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Fractal Fract
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New Insights into Nonlinear Coupled Differential Equations with Its Applications
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New Insights into Nonlinear Coupled Differential Equations with Its Applications

A special issue of Fractal and Fractional (ISSN 2504-3110). This special issue belongs to the section "General Mathematics, Analysis".

Deadline for manuscript submissions: closed (31 July 2023) | Viewed by 21663

Special Issue Editors

Dr. Nallappan Gunasekaran

E-Mail Website
Guest Editor
Computational Intelligence Laboratory, Toyota Technological Institute, Nagoya 468-8511, Japan
Interests: time-varying delay; stability analysis; multi-agent systems; complex dynamical networks
Dr. R. Vadivel

E-Mail Website
Guest Editor
Faculty of Science and Technology, Phuket Rajabhat University, Phuket 83000, Thailand
Interests: time-varying delay; stability analysis; mathematical modeling; neural networks
Special Issues, Collections and Topics in MDPI journals
Dr. Zipeng Wang

E-Mail Website
Guest Editor
School of Electrical Engineering, University of Jinan, Jinan, China
Interests: robust control and filtering; fuzzy modeling and control; secure control; networked control systems; distributed
Prof. Dr. Sandra Pinelas

E-Mail Website
Guest Editor
Departamento De Ciencias Exatas E Engenharia Academia Militar, Av. Conde Castro Guimaraes, 2720-113 Amadora, Portugal
Interests: differential equations; difference equations; oscillatory behavior; asymptotic behavior
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

The tools of nonlinear coupled differential equations have been proven to be quite useful in simulating a variety of real-world issues encountered in scientific and technical domains. These equations are crucial in modeling every physical, chemical, biological, and economic activity. The existence and uniqueness of solutions are the emphasis of pure mathematics, but the formal justification of methods for approximating solutions is the focus of applied mathematics.

Nonlinear coupled differential equations are used to address a wide range of real-world issues. Furthermore, they may be tackled using a variety of methodologies and strategies. Because of their use in the mathematical modeling of a variety of physical and engineering processes, these differential systems with a variety of boundary conditions have attracted a lot of attention.

This Special Issue offers a platform for researchers to share their research. We welcome innovative research articles to be submitted in order to generate interest in the development of mathematical approaches for nonlinear coupled differential equations and related topics.  

Dr. Nallappan Gunasekaran
Dr. R. Vadivel
Dr. Zipeng Wang
Prof. Dr. Sandra Pinelas
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. Fractal and Fractional 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 2700 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

  • fractional calculus and applications numerical methods for nonlinear problems
  • functional analysis
  • fixed point theory
  • stability theory in fractional-order systems
  • continuous and discrete dynamical systems
  • stability analysis with time varying delay
  • nonlinear differential equation models in physics, biology, chemistry, engineering, etc.
  • mathematical models for nonlinear problems for engineering for both ODE and PDE

Published Papers (18 papers)

