Advances in Dynamical Systems and Control

A special issue of Axioms (ISSN 2075-1680). This special issue belongs to the section "Mathematical Analysis".

Deadline for manuscript submissions: 20 July 2024 | Viewed by 5602

Special Issue Editors


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Instituto Tecnológico de Tijuana—Tecnológico Nacional de México, Tijuana 22414, Mexico
Interests: mathematical and computational modeling; fuzzy differential equations; fuzzy systems; robotics; nonlinear control; genetic algorithms and applications
Special Issues, Collections and Topics in MDPI journals

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Guest Editor
Centre for Computational and Mathematical Modelling, Analysis and Aplications, Tecnológico Nacional de México—Instituto Tecnológico de Tijuana (Tijuana Institute of Technology), Tijuana 22414, Mexico
Interests: neuro-fuzzy systems; numerical optimization; mathematical and computational modeling; robotics; intelligent control; fuzzy differential equations
Special Issues, Collections and Topics in MDPI journals

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CONACyT-Tecnológico nacional de México—Instituto Tecnológico de Tijuana (Tijuana Institute of Technology), Tijuana 22414, Mexico
Interests: dynamical systems and control; bifurcation theory; fractional calculus and systems; stability theory
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

This Special Issue will compile frontier research in the areas of dynamical systems and control, both in theoretical and application advances. The study of dynamical systems and control is fundamental to promote advances in engineering; therefore, submissions on (but not limited to) the following topics are welcome:

  • Chaos and bifurcations;
  • Complex systems;
  • Fractional difference equations;
  • Fractional differential equations;
  • Fuzzy control and fuzzy systems;
  • Linear control systems;
  • Math education in science and engineering;
  • Matrix and spectral analysis;
  • Modeling;
  • Non-linear control systems;
  • Stability and robust stability;
  • Stability of pseudo-polynomials and quasi-polynomias.

Prof. Dr. Nohe R. Cazarez-Castro
Prof. Dr. Selene L. Cardenas-Maciel
Prof. Dr. Jorge A. Lopez-Renteria
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. Axioms is an international peer-reviewed open access monthly 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 2400 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.

Published Papers (6 papers)

