• Laura UNGUREANU Spiru Haret University, Romania


Models are better means of approximating reality, suitable for most economic phenomena which are generally represented by dynamical processes. Economic mathematicians have begun their study of this type of processes and have reached so far that today they are able to elaborate dynamical bifurcation diagrams that include all mathematical phenomena and Hopf bifurcation, in particular. In this paper, we have explained the behavior of an advertising model that consists out of a Cauchy problem made for/from a system of ordinary differential equations.

An advertising model is written in the form a Cauchy problem for a system of two first order ordinary differential equations involving two real parameters. For two particular values of them it is shown that a degenerate Bogdanov-Takens bifurcation phenomenon occurs. This implies an extremely complex behavior of the economic model for advertising.


[1] Arrowsmith, D. K., and Place, C. M. 1990. An Introduction to Dynamical Systems. Cambridge University Press.
[2] Beltrami, E. 1990. Mathematics for Dynamic Modeling. Academic Press, New York
[3] Braun, M. 1983. Differential Equations and their Applications. Third Edition, Springer, New York.
[4] Gandolfo, G. 1996. Economic dynamics, Springer, Berlin.
[5] Georgescu, A., Moroianu, M. and Oprea, I. 1999. Teoria bifurcaţiei. Piteşti University Publishing House, in Romanian.
[6] Hirsch, M. W. and Smale, S. 1996. Differential Equations, Dynamical Systems and Linear Algebra. Academic Press, New York.
[7] Kuznetsov, Y. A. 1995. Elements of applied bifurcation theory. Springer, New York.
[8] Tu, P.N.V. 1994. Dynamical Systems, Springer.
[9] Ungureanu, L. 2004. Structural Stability and Bifurcation in two Models of Economic Dynamics, Piteşti University Press, Piteşti (in Romanian).
[10] Zhang, W.B. 1990. Economic Dynamics. Springer-Verlag, Berlin.
How to Cite
UNGUREANU, Laura. A MATHEMATICAL MODEL FOR A COMPANY’S ADVERTISING STRATEGY. Theoretical and Practical Research in the Economic Fields, [S.l.], v. 2, n. 2, p. 196-204, may 2017. ISSN 2068-7710. Available at: <https://journals.aserspublishing.eu/tpref/article/view/1102>. Date accessed: 25 apr. 2019.