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Research

12 pages, 339 KiB  
Article
Existence of Mild Solution of the Hilfer Fractional Differential Equations with Infinite Delay on an Infinite Interval
by Chandrabose Sindhu Varun Bose, Ramalingam Udhayakumar, Milica Savatović, Arumugam Deiveegan, Vesna Todorčević and Stojan Radenović
Fractal Fract. 2023, 7(10), 724; https://doi.org/10.3390/fractalfract7100724 - 30 Sep 2023
Cited by 3 | Viewed by 781
Abstract
In this study, we present a mild solution to the Hilfer fractional differential equations with infinite delay. Firstly, we establish the results on an infinite interval; to achieve this, we use the generalized Ascoli–Arzelà theorem and Mönch’s fixed point theorem via a measure [...] Read more.
In this study, we present a mild solution to the Hilfer fractional differential equations with infinite delay. Firstly, we establish the results on an infinite interval; to achieve this, we use the generalized Ascoli–Arzelà theorem and Mönch’s fixed point theorem via a measure of noncompactness. Secondly, we consider the existence of a mild solution when the semigroup is compact, and the Schauder fixed-point theorem is used. The outcome is demonstrated using an infinitesimal operator, fractional calculus, semigroup theory, and abstract space. Finally, we present an example to support the results. Full article
(This article belongs to the Special Issue New Insights into Nonlinear Coupled Differential Equations with Its Applications)
20 pages, 3540 KiB  
Article
Adaptive Control for Finite-Time Cluster Synchronization of Fractional-Order Fully Complex-Valued Dynamical Networks
by Kaiquan Xiang, Qiaokun Kang, Hao Chang and Jing Yang
Fractal Fract. 2023, 7(9), 645; https://doi.org/10.3390/fractalfract7090645 - 24 Aug 2023
Viewed by 934
Abstract
This paper aims to address finite-time cluster synchronization (FTCS) issues for fractional-order fully complex-valued dynamical networks (FFCVDNs) with time delay. To compensate for the limited application of one controller, the delay-dependent and delay-independent adaptive controllers with regard to quadratic and absolute-valued norms are [...] Read more.
This paper aims to address finite-time cluster synchronization (FTCS) issues for fractional-order fully complex-valued dynamical networks (FFCVDNs) with time delay. To compensate for the limited application of one controller, the delay-dependent and delay-independent adaptive controllers with regard to quadratic and absolute-valued norms are developed, respectively. Based on the finite-time stability theorem and auxiliary inequality techniques, detailed Lyapunov analysis is provided to ensure that FFCVDNs can achieve FTCS, and the settling times (STs) are estimated on the basis of system and control parameters characterized by system models to decrease the conservativeness of the existing results. Finally, simulation examples are provided to verify the correctness of theoretical analysis. Full article
(This article belongs to the Special Issue New Insights into Nonlinear Coupled Differential Equations with Its Applications)
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13 pages, 1745 KiB  
Article
The Analytical Fractional Solutions for Coupled Fokas System in Fiber Optics Using Different Methods
by Wael W. Mohammed, Clemente Cesarano, Elsayed M. Elsayed and Farah M. Al-Askar
Fractal Fract. 2023, 7(7), 556; https://doi.org/10.3390/fractalfract7070556 - 18 Jul 2023
Cited by 6 | Viewed by 739
Abstract
The Fokas system with M-truncated derivative (FS-MTD) was considered in this study. To get analytical solutions of FS-MTD in the forms of elliptic, rational, hyperbolic, and trigonometric functions, we employed the extend F-expansion approach and the Jacobi elliptic function method. Since nonlinear [...] Read more.
The Fokas system with M-truncated derivative (FS-MTD) was considered in this study. To get analytical solutions of FS-MTD in the forms of elliptic, rational, hyperbolic, and trigonometric functions, we employed the extend F-expansion approach and the Jacobi elliptic function method. Since nonlinear pulse transmission in monomode optical fibers is explained by the Fokas system, the derived solutions may be utilized to analyze a broad range of important physical processes. In order to comprehend the impacts of MTD on the solutions, the dynamic behavior of the various generated solutions are shown using 2D and 3D figures. Full article
(This article belongs to the Special Issue New Insights into Nonlinear Coupled Differential Equations with Its Applications)
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19 pages, 351 KiB  
Article
Octonion Special Affine Fourier Transform: Pitt’s Inequality and the Uncertainty Principles
