Far East Journal of Dynamical Systems

The Far East Journal of Dynamical Systems publishes original research papers and survey articles in all aspects of dynamical systems, including chaos, fractals, and ergodic theory. It encourages application-oriented research in physics, life sciences, and social sciences.

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CENTER MANIFOLD ANALYSIS OF A DELAYED MODEL WITH R&D SPILLOVERS

Authors

  • Luca Guerrini

Keywords:

center manifold, R&D, time delay.

DOI:

https://doi.org/10.17654/0972111822001

Abstract

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.

Received: December 15, 2021 
Accepted: February 16, 2022

References

A. C. d’Aspremont and A. Jacquemin, Cooperative and noncooperative R&D in duopoly with spillovers, The American Economic Review 78 (1988), 1133-1137.

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

C. Fershtman and N. Gandal, Disadvantageous semicollusion, International Journal of Industrial Organization 12 (1994), 141-154.

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.

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.

M. I. Kamien, E. Muller and I. Zang, Cooperative joint ventures and R&D cartels, American Economic Review 82 (1992), 1293-1306.

M. I. Kamien and I. Zang, Meet me halfway: research joint ventures and absorptive capacity, International Journal of Industrial Organization 18 (2000), 995-1012.

L. Qiu, On the dynamic efficiency of Bertrand and Cournot equilibria, J. Econom. Theory 75 (1997), 213-229.

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.

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Published

2022-02-23

Issue

Vol. 34 (2022)

Section

Articles

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How to Cite

CENTER MANIFOLD ANALYSIS OF A DELAYED MODEL WITH R&D SPILLOVERS. (2022). Far East Journal of Dynamical Systems, 34, 1-9. https://doi.org/10.17654/0972111822001