Hopf bifurcation analysis in a modified R&D model with delay

first_pageDownload PDFsettingsOrder Article Reprints Open AccessArticle Hopf Bifurcation Analysis in a Modified R&D Model with Delay by Yang Cao 1,Ferrara Massimiliano 2,3,4,*ORCID,Gangemi Mariangela 2,4ORCID andGuerrini Luca 4,5ORCID 1 School of Cyber Science and Engineering, Southeast University, Nanjing 210096, China 2 Department of Law, Economics and Human Sciences, “Mediterranea” University of Reggio Calabria, Via dell’Università, 25, 89124 Reggio Calabria, Italy 3 ICRIOS—The Invernizzi Centre for Research in Innovation, Organization, Strategy and Entrepreneurship, Department of Management and Technology, Bocconi University, Via Sarfatti, 25, 20100 Milano, Italy 4 Decision Lab, “Mediterranea” University of Reggio Calabria, Via dell’Università, 25, 89124 Reggio Calabria, Italy 5 Department of Management, Polytechnic University of Marche, Piazzale Martelli 8, 60121 Ancona, Italy * Author to whom correspondence should be addressed. Axioms 2022, 11(4), 148; https://doi.org/10.3390/axioms11040148 Submission received: 28 November 2021 / Revised: 20 March 2022 / Accepted: 21 March 2022 / Published: 24 March 2022 (This article belongs to the Special Issue Dynamical Systems: Advances in Theory and Applications) Downloadkeyboard_arrow_down Browse Figures Versions Notes Abstract We consider a duopoly game model of R&D (research and development) rivalry between two high-tech firms with time delay, in which a monopoly sector with R&D spillover is studied using a mixture of game theory and nonlinear dynamics theory. The local asymptotic stability of the equilibrium point is studied by analyzing the corresponding characteristic equation. It is found that the delay can lead the system dynamic behavior to exhibit stability switches and Hopf bifurcations appear.