by Mohammad Younus Bhat, Aamir Hamid Dar, Mohra Zayed and Serkan Araci
Fractal Fract. 2023, 7(5), 356; https://doi.org/10.3390/fractalfract7050356 - 27 Apr 2023
Viewed by 911
Abstract
The special affine Fourier transform (SAFT) is an extended version of the classical Fourier transform and incorporates various signal processing tools which include the Fourier transforms, the fractional Fourier transform, the linear canonical transform, and other related transforms. This paper aims to introduce [...] Read more.
The special affine Fourier transform (SAFT) is an extended version of the classical Fourier transform and incorporates various signal processing tools which include the Fourier transforms, the fractional Fourier transform, the linear canonical transform, and other related transforms. This paper aims to introduce a novel octonion special affine Fourier transform (O−SAFT) and establish several classes of uncertainty inequalities for the proposed transform. We begin by studying the norm split and energy conservation properties of the proposed (O−SAFT). Afterwards, we generalize several uncertainty relations for the (O−SAFT) which include Pitt’s inequality, Heisenberg–Weyl inequality, logarithmic uncertainty inequality, Hausdorff–Young inequality, and local uncertainty inequalities. Finally, we provide an illustrative example and some possible applications of the proposed transform. Full article
(This article belongs to the Special Issue New Insights into Nonlinear Coupled Differential Equations with Its Applications)
14 pages, 332 KiB  
Article
On Coupled System of Langevin Fractional Problems with Different Orders of μ-Caputo Fractional Derivatives
by Lamya Almaghamsi, Ymnah Alruwaily, Kulandhaivel Karthikeyan and El-sayed El-hady
Fractal Fract. 2023, 7(4), 337; https://doi.org/10.3390/fractalfract7040337 - 18 Apr 2023
Cited by 1 | Viewed by 1176
Abstract
In this paper, we study coupled nonlinear Langevin fractional problems with different orders of μ-Caputo fractional derivatives on arbitrary domains with nonlocal integral boundary conditions. In order to ensure the existence and uniqueness of the solutions to the problem at hand, the [...] Read more.
In this paper, we study coupled nonlinear Langevin fractional problems with different orders of μ-Caputo fractional derivatives on arbitrary domains with nonlocal integral boundary conditions. In order to ensure the existence and uniqueness of the solutions to the problem at hand, the tools of the fixed-point theory are applied. An overview of the main results of this study is presented through examples. Full article
(This article belongs to the Special Issue New Insights into Nonlinear Coupled Differential Equations with Its Applications)
14 pages, 331 KiB  
Article
Investigation of a Coupled System of Hilfer–Hadamard Fractional Differential Equations with Nonlocal Coupled Hadamard Fractional Integral Boundary Conditions
by Bashir Ahmad and Shorog Aljoudi
Fractal Fract. 2023, 7(2), 178; https://doi.org/10.3390/fractalfract7020178 - 10 Feb 2023
Cited by 7 | Viewed by 1149
Abstract
We investigate the existence criteria for solutions of a nonlinear coupled system of Hilfer–Hadamard fractional differential equations of different orders complemented with nonlocal coupled Hadamard fractional integral boundary conditions. The desired results are accomplished with the aid of standard fixed-point theorems. We emphasize [...] Read more.
We investigate the existence criteria for solutions of a nonlinear coupled system of Hilfer–Hadamard fractional differential equations of different orders complemented with nonlocal coupled Hadamard fractional integral boundary conditions. The desired results are accomplished with the aid of standard fixed-point theorems. We emphasize that the fixed point approach is one of the effective methods to establish the existence results for boundary value problems. Examples illustrating the obtained results are constructed. Full article
(This article belongs to the Special Issue New Insights into Nonlinear Coupled Differential Equations with Its Applications)
14 pages, 321 KiB  
Article
An Interplay of Wigner–Ville Distribution and 2D Hyper-Complex Quadratic-Phase Fourier Transform
by Mohammad Younus Bhat, Aamir Hamid Dar, Irfan Nurhidayat and Sandra Pinelas
Fractal Fract. 2023, 7(2), 159; https://doi.org/10.3390/fractalfract7020159 - 6 Feb 2023
Cited by 5 | Viewed by 1229
Abstract
Two-dimensional hyper-complex (Quaternion) quadratic-phase Fourier transforms (Q-QPFT) have gained much popularity in recent years because of their applications in many areas, including color image and signal processing. At the same time, the applications of Wigner–Ville distribution (WVD) in signal analysis and image processing [...] Read more.
