Some explicit equations for estimating the stability and direction of Hopf bifurcation periodic solutions for the model proposed by Cao et al. [2] are derived based on using normal form theory and center manifold theory.

center manifold, R&D, time delay.

Received: December 15, 2021; Accepted: February 16, 2022; Published: February 23, 2022

How to cite this article: Luca Guerrini, Center manifold analysis of a delayed model with R&D spillovers, Far East Journal of Dynamical Systems 34 (2022), 1-9. http://dx.doi.org/10.17654/0972111822001

This Open Access Article is Licensed under Creative Commons Attribution 4.0 International License

References:

[1] A. C. d’Aspremont and A. Jacquemin, Cooperative and noncooperative R&D in duopoly with spillovers, The American Economic Review 78 (1988), 1133-1137.
[2] Y. Cao, R. Colucci and L. Guerrini, On the stability analysis of a delayed two-stage Cournot model with R&D spillovers, Math. Comput. Simulation (2021) (in press). https://doi.org/10.1016/j.matcom.2021.03.007
[3] C. Fershtman and N. Gandal, Disadvantageous semicollusion, International Journal of Industrial Organization 12 (1994), 141-154.
[4] L. Gori, L. Guerrini and M. Sodini, Different modelling approaches for time lags in a monopoly, Essays in Economic Dynamics: Theory, Simulation Analysis, and Methodological Study, A. Matsumoto, F. Szidarovszky and T. Asada, eds., Springer, Singapore, 2016.
[5] N. D. Hassard, Y. H. Kazarinoff and Y. H. Wan, Theory and applications of Hopf bifurcation, London Math. Soc. Lecture Notes, Vol. 41, Cambridge University Press, Cambridge, 1981.
[6] M. I. Kamien, E. Muller and I. Zang, Cooperative joint ventures and R&D cartels, American Economic Review 82 (1992), 1293-1306.
[7] M. I. Kamien and I. Zang, Meet me halfway: research joint ventures and absorptive capacity, International Journal of Industrial Organization 18 (2000), 995-1012.
[8] L. Qiu, On the dynamic efficiency of Bertrand and Cournot equilibria, J. Econom. Theory 75 (1997), 213-229.
[9] Y. Zhang, W. Zhou, T. Chu, Y. Chu and J. Yu, Complex dynamics analysis for a two-stage Cournot duopoly game of semi-collusion in production, Nonlinear Dynamics 91 (2018), 819-835.