a model of economic growth driven by competitive innovation
Open Access
Author:
Shen, Sijia
Area of Honors:
Mathematics
Degree:
Bachelor of Science
Document Type:
Thesis
Thesis Supervisors:
Alberto Bressan, Thesis Supervisor Luen Chau Li, Thesis Honors Advisor
Keywords:
economy math piazza periodic orbit ODE
Abstract:
The Piazza model is a simplied economic growth model describing the competition between a leader company and a follower company within the same sector. It is described by a system of generalized evolution equations. We split the admissible domain into four regions and in each domain, the variables evolve in time according to a system of ODEs. We examine the dynamics of the system in each domain and try to nd a periodic trajectory of the system. We nd that such an orbit cannot exist in domain one or four by examining the equilibrium points; therefore it can only switch between regime two and three. To do so, we research on the vector elds of these two ODE systems, looking for a location where the vectors of the two dynamical systems point in opposite directions. But nally we prove that in nowhere the vector elds behave so with the assigned parameters, which means, there exists no periodic trajectory of this model under the given parameters. We also give conditions that the parameters have to meet in order to allow a periodic orbit to exist.