Two-dimensional hyper-complex (Quaternion) quadratic-phase Fourier transforms (Q-QPFT) have gained much popularity in recent years because of their applications in many areas, including color image and signal processing. At the same time, the applications of Wigner–Ville distribution (WVD) in signal analysis and image processing cannot be ruled out. In this paper, we study the two-dimensional hyper-complex (Quaternion) Wigner–Ville distribution associated with the quadratic-phase Fourier transform (WVD-QQPFT) by employing the advantages of quaternion quadratic-phase Fourier transforms (Q-QPFT) and Wigner–Ville distribution (WVD). First, we propose the definition of the WVD-QQPFT and its relationship with the classical Wigner–Ville distribution in the quaternion setting. Next, we investigate the general properties of the newly defined WVD-QQPFT, including complex conjugate, symmetry-conjugation, nonlinearity, boundedness, reconstruction formula, Moyal’s formula, and Plancherel formula. Finally, we propose the convolution and correlation theorems associated with WVD-QQPFT. Full article
(This article belongs to the Special Issue New Insights into Nonlinear Coupled Differential Equations with Its Applications)
14 pages, 407 KiB  
Article
Finite-Time Stabilization Criteria of Delayed Inertial Neural Networks with Settling-Time Estimation Protocol and Reliable Control Mechanism
by Wenhao Wang, Lanfeng Hua, Hong Zhu, Jun Wang, Kaibo Shi and Shouming Zhong
Fractal Fract. 2023, 7(2), 114; https://doi.org/10.3390/fractalfract7020114 - 25 Jan 2023
Cited by 1 | Viewed by 1067
Abstract
This work investigates the finite-time stability (FTS) issue for a class of inertial neural networks (INNs) with mixed-state time-varying delays, proposing a novel analytical approach. Firstly, we establish a novel FTS lemma, which is entirely different from the existing FTS theorems, and extend [...] Read more.
This work investigates the finite-time stability (FTS) issue for a class of inertial neural networks (INNs) with mixed-state time-varying delays, proposing a novel analytical approach. Firstly, we establish a novel FTS lemma, which is entirely different from the existing FTS theorems, and extend the current research results. Secondly, an improved discontinuous reliable control mechanism is developed, which is more valid and widens the application scope compared to previous results. Then, by using a novel non-reduced order approach (NROA) and the Lyapunov functional theory, novel sufficient criteria are established using FTS theorems to estimate the settling time with respect to a finite-time stabilization of INNs. Finally, the simulation results are given to validate the usefulness of the theoretical results. Full article
(This article belongs to the Special Issue New Insights into Nonlinear Coupled Differential Equations with Its Applications)
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14 pages, 333 KiB  
Article
Numerical Scheme for Singularly Perturbed Mixed Delay Differential Equation on Shishkin Type Meshes
by Sekar Elango and Bundit Unyong
Fractal Fract. 2023, 7(1), 43; https://doi.org/10.3390/fractalfract7010043 - 30 Dec 2022
Cited by 2 | Viewed by 1238
Abstract
Two non-uniform meshes used as part of the finite difference method to resolve singularly perturbed mixed-delay differential equations are studied in this article. The second-order derivative is multiplied by a small parameter which gives rise to boundary layers at x=0 and [...] Read more.
Two non-uniform meshes used as part of the finite difference method to resolve singularly perturbed mixed-delay differential equations are studied in this article. The second-order derivative is multiplied by a small parameter which gives rise to boundary layers at x=0 and x=3 and strong interior layers at x=1 and x=2 due to the delay terms. We prove that this method is almost first-order convergent on Shishkin mesh and is first-order convergent on Bakhvalov–Shishkin mesh. Error estimates are derived in the discrete maximum norm. Some examples are provided to validate the theoretical result. Full article
(This article belongs to the Special Issue New Insights into Nonlinear Coupled Differential Equations with Its Applications)
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28 pages, 392 KiB  
Article
Local and Global Mild Solution for Gravitational Effects of the Time Fractional Navier–Stokes Equations
by Kinda Abuasbeh, Ramsha Shafqat, Azmat Ullah Khan Niazi, Hassan J. Al Salman, Ahmed A. Al Ghafli and Muath Awadalla
Fractal Fract. 2023, 7(1), 26; https://doi.org/10.3390/fractalfract7010026 - 26 Dec 2022
