":"Chi","family":"Zhang","sequence":"first","affiliation":[{"name":"School of Economics and Management, Nanjing Tech University, Nanjing 211816, China"}]},{"given":"Yutong","family":"Wang","sequence":"additional","affiliation":[{"name":"School of Economics and Management, Nanjing Tech University, Nanjing 211816, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3013-243X","authenticated-orcid":false,"given":"Tingqiang","family":"Chen","sequence":"additional","affiliation":[{"name":"School of Economics and Management, Nanjing Tech University, Nanjing 211816, China"}]}],"member":"1968","published-online":{"date-parts":[[2023,11,17]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"65","DOI":"10.2307\/1884513","article-title":"A Contribution to the Theory of Economic Growth","volume":"70","author":"Solow","year":"1956","journal-title":"Q. 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