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Mathematics
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Mathematical Methods on Economic Dynamics
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Mathematical Methods on Economic Dynamics

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "Dynamical Systems".

Deadline for manuscript submissions: closed (30 November 2021) | Viewed by 12882

Special Issue Editor

Prof. Dr. Jose Cánovas

E-Mail Website
Guest Editor
Department of Applied Mathematics and Statisitcs, Technical University of Cartagena, Cartagena, Spain
Interests: dynamical systems; time series and signal analysis; economic dynamics

Special Issue Information

Dear Colleagues,

In recent decades, there has been substantial development in the application of mathematics in natural and social sciences. On one hand, there are a large number of models that require knowledge of new mathematical techniques to be analyzed. On the other hand, developing new mathematical techniques has become necessary to handle models that exhibit complex behavior. Economics is a branch of knowledge for which mathematical methods play a very important role. From purely deterministic models, for example, oligopoly models, to real-time analysis of financial time series, mathematics provides tools for a better understanding of the economic phenomena. This Special Issue is devoted to papers on economic models for which mathematics plays an important role. New mathematical techniques for analyzing economic processes, as well as the analysis of economic models requiring deep mathematical tools are especially welcome. A non-exhaustive list of topics includes economic growth, oligopoly dynamics, evolutionary game theory, and time series analysis, etcetera.

Prof. Dr. Jose Cánovas
Guest Editor

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Mathematics is an international peer-reviewed open access semimonthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2600 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • existence and stability conditions of equilibrium
  • dynamic analysis
  • computational techniques
  • cooperative and noncooperative games
  • stochastic and dynamic games
  • time-series models

Published Papers (7 papers)