Cited by 2 | Viewed by 953
Abstract
The gravitational effect is a physical phenomenon that explains the motion of a conductive fluid flowing under the impact of an exterior gravitational force. In this paper, we work on the Navier–Stokes equations (NSES) of the fluid flowing under the impact of an [...] Read more.
The gravitational effect is a physical phenomenon that explains the motion of a conductive fluid flowing under the impact of an exterior gravitational force. In this paper, we work on the Navier–Stokes equations (NSES) of the fluid flowing under the impact of an exterior gravitational force inclined at an angle of 45∘ with A time-fractional derivative of order β∈(0,1). To encourage anomalous diffusion in fractal media, we apply these equations. In Hδ,r, we prove the existence and uniqueness of local and global mild solutions. Additionally, we provide moderate local solutions in Jr. Additionally, we establish the regularity and existence of classical solutions to these equations in Jr. Full article
(This article belongs to the Special Issue New Insights into Nonlinear Coupled Differential Equations with Its Applications)
14 pages, 1765 KiB  
Article
An Approach for Numerical Solutions of Caputo–Hadamard Uncertain Fractional Differential Equations
by Yiyu Liu, Hanjie Liu and Yuanguo Zhu
Fractal Fract. 2022, 6(12), 693; https://doi.org/10.3390/fractalfract6120693 - 23 Nov 2022
Cited by 5 | Viewed by 1041
Abstract
This paper is devoted to investigating a numerical scheme for solving the Caputo–Hadamard uncertain fractional differential equations (UFDEs) arising from nonlinear uncertain dynamic systems. In our approach, we define an α-path, which is a link between a Caputo–Hadamard UFDE and a Caputo–Hadamard [...] Read more.
This paper is devoted to investigating a numerical scheme for solving the Caputo–Hadamard uncertain fractional differential equations (UFDEs) arising from nonlinear uncertain dynamic systems. In our approach, we define an α-path, which is a link between a Caputo–Hadamard UFDE and a Caputo–Hadamard fractional differential equation and is the inverse uncertainty distribution of a Caputo–Hadamard UFDE. Then, a formula for calculating the expected value of the Caputo–Hadamard UFDE is studied. With the help of the modified predictor–corrector method, some numerical algorithms for the inverse uncertainty distribution and the expected value of the solution of Caputo–Hadamard UFDEs are designed. Corresponding numerical examples are given to confirm the validity and accuracy of the proposed algorithms. Full article
(This article belongs to the Special Issue New Insights into Nonlinear Coupled Differential Equations with Its Applications)
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26 pages, 409 KiB  
Article
Existence and Ulam–Hyers Stability Analysis for Coupled Differential Equations of Fractional-Order with Nonlocal Generalized Conditions via Generalized Liouville–Caputo Derivative
by Muthaiah Subramanian and Shorog Aljoudi
Fractal Fract. 2022, 6(11), 629; https://doi.org/10.3390/fractalfract6110629 - 28 Oct 2022
Cited by 5 | Viewed by 1260
Abstract
In this paper, we investigate the existence and Hyers–Ulam stability of a coupled differential equations of fractional-order with multi-point (discrete) and integral boundary conditions that are related to Katugampola integrals. This manuscript can be categorized into four parts: The Leray–Schauder alternative and Krasnoselskii’s [...] Read more.
In this paper, we investigate the existence and Hyers–Ulam stability of a coupled differential equations of fractional-order with multi-point (discrete) and integral boundary conditions that are related to Katugampola integrals. This manuscript can be categorized into four parts: The Leray–Schauder alternative and Krasnoselskii’s fixed point theorems are used to prove the existence of a solution in the first and third section. The second section emphasizes the analysis of uniqueness, which is based on the Banach fixed point theorem’s concept of contraction mapping, and the fourth section establishes the Hyers–Ulam stability results. We demonstrate Hyers–Ulam stability using the traditional functional analysis technique. Finally, the consequences are validated using examples. Full article
(This article belongs to the Special Issue New Insights into Nonlinear Coupled Differential Equations with Its Applications)
20 pages, 545 KiB  
Article
An Extended Dissipative Analysis of Fractional-Order Fuzzy Networked Control Systems
by Rajarathinam Vadivel, Porpattama Hammachukiattikul, Seralan Vinoth, Kantapon Chaisena and Nallappan Gunasekaran
Fractal Fract. 2022, 6(10), 591; https://doi.org/10.3390/fractalfract6100591 - 13 Oct 2022
