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Axioms
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Mathematical Modeling and Analysis of Fractional Chaotic Systems and Their...
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Mathematical Modeling and Analysis of Fractional Chaotic Systems and Their Applications

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

Deadline for manuscript submissions: closed (20 April 2023) | Viewed by 5381

Special Issue Editors

Dr. Antonio Coronel-Escamilla

E-Mail Website
Guest Editor
División Académica de Mecánica Industrial, Universidad Tecnológica Emiliano Zapata, Emiliano Zapata, Morelos 62765, Mexico
Interests: control theory; fractional calculus; computational neuroscience; robotics and mechatronics
Special Issues, Collections and Topics in MDPI journals
Dr. Jesús Emmanuel Solís-Pérez

E-Mail Website
Guest Editor
National School of Higher Studies (ENES), Universidad Nacional Autónoma de México (UNAM), Morelia 58190, Mexico
Interests: fractional calculus; numerical methods; chaotic systems and synchronization; optimization

Special Issue Information

Dear Colleagues,

We invite you to submit your recent and novel work in this Special Issue of Axioms. The main aim is to showcase recent advances in the modeling and analysis of chaotic systems and their applications using fractional calculus. Through high-quality research, we want to show the advantages of using fractional calculus to chaotic systems applied to tasks, including but not limited to modeling, synchronization, control, chaos, and fractals. In general, fractional-order differential equations provide what is known as intrinsic memory. Based on this premise, we would like to show the effects of such properties on chaotic systems.

This Special Issue is also open to receiving ideas beyond the topics mentioned above. We look forward to receiving your submissions to this Special Issue.

Dr. Antonio Coronel-Escamilla
Dr. Jesús Emmanuel Solís-Pérez
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.

Keywords

  • chaotic systems
  • modeling
  • fractional calculus
  • memory trace
  • calculus of variations
  • synchronization
  • control

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Published Papers (3 papers)

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Research

16 pages, 2881 KiB  
Article
Complexity and Chaos Analysis for Two-Dimensional Discrete-Time Predator–Prey Leslie–Gower Model with Fractional Orders
by Tareq Hamadneh, Abderrahmane Abbes, Ibraheem Abu Falahah, Yazan Alaya AL-Khassawneh, Ahmed Salem Heilat, Abdallah Al-Husban and Adel Ouannas
Axioms 2023, 12(6), 561; https://doi.org/10.3390/axioms12060561 - 6 Jun 2023
Cited by 7 | Viewed by 1473
Abstract
The paper introduces a novel two-dimensional fractional discrete-time predator–prey Leslie–Gower model with an Allee effect on the predator population. The model’s nonlinear dynamics are explored using various numerical techniques, including phase portraits, bifurcations and maximum Lyapunov exponent, with consideration given to both commensurate [...] Read more.
The paper introduces a novel two-dimensional fractional discrete-time predator–prey Leslie–Gower model with an Allee effect on the predator population. The model’s nonlinear dynamics are explored using various numerical techniques, including phase portraits, bifurcations and maximum Lyapunov exponent, with consideration given to both commensurate and incommensurate fractional orders. These techniques reveal that the fractional-order predator–prey Leslie–Gower model exhibits intricate and diverse dynamical characteristics, including stable trajectories, periodic motion, and chaotic attractors, which are affected by the variance of the system parameters, the commensurate fractional order, and the incommensurate fractional order. Finally, we employ the 0–1 method, the approximate entropy test and the C0 algorithm to measure complexity and confirm chaos in the proposed system. Full article
(This article belongs to the Special Issue Mathematical Modeling and Analysis of Fractional Chaotic Systems and Their Applications)
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11 pages, 772 KiB  
Article
Chaos Controllability in Non-Identical Complex Fractional Order Chaotic Systems via Active Complex Synchronization Technique
by Mohammad Sajid, Harindri Chaudhary and Santosh Kaushik
Axioms 2023, 12(6), 530; https://doi.org/10.3390/axioms12060530 - 28 May 2023
Cited by 3 | Viewed by 1209
Abstract
In this paper, we primarily investigate the methodology for the hybrid complex projective synchronization (HCPS) scheme in non-identical complex fractional order chaotic systems via an active complex synchronization technique (ACST). Appropriate controllers of a nonlinear type are designed in view of master–slave composition [...] Read more.
In this paper, we primarily investigate the methodology for the hybrid complex projective synchronization (HCPS) scheme in non-identical complex fractional order chaotic systems via an active complex synchronization technique (ACST). Appropriate controllers of a nonlinear type are designed in view of master–slave composition and Lyapunov’s stability criterion (LSC). The HCPS is an extended version of the previously designed projective synchronization scheme. In the HCPS scheme, by using a complex scale matrix, the system taken as slave system is asymptotically synchronized with another system taken as the master system. By utilizing a complex scale matrix, the unpredictability and security of communication are increased along with image encryption. An efficient computational method has been employed to validate and visualize the HCPS method’s efficacy by performing numerical simulation outcomes in MATLAB (version 2021). Full article
(This article belongs to the Special Issue Mathematical Modeling and Analysis of Fractional Chaotic Systems and Their Applications)
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18 pages, 335 KiB  
Article
Multiterm Impulsive Caputo–Hadamard Type Differential Equations of Fractional Variable Order
by Amar Benkerrouche, Mohammed Said Souid, Gani Stamov and Ivanka Stamova
Axioms 2022, 11(11), 634; https://doi.org/10.3390/axioms11110634 - 10 Nov 2022
Cited by 8 | Viewed by 1893
Abstract
In this study, we deal with an impulsive boundary value problem (BVP) for differential equations of variable fractional order involving the Caputo–Hadamard fractional derivative. The fundamental problems of existence and uniqueness of solutions are studied, and new existence and uniqueness results are established [...] Read more.
In this study, we deal with an impulsive boundary value problem (BVP) for differential equations of variable fractional order involving the Caputo–Hadamard fractional derivative. The fundamental problems of existence and uniqueness of solutions are studied, and new existence and uniqueness results are established in the form of two fixed point theorems. In addition, Ulam–Hyers stability sufficient conditions are proved illustrating the suitability of the derived fundamental results. The obtained results are supported also by an example. Finally, the conclusion notes are highlighted. Full article
(This article belongs to the Special Issue Mathematical Modeling and Analysis of Fractional Chaotic Systems and Their Applications)
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