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Article overview
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Complex dynamics of knowledgeable monopoly models with gradient mechanisms | Xiaoliang Li
; Jiacheng Fu
; Wei Niu
; | Date: |
4 Jan 2023 | Abstract: | In this paper, we explore the dynamics of two monopoly models with
knowledgeable players. The first model was initially introduced by Naimzada and
Ricchiuti, while the second one is simplified from a famous monopoly introduced
by Puu. We employ several tools based on symbolic computations to analyze the
local stability and bifurcations of the two models. To the best of our
knowledge, the complete stability conditions of the second model are obtained
for the first time. We also investigate periodic solutions as well as their
stability. Most importantly, we discover that the topological structure of the
parameter space of the second model is much more complex than that of the first
one. Specifically, in the first model, the parameter region for the stability
of any periodic orbit with a fixed order constitutes a connected set. In the
second model, however, the stability regions for the 3-cycle, 4-cycle, and
5-cycle orbits are disconnected sets formed by many disjoint portions.
Furthermore, we find that the basins of the two stable equilibria in the second
model are disconnected and also have complicated topological structures. In
addition, the existence of chaos in the sense of Li-Yorke is rigorously proved
by finding snapback repellers and 3-cycle orbits in the two models,
respectively. | Source: | arXiv, 2301.01497 | Services: | Forum | Review | PDF | Favorites |
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