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Mathematics
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Mathematical Modeling: From Nonlinear Dynamics to Complex Systems
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Mathematical Modeling: From Nonlinear Dynamics to Complex Systems

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

Deadline for manuscript submissions: closed (30 November 2019) | Viewed by 22700

Special Issue Editors

Prof. Dr. Luigi Fortuna

E-Mail Website
Guest Editor
Dipartimento di Ingegneria Elettrica Elettronica e Informatica, Universita degli Studi di Catania, Viale A. Doria 6, 95125 Catania, Italy
Interests: non-linear dynamical systems; automatic control; autonomous system control; non-linear electronic circuits and devices
Special Issues, Collections and Topics in MDPI journals
Dr. Claudia Corradino

E-Mail Website
Guest Editor
University of Maryland University Collage, College Park, MD 20742, USA
Interests: nonlinear dynamics; nuclear fusion technology

Special Issue Information

Dear Colleagues,

This Special Issue is focused on advanced nonlinear dynamical systems, both in theory and application. Particular emphasis will be given to the control of electronic nonlinear circuits and devices. Moreover, this issue is addressed to the study of distributed systems like electrical networks and complex systems. Therefore, the essential aim of this Special Issue is to encourage authors to integrate contributions, from local behaviors to global behaviors. Papers taking into account big data to build models are welcome, as are experimental papers. Advanced ideas with preliminary results should also be presented to stimulate future wide audience studies.

Mathematical modeling should be stressed and numerical methods are also well accepted.

Topics of the Special Issue are:

-nonlinear devices control techniques;

-bifurcation analysis of strong nonlinear systems;

-nonlinear electronic circuits;

-identification from experimental data of dynamics systems;

-complex networks;

-power grid;

-networks from local unit to global behavior;

-cellular nonlinear networks from nano scale to tera node numbers;

-networks of reservoir memory;

-memristors based networks.

Prof. Dr. Luigi Fortuna
Dr. Claudia Corradino
Guest Editors

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.

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Further information on MDPI's Special Issue polices can be found here.

Published Papers (5 papers)