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Research

15 pages, 993 KiB  
Article
Monopolistic Dynamics with Endogenous Product Differentiation
by Andrea Caravaggio, Luca Gori and Mauro Sodini
Mathematics 2022, 10(3), 302; https://0-doi-org.brum.beds.ac.uk/10.3390/math10030302 - 19 Jan 2022
Viewed by 1402
Abstract
This research considers the problem of a price-discriminating monopolist aiming at choosing output and investing in product differentiation to foster consumers perceiving products as being heterogeneous in different market segments. It then introduces bounded rationality and concentrates on the dynamic analysis showing the [...] Read more.
This research considers the problem of a price-discriminating monopolist aiming at choosing output and investing in product differentiation to foster consumers perceiving products as being heterogeneous in different market segments. It then introduces bounded rationality and concentrates on the dynamic analysis showing the existence of several dynamic phenomena caused by the interaction between endogenous product differentiation and gradient dynamics. Though product differentiation can generally increase market power and profits, in this context it can generate a lack of coordination between the managers working in each segment. Full article
(This article belongs to the Special Issue Mathematical Methods on Economic Dynamics)
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21 pages, 359 KiB  
Article
Statistical Tests of Symbolic Dynamics
by Fernando López, Mariano Matilla-García, Jesús Mur and Manuel Ruiz Marín
Mathematics 2021, 9(8), 817; https://0-doi-org.brum.beds.ac.uk/10.3390/math9080817 - 09 Apr 2021
Cited by 1 | Viewed by 1304
Abstract
A novel general method for constructing nonparametric hypotheses tests based on the field of symbolic analysis is introduced in this paper. Several existing tests based on symbolic entropy that have been used for testing central hypotheses in several branches of science (particularly in [...] Read more.
A novel general method for constructing nonparametric hypotheses tests based on the field of symbolic analysis is introduced in this paper. Several existing tests based on symbolic entropy that have been used for testing central hypotheses in several branches of science (particularly in economics and statistics) are particular cases of this general approach. This family of symbolic tests uses few assumptions, which increases the general applicability of any symbolic-based test. Additionally, as a theoretical application of this method, we construct and put forward four new statistics to test for the null hypothesis of spatiotemporal independence. There are very few tests in the specialized literature in this regard. The new tests were evaluated with the mean of several Monte Carlo experiments. The results highlight the outstanding performance of the proposed test. Full article
(This article belongs to the Special Issue Mathematical Methods on Economic Dynamics)
33 pages, 1474 KiB  
Article
A Full Description of ω-Limit Sets of Cournot Maps Having Non-Empty Interior and Some Economic Applications
by Antonio Linero-Bas and María Muñoz-Guillermo
Mathematics 2021, 9(4), 452; https://0-doi-org.brum.beds.ac.uk/10.3390/math9040452 - 23 Feb 2021
Cited by 1 | Viewed by 1560
Abstract
Given a continuous Cournot map F(x,y)=(f2(y),f1(x)) defined from I2=[0,1]×[0,1] into itself, [...] Read more.
Given a continuous Cournot map F(x,y)=(f2(y),f1(x)) defined from I2=[0,1]×[0,1] into itself, we give a full description of its ω-limit sets with non-empty interior. Additionally, we present some partial results for the empty interior case. The distribution of the ω-limits with non-empty interior gives information about the dynamics and the possible outputs of each firm in a Cournot model. We present some economic models to illustrate, with examples, the type of ω-limits that appear. Full article
(This article belongs to the Special Issue Mathematical Methods on Economic Dynamics)
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36 pages, 1270 KiB  
Article
About the Structure of Attractors for a Nonlocal Chafee-Infante Problem
by Rubén Caballero, Alexandre N. Carvalho, Pedro Marín-Rubio and José Valero
Mathematics 2021, 9(4), 353; https://0-doi-org.brum.beds.ac.uk/10.3390/math9040353 - 10 Feb 2021
Cited by 5 | Viewed by 1705
Abstract
In this paper, we study the structure of the global attractor for the multivalued semiflow generated by a nonlocal reaction-diffusion equation in which we cannot guarantee the uniqueness of the Cauchy problem. First, we analyse the existence and properties of stationary points, showing [...] Read more.
In this paper, we study the structure of the global attractor for the multivalued semiflow generated by a nonlocal reaction-diffusion equation in which we cannot guarantee the uniqueness of the Cauchy problem. First, we analyse the existence and properties of stationary points, showing that the problem undergoes the same cascade of bifurcations as in the Chafee-Infante equation. Second, we study the stability of the fixed points and establish that the semiflow is a dynamic gradient. We prove that the attractor consists of the stationary points and their heteroclinic connections and analyse some of the possible connections. Full article
(This article belongs to the Special Issue Mathematical Methods on Economic Dynamics)
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27 pages, 436 KiB  
Article
On a Retarded Nonlocal Ordinary Differential System with Discrete Diffusion Modeling Life Tables
by Francisco Morillas and José Valero
Mathematics 2021, 9(3), 220; https://0-doi-org.brum.beds.ac.uk/10.3390/math9030220 - 22 Jan 2021
Cited by 1 | Viewed by 1666
Abstract
In this paper, we consider a system of ordinary differential equations with non-local discrete diffusion and finite delay and with either a finite or an infinite number of equations. We prove several properties of solutions such as comparison, stability and symmetry. We create [...] Read more.
In this paper, we consider a system of ordinary differential equations with non-local discrete diffusion and finite delay and with either a finite or an infinite number of equations. We prove several properties of solutions such as comparison, stability and symmetry. We create a numerical simulation showing that this model can be appropriate to model dynamical life tables in actuarial or demographic sciences. In this way, some indicators of goodness and smoothness are improved when comparing with classical techniques. Full article
(This article belongs to the Special Issue Mathematical Methods on Economic Dynamics)
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19 pages, 1283 KiB  
Article
Delay Cournot Duopoly Game with Gradient Adjustment: Berezowski Transition from a Discrete Model to a Continuous Model
by Akio Matsumoto, Ferenc Szidarovszky and Keiko Nakayama
Mathematics 2021, 9(1), 32; https://0-doi-org.brum.beds.ac.uk/10.3390/math9010032 - 24 Dec 2020
Cited by 3 | Viewed by 2002
Abstract
This paper investigates the asymptotical behavior of the equilibrium of linear classical duopolies by reconsidering the two-delay model with two different positive delays. In a two-dimensional analysis, the stability switching curves were first analytically determined. Numerical studies verified and illustrated the theoretical results. [...] Read more.
This paper investigates the asymptotical behavior of the equilibrium of linear classical duopolies by reconsidering the two-delay model with two different positive delays. In a two-dimensional analysis, the stability switching curves were first analytically determined. Numerical studies verified and illustrated the theoretical results. In the sensitivity analysis it was demonstrated that the inertia coefficient has a twofold effect: enlarges the stability region as well as simplifies the complicated dynamics with period-halving cascade. In contrary, the adjustment speed contracts the stability region and complicates simple dynamics with period-doubling bifurcation. In addition, for various values of τ1 and τ2, a wide variety of dynamics appears ranging from simple cycle via a Hopf bifurcation to chaotic oscillations. Full article
(This article belongs to the Special Issue Mathematical Methods on Economic Dynamics)
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13 pages, 6971 KiB  
Article
Chaos Control and Anti-Control of the Heterogeneous Cournot Oligopoly Model
by Marek Lampart and Alžběta Lampartová
Mathematics 2020, 8(10), 1670; https://0-doi-org.brum.beds.ac.uk/10.3390/math8101670 - 28 Sep 2020
Cited by 7 | Viewed by 2364
Abstract
The main aim of this paper focuses on chaos suppression (control) and stimulation (anti-control) of a heterogeneous Cournot oligopoly model. This goal is reached by applying the theory of dynamical systems, namely impulsive control. The main aim was to demonstrate, through massive numerical [...] Read more.
The main aim of this paper focuses on chaos suppression (control) and stimulation (anti-control) of a heterogeneous Cournot oligopoly model. This goal is reached by applying the theory of dynamical systems, namely impulsive control. The main aim was to demonstrate, through massive numerical simulations and estimation of the maximal Lyapunov exponent, the 0-1test for chaos, and bifurcation analysis, that it is possible to control the dynamical behavior of the investigated model by finding injection values under which the desired phenomena are attained. Moreover, it was shown that there are injection values for which the injected system admits a self-excited cycle or chaotic trajectory. Full article
(This article belongs to the Special Issue Mathematical Methods on Economic Dynamics)
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