Cited by 4 | Viewed by 1342
Abstract
This study presents an extended dissipative analysis of fractional order fuzzy networked control system with uncertain parameters. First, we designed the network-based fuzzy controller for the considered model. Second, a novel Lyapunov-Krasovskii functional (LKF) approach, inequality techniques, and some sufficient conditions are established, [...] Read more.
This study presents an extended dissipative analysis of fractional order fuzzy networked control system with uncertain parameters. First, we designed the network-based fuzzy controller for the considered model. Second, a novel Lyapunov-Krasovskii functional (LKF) approach, inequality techniques, and some sufficient conditions are established, which make the proposed system quadratically stable under the extended dissipative criteria. Subsequently, the resultant conditions are expressed with respect to linear matrix inequalities (LMIs). Meanwhile, the corresponding controller gains are designed under the larger sampling interval. Finally, two numerical examples are presented to illustrate the viability of the obtained criteria. Full article
(This article belongs to the Special Issue New Insights into Nonlinear Coupled Differential Equations with Its Applications)
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15 pages, 337 KiB  
Article
A Novel Implementation of Mönch’s Fixed Point Theorem to a System of Nonlinear Hadamard Fractional Differential Equations
by Abeer Al Elaiw, Muath Awadalla, Murugesan Manigandan and Kinda Abuasbeh
Fractal Fract. 2022, 6(10), 586; https://doi.org/10.3390/fractalfract6100586 - 12 Oct 2022
Cited by 5 | Viewed by 1193
Abstract
In this article, we employed Mönch’s fixed point theorem to investigate the existence of solutions for a system of nonlinear Hadamard fractional differential equations and nonlocal non-conserved boundary conditions in terms of Hadamard integral. Followed by a study of the stability of this [...] Read more.
In this article, we employed Mönch’s fixed point theorem to investigate the existence of solutions for a system of nonlinear Hadamard fractional differential equations and nonlocal non-conserved boundary conditions in terms of Hadamard integral. Followed by a study of the stability of this solution using the Ulam-Hyres technique. This study concludes with an applied numerical example that helps in understanding the theoretical results obtained. Full article
(This article belongs to the Special Issue New Insights into Nonlinear Coupled Differential Equations with Its Applications)
13 pages, 1057 KiB  
Article
Collective Sensitivity and Collective Accessibility of Non-Autonomous Discrete Dynamical Systems
by Jingmin Pi, Tianxiu Lu and Yuanlin Chen
Fractal Fract. 2022, 6(10), 535; https://doi.org/10.3390/fractalfract6100535 - 22 Sep 2022
Cited by 4 | Viewed by 1100
Abstract
The concepts of collectively accessible, collectively sensitive, collectively infinitely sensitive, and collectively Li–Yorke sensitive are defined in non-autonomous discrete systems. It is proved that, if the mapping sequence h1,∞=(h1,h2,…) is [...] Read more.
The concepts of collectively accessible, collectively sensitive, collectively infinitely sensitive, and collectively Li–Yorke sensitive are defined in non-autonomous discrete systems. It is proved that, if the mapping sequence h1,∞=(h1,h2,…) is W-chaotic, then hn,∞=(hn,hn+1,…)(∀n∈N={1,2,…}) would also be W-chaotic. W-chaos represents one of the following five properties: collectively accessible, sensitive, collectively sensitive, collectively infinitely sensitive, and collectively Li–Yorke sensitive. Then, the relationship of chaotic properties between the product system (H1×H2,f1,∞×g1,∞) and factor systems (H1,f1,∞) and (H2,g1,∞) was presented. Furthermore, in this paper, it is also proved that, if the autonomous discrete system (X,h^) induced by the p-periodic discrete system (H,h1,∞) is W-chaotic, then the p-periodic discrete system (H,f1,∞) would also be W-chaotic. Full article
(This article belongs to the Special Issue New Insights into Nonlinear Coupled Differential Equations with Its Applications)
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19 pages, 1069 KiB  
Article
New Adaptive Finite-Time Cluster Synchronization of Neutral-Type Complex-Valued Coupled Neural Networks with Mixed Time Delays
by Nattakan Boonsatit, Santhakumari Rajendran, Chee Peng Lim, Anuwat Jirawattanapanit and Praneesh Mohandas
Fractal Fract. 2022, 6(9), 515; https://doi.org/10.3390/fractalfract6090515 - 13 Sep 2022
Cited by 8 | Viewed by 1292
Abstract