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33 pages, 11857 KiB  
Article
Modeling of the Public Opinion Polarization Process with the Considerations of Individual Heterogeneity and Dynamic Conformity
by Tinggui Chen, Qianqian Li, Jianjun Yang, Guodong Cong and Gongfa Li
Mathematics 2019, 7(10), 917; https://doi.org/10.3390/math7100917 - 2 Oct 2019
Cited by 47 | Viewed by 5722
Abstract
Nowadays, hot issues are likely become bipolar or multipolar after heated discussion on the Internet. This article is focused on the study of the polarization phenomenon and establishes a public opinion polarization model with the considerations of individual heterogeneity and dynamic conformity. At [...] Read more.
Nowadays, hot issues are likely become bipolar or multipolar after heated discussion on the Internet. This article is focused on the study of the polarization phenomenon and establishes a public opinion polarization model with the considerations of individual heterogeneity and dynamic conformity. At first, this article introduces the dynamic changing function of an individual’s conformity tendency to other’s attitudes in the interaction process. It further defines the influential weight between different interactive individuals, and expands the interactive individual from complete homogeneity to initial attitude heterogeneity, and finally, conformity heterogeneity. Then, through simulation experiments, we find that the degree of changing in individual attitude is limited. That is, it is difficult for the individuals who have one directional attitude at the initial time to change into another opposite attitude through interaction. In addition, individuals with low conformity within a certain threshold are more likely to form polarization. Finally, the rationality and effectiveness of the proposed model are verified by the typical case “Mimeng Event”. Full article
(This article belongs to the Special Issue Mathematical Modeling: From Nonlinear Dynamics to Complex Systems)
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34 pages, 18308 KiB  
Article
Modeling and Control of IPMC Actuators Based on LSSVM-NARX Paradigm
by Liangsong Huang, Yu Hu, Yun Zhao and Yuxia Li
Mathematics 2019, 7(8), 741; https://doi.org/10.3390/math7080741 - 13 Aug 2019
Cited by 12 | Viewed by 3612
Abstract
Ionic polymer-metal composites are electrically driven intelligent composites that are readily exposed to bending deformations in the presence of external electric fields. Owing to their advantages, ionicpolymer-metal composites are promising candidates for actuators. However, ionicpolymer-metal composites exhibit strong nonlinear properties, especially hysteresis characteristics, [...] Read more.
Ionic polymer-metal composites are electrically driven intelligent composites that are readily exposed to bending deformations in the presence of external electric fields. Owing to their advantages, ionicpolymer-metal composites are promising candidates for actuators. However, ionicpolymer-metal composites exhibit strong nonlinear properties, especially hysteresis characteristics, resulting in severely reduced control accuracy. This study proposes an ionic polymer-metal composite platform and investigates its modeling and control. First, the hysteresis characteristics of the proposed Pt-electrode ionic polymer-metal composite are tested. Based on the hysteresis characteristics, ionic polymer-metal composites are modeled using the Prandtl-Ishlinskii model and the least squares support vector machine-nonlinear autoregressive model, respectively. Then, the ionic polymer-metal composite is driven by a random sinusoidal voltage, and the LSSVM-NARX model is established on the basis of the displacement data obtained. In addition, an artificial bee colony algorithm is proposed for accuracy optimization of the model parameters. Finally, an inverse controller based on the least squares support vector machine-nonlinear autoregressive model is proposed to compensate the hysteresis characteristics of the ionic polymer-metal composite. A hybrid PID feedback controller is developed by combining the inverse controller with PID feedback control, followed by simulation and testing of its actual position control on the ionic polymer-metal composite platform. The results show that the hybrid PID feedback control system can effectively eliminate the effects of the hysteresis characteristics on ionic polymer-metal composite control. Full article
(This article belongs to the Special Issue Mathematical Modeling: From Nonlinear Dynamics to Complex Systems)
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13 pages, 279 KiB  
Article
Spatially Distributed Differential Game Theoretic Model of Fisheries
by Guennady Ougolnitsky and Anatoly Usov
Mathematics 2019, 7(8), 732; https://doi.org/10.3390/math7080732 - 11 Aug 2019
Cited by 4 | Viewed by 2285
Abstract
We consider a differential game of fisheries in a fan-like control structure of the type “supervisor—several agents”. The dynamics of the controlled system is described by a non-linear differential equation model which is identified on the Azov Sea data. An averaging by two [...] Read more.
We consider a differential game of fisheries in a fan-like control structure of the type “supervisor—several agents”. The dynamics of the controlled system is described by a non-linear differential equation model which is identified on the Azov Sea data. An averaging by two spatial coordinates is conducted. Different information structures of the game are generated by the control methods of compulsion (supervisor restricts the feasible strategies of agents) and impulsion (she exerts an impact to their payoff functionals). Both Stackerlberg and inverse Stackelberg games are considered. For the numerical investigation we use a discretization of the initial model and the method of qualitatively representative scenarios in simulation modeling. Full article
(This article belongs to the Special Issue Mathematical Modeling: From Nonlinear Dynamics to Complex Systems)
16 pages, 1196 KiB  
Article
Credit Risk Contagion and Systemic Risk on Networks
by Marina Dolfin, Damian Knopoff, Michele Limosani and Maria Gabriella Xibilia
Mathematics 2019, 7(8), 713; https://doi.org/10.3390/math7080713 - 7 Aug 2019
Cited by 14 | Viewed by 4733
Abstract
This paper proposes a model of the dynamics of credit contagion through non-performing loans on financial networks. Credit risk contagion is modeled in the context of the classical SIS (Susceptibles-Infected-Susceptibles) epidemic processes on networks but with a fundamental novelty. In fact, we assume [...] Read more.
This paper proposes a model of the dynamics of credit contagion through non-performing loans on financial networks. Credit risk contagion is modeled in the context of the classical SIS (Susceptibles-Infected-Susceptibles) epidemic processes on networks but with a fundamental novelty. In fact, we assume the presence of two different classes of infected agents, and then we differentiate the dynamics of assets subject to idiosyncratic risk from those affected by systemic risk by adopting a SIIS (Susceptible-Infected1-Infected2-Susceptible) model. In the recent literature in this field, the effect of systemic credit risk on the performance of the financial network is a hot topic. We perform numerical simulations intended to explore the roles played by two different network structures on the long-term behavior of assets affected by systemic risk in order to analyze the effect of the topology of the underlying network structure on the spreading of systemic risk on the structure. Random graphs, i.e., the Erdös–Rényi model, are considered “benchmark” network structures while core-periphery structures are often indicated in the literature as idealized structures, although they are able to capture interesting, specific features of real-world financial networks. Moreover, as a matter of comparison, we also perform numerical experiments on small-world networks. Full article
(This article belongs to the Special Issue Mathematical Modeling: From Nonlinear Dynamics to Complex Systems)
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13 pages, 871 KiB  
Article
An Empirical Test on Harrod’s Open Economy Dynamics
by Giuseppe Orlando and Fabio Della Rossa
Mathematics 2019, 7(6), 524; https://doi.org/10.3390/math7060524 - 8 Jun 2019
Cited by 7 | Viewed by 5457
Abstract
This paper has the objective to empirically test Harrod’s explanations of economic dynamics addressing both growth and business cycles. In particular we test Harrod’s speculation that opening the economy to foreign trade could lead to a reduction of cyclical instability. The main variables [...] Read more.
This paper has the objective to empirically test Harrod’s explanations of economic dynamics addressing both growth and business cycles. In particular we test Harrod’s speculation that opening the economy to foreign trade could lead to a reduction of cyclical instability. The main variables determining the dynamic behaviour are wealth, savings, competitiveness and, therefore, balance of trade. The behaviour of the model under scrutiny is highly non-linear and the conclusion is that stable cycles are possible only under particular conditions. In fact, this empirical test shows a stable long-run pattern for those specific parameters. Full article
(This article belongs to the Special Issue Mathematical Modeling: From Nonlinear Dynamics to Complex Systems)
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