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Research

15 pages, 337 KiB  
Article
Dynamical Behaviors of Stochastic SIS Epidemic Model with Ornstein–Uhlenbeck Process
by Huina Zhang, Jianguo Sun, Peng Yu and Daqing Jiang
Axioms 2024, 13(6), 353; https://doi.org/10.3390/axioms13060353 - 24 May 2024
Viewed by 337
Abstract
Controlling infectious diseases has become an increasingly complex issue, and vaccination has become a common preventive measure to reduce infection rates. It has been thought that vaccination protects the population. However, there is no fully effective vaccine. This is based on the fact [...] Read more.
Controlling infectious diseases has become an increasingly complex issue, and vaccination has become a common preventive measure to reduce infection rates. It has been thought that vaccination protects the population. However, there is no fully effective vaccine. This is based on the fact that it has long been assumed that the immune system produces corresponding antibodies after vaccination, but usually does not achieve the level of complete protection for undergoing environmental fluctuations. In this paper, we investigate a stochastic SIS epidemic model with incomplete inoculation, which is perturbed by the Ornstein–Uhlenbeck process and Brownian motion. We determine the existence of a unique global solution for the stochastic SIS epidemic model and derive control conditions for the extinction. By constructing two suitable Lyapunov functions and using the ergodicity of the Ornstein–Uhlenbeck process, we establish sufficient conditions for the existence of stationary distribution, which means the disease will prevail. Furthermore, we obtain the exact expression of the probability density function near the pseudo-equilibrium point of the stochastic model while addressing the four-dimensional Fokker–Planck equation under the same conditions. Finally, we conduct several numerical simulations to validate the theoretical results. Full article
(This article belongs to the Special Issue Advances in Dynamical Systems and Control)
17 pages, 4756 KiB  
Article
The Existence of Li–Yorke Chaos in a Discrete-Time Glycolytic Oscillator Model
by Mirela Garić-Demirović, Mustafa R. S. Kulenović, Mehmed Nurkanović and Zehra Nurkanović
Axioms 2024, 13(4), 280; https://doi.org/10.3390/axioms13040280 - 22 Apr 2024
Viewed by 697
Abstract
This paper investigates an autonomous discrete-time glycolytic oscillator model with a unique positive equilibrium point which exhibits chaos in the sense of Li–Yorke in a certain region of the parameters. We use Marotto’s theorem to prove the existence of chaos by finding a [...] Read more.
This paper investigates an autonomous discrete-time glycolytic oscillator model with a unique positive equilibrium point which exhibits chaos in the sense of Li–Yorke in a certain region of the parameters. We use Marotto’s theorem to prove the existence of chaos by finding a snap-back repeller. The illustration of the results is presented by using numerical simulations. Full article
(This article belongs to the Special Issue Advances in Dynamical Systems and Control)
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23 pages, 776 KiB  
Article
Simpson’s Variational Integrator for Systems with Quadratic Lagrangians
by Juan Antonio Rojas-Quintero, François Dubois and José Guadalupe Cabrera-Díaz
Axioms 2024, 13(4), 255; https://doi.org/10.3390/axioms13040255 - 11 Apr 2024
Viewed by 796
Abstract
This contribution proposes a variational symplectic integrator aimed at linear systems issued from the least action principle. An internal quadratic finite-element interpolation of the state is performed at each time step. Then, the action is approximated by Simpson’s quadrature formula. The implemented scheme [...] Read more.
This contribution proposes a variational symplectic integrator aimed at linear systems issued from the least action principle. An internal quadratic finite-element interpolation of the state is performed at each time step. Then, the action is approximated by Simpson’s quadrature formula. The implemented scheme is implicit, symplectic, and conditionally stable. It is applied to the time integration of systems with quadratic Lagrangians. The example of the linearized double pendulum is treated. Our method is compared with Newmark’s variational integrator. The exact solution of the linearized double pendulum example is used for benchmarking. Simulation results illustrate the precision and convergence of the proposed integrator. Full article
(This article belongs to the Special Issue Advances in Dynamical Systems and Control)
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22 pages, 1089 KiB  
Article
On Population Models with Delays and Dependence on Past Values
by Benito Chen-Charpentier
Axioms 2024, 13(3), 206; https://doi.org/10.3390/axioms13030206 - 20 Mar 2024
Viewed by 909
Abstract
The current values of many populations depend on the past values of the population. In many cases, this dependence is caused by the time certain processes take. This dependence on the past can be introduced into mathematical models by adding delays. For example, [...] Read more.
The current values of many populations depend on the past values of the population. In many cases, this dependence is caused by the time certain processes take. This dependence on the past can be introduced into mathematical models by adding delays. For example, the growth rate of a population depends on the population τ time units ago, where τ is the maturation time. For an epidemic, there is a time τ between the contact of an infected individual and a susceptible one, and the time the susceptible individual actually becomes infected. This time τ is also a delay. So, the number of infected individuals depends on the population at the time τ units ago. A second way of introducing this dependence on past values is to use non-local operators in the description of the model. Fractional derivatives have commonly been used to provide non-local effects. In population growth models, it can also be done by introducing a new compartment, the immature population, and in epidemic models, by introducing an additional exposed population. In this paper, we study and compare these methods of adding dependence on past values. For models of processes that involve delays, all three methods include dependence on past values, but fractional-order models do not justify the form of the dependence. Simulations show that for the models studied, the fractional differential equation method produces similar results to those obtained by explicitly incorporating the delay, but only for specific values of the fractional derivative order, which is an extra parameter. But in all three methods, the results are improved compared to using ordinary differential equations. Full article
(This article belongs to the Special Issue Advances in Dynamical Systems and Control)
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16 pages, 78304 KiB  
Article
Fractal Fractional Derivative Models for Simulating Chemical Degradation in a Bioreactor
by Ali Akgül and J. Alberto Conejero
Axioms 2024, 13(3), 151; https://doi.org/10.3390/axioms13030151 - 26 Feb 2024
Viewed by 888
Abstract
A three-differential-equation mathematical model is presented for the degradation of phenol and p-cresol combination in a bioreactor that is continually agitated. The stability analysis of the model’s equilibrium points, as established by the study, is covered. Additionally, we used three alternative kernels to [...] Read more.
A three-differential-equation mathematical model is presented for the degradation of phenol and p-cresol combination in a bioreactor that is continually agitated. The stability analysis of the model’s equilibrium points, as established by the study, is covered. Additionally, we used three alternative kernels to analyze the model with the fractal–fractional derivatives, and we looked into the effects of the fractal size and fractional order. We have developed highly efficient numerical techniques for the concentration of biomass, phenol, and p-cresol. Lastly, numerical simulations are used to illustrate the accuracy of the suggested method. Full article
(This article belongs to the Special Issue Advances in Dynamical Systems and Control)
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16 pages, 16818 KiB  
Article
Chaotic Steady States of the Reinartz Oscillator: Mathematical Evidence and Experimental Confirmation
by Jiri Petrzela
Axioms 2023, 12(12), 1101; https://doi.org/10.3390/axioms12121101 - 1 Dec 2023
Cited by 1 | Viewed by 1069
Abstract
This paper contributes to the problem of chaos and hyperchaos localization in the fundamental structure of analog building blocks dedicated to single-tone harmonic signal generation. This time, the known Reinartz sinusoidal oscillator is addressed, considering its conventional topology, both via numerical analysis and [...] Read more.
This paper contributes to the problem of chaos and hyperchaos localization in the fundamental structure of analog building blocks dedicated to single-tone harmonic signal generation. This time, the known Reinartz sinusoidal oscillator is addressed, considering its conventional topology, both via numerical analysis and experiments using a flow-equivalent lumped electronic circuit. It is shown that physically reasonable values of circuit parameters can result in robust dynamical behavior characterized by a pair of positive Lyapunov exponents. Mandatory numerical results prove that discovered strange attractors exhibit all necessary fingerprints of structurally stable chaos. The new “chaotic” parameters are closely related to the standard operation of the investigated analog functional block. A few interestingly shaped, strange attractors have been captured as oscilloscope screenshots. Full article
(This article belongs to the Special Issue Advances in Dynamical Systems and Control)
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