The issue of adaptive finite-time cluster synchronization corresponding to neutral-type coupled complex-valued neural networks with mixed delays is examined in this research. A neutral-type coupled complex-valued neural network with mixed delays is more general than that of a traditional neural network, since it [...] Read more.
The issue of adaptive finite-time cluster synchronization corresponding to neutral-type coupled complex-valued neural networks with mixed delays is examined in this research. A neutral-type coupled complex-valued neural network with mixed delays is more general than that of a traditional neural network, since it considers distributed delays, state delays and coupling delays. In this research, a new adaptive control technique is developed to synchronize neutral-type coupled complex-valued neural networks with mixed delays in finite time. To stabilize the resulting closed-loop system, the Lyapunov stability argument is leveraged to infer the necessary requirements on the control factors. The effectiveness of the proposed method is illustrated through simulation studies. Full article
(This article belongs to the Special Issue New Insights into Nonlinear Coupled Differential Equations with Its Applications)
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24 pages, 708 KiB  
Article
Sampled-Data Based Fault-Tolerant Control Design for Uncertain CE151 Helicopter System with Random Delays: Takagi-Sugeno Fuzzy Approach
by V. Dhanya, A. Arunkumar and Kantapon Chaisena
Fractal Fract. 2022, 6(9), 498; https://doi.org/10.3390/fractalfract6090498 - 5 Sep 2022
Viewed by 1086
Abstract
This study inspects the issue of robust reliable sampled data control (SDC) for a class of Takagi-Sugeno (TS) fuzzy CE151 Helicopter systems with time-varying delays and linear fractional uncertainties. Specifically, both the variation range and the distribution probability of the time delay are [...] Read more.
This study inspects the issue of robust reliable sampled data control (SDC) for a class of Takagi-Sugeno (TS) fuzzy CE151 Helicopter systems with time-varying delays and linear fractional uncertainties. Specifically, both the variation range and the distribution probability of the time delay are considered in the control input. The essential aspect of the suggested results in this study is that the time variable delay in the control input is dependent not only on the bound but also on the distribution probability of the time delay. The prime intent of this study is to enhance a state feedback reliable sampled-data controller. By constructing an appropriate Lyapunov-Krasovskii functional (LKF) and employing a linear matrix inequalities (LMIs) approach, a new set of delay-dependent necessary conditions is obtained to ensure the asymptotic stabilisation of a TS fuzzy CE151 Helicopter system with a prescribed mixed H∞ and passivity (MH∞P) performance index. The acquired results are expressed as LMIs, which are easily addressed using standard optimization algorithms. In addition, an exemplary scenario based on the CE151 helicopter model is presented to demonstrate the less conservative nature of the obtained results as well as the application of the recommended unique design approaches. Full article
(This article belongs to the Special Issue New Insights into Nonlinear Coupled Differential Equations with Its Applications)
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14 pages, 4358 KiB  
Article
Identifying Partial Topological Structures of Stochastic Multi-Group Models with Multiple Dispersals via Graph-Theoretic Method
by Chunmei Zhang, Dan Xia, Huiling Chen, Hui Yang, Ran Li and Nallappan Gunasekaran
Fractal Fract. 2022, 6(7), 371; https://doi.org/10.3390/fractalfract6070371 - 1 Jul 2022
Cited by 15 | Viewed by 1366
Abstract
In this paper, the partial topology identification of stochastic multi-group models with multiple dispersals is investigated. Based on adaptive pinning control and a graph-theoretic method, some sufficient criteria about partial topology identification of stochastic multi-group models with multiple dispersals are obtained. That is [...] Read more.
In this paper, the partial topology identification of stochastic multi-group models with multiple dispersals is investigated. Based on adaptive pinning control and a graph-theoretic method, some sufficient criteria about partial topology identification of stochastic multi-group models with multiple dispersals are obtained. That is to say, the unknown partial topological structures can be identified successfully. In the end, numerical examples are provided to verify the effectiveness of theoretical results. Full article
(This article belongs to the Special Issue New Insights into Nonlinear Coupled Differential Equations with Its Applications)
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