BIFURCATION ANALYSIS IN A MODEL WITH R&D SPILLOVER AND DISTRIBUTED DELAYS
The dynamical behaviors of an R&D model with distributed delays are investigated. When the mean delay is considered as a bifurcation parameter, explicit algorithms for determining the conditions of Hopf bifurcation are derived.
distributed delay, R&D, spillover.
Received: December 15, 2021; Accepted: March 7, 2022; Published: March 10, 2022
How to cite this article: Luca Guerrini, Bifurcation analysis in a model with R&D spillover and distributed delays, Far East Journal of Applied Mathematics 113 (2022), 1-10. http://dx.doi.org/10.17654/0972096022006
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References:
[1] R. Amir and J. Wooders, Effects of one-way spillovers on market shares, industry price, welfare, and R&D cooperation, Journal of Economics 8 (1999), 223-249.[2] S. S. Askar, A. M. Alshamrani and K. Alnowibet, Dynamic Cournot duopoly games with nonlinear demand function, Appl. Math. Comput. 259 (2015), 427-437.[3] G. I. Bischi and F. Lamantia, A dynamic model of oligopoly with R&D externalities along networks, Part I, Math. Comput. Simulation 84 (2012), 51-65.[4] J. A. Brander and B. Spencer, Strategic commitment with R&D: the symmetric case, Bell Journal of Economics 14 (1983), 225-235.[5] C. D’Aspremont and A. Jacquemin, Cooperative and noncooperative R&D in duopoly with spillovers, The American Economic Review 78 (1988), 1133-1137.[6] C. D’Aspremont and A. Jacquemin, Cooperative and noncooperative R&D in duopoly with spillovers: erratum, The American Economic Review 80 (1990), 641-642.[7] M. F. Elettreby, Dynamical analysis of a Cournot duopoly model, J. Egyptian Math. Soc. 24 (2016), 681-686.[8] M. I. Kamien, E. Muller and I. Zang, Cooperative joint ventures and R&D cartels, American Economic Review 82 (1992), 1293-1306.[9] M. Katz, An analysis of cooperative research and development, Rand Journal of Economics 17 (1986), 527-543.[10] J. Ma and Z. Guo, The parameter basin and complex of dynamic game with estimation and two-stage consideration, Appl. Math. Comput. 248 (2014), 131-142. [11] J. Ma and H. Ren, The impact of variable cost on a dynamic Cournot Stackelberg game with two decision-making stages, Commun. Nonlinear Sci. Numer. Simul. 62 (2018), 184-201. [12] N. MacDonald, Time lags in biological models, Lecture Notes in Biomathematics, 27, Berlin Heidelberg New York, Springer, 1978.[13] B. A. Pansera, L. Guerrini, M. Ferrara and T. Ciano, Bifurcation analysis of a duopoly game with R&D spillover, price competition and time delays, Symmetry 12 (2020), 257-268.[14] W. J. Spencer and P. Grindley, SEMATECH after five years: high technology consortia and U.S. competitiveness, California Management Review 35 (1993), 9-32.[15] J. Zhou, W. Zhou, T. Chu, Y. X. Chang and M. J. Huang, Bifurcation, intermittent chaos and multi-stability in a two-stage Cournot game with R&D spillover and product differentiation, Appl. Math. Comput. 341 (2019), 358-378.[16] W. Zhou and X. X. Wang, On the stability and multistability in a duopoly game with R&D spillover and price competition, Discrete Dyn. Nat. Soc. 2019, Art. ID 2369898, 20 pp. https://doi.org/10.1155/2019/2369898.