Special Issue "Nonlinear Dynamics and Analysis"

A special issue of Entropy (ISSN 1099-4300). This special issue belongs to the section "Complexity".

Deadline for manuscript submissions: closed (31 July 2021).

Special Issue Editors

Prof. Dr. Ravi P. Agarwal
grade E-Mail Website
Guest Editor
Prof. Dr. Maria Alessandra Ragusa
E-Mail Website
Guest Editor
Dipartimento di matematica e Informatica, Università di Catania, Italy
Interests: nonlinear analysis; mathematical models in applied sciences; partial differential equations; environmental applications of mathematical methods
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

The scope of this Special Issue is to bring together theory, methods, and real-world applications of Nonlinear Dynamics. It will consist of topical research in but not limited to the following areas: 

Ordinary differential equations;

Delay differential equations;

Fixed point theory;

Fractional differential equations

Functional equations;

Equations on time scales;

Partial differential equations;

Fractional differential equations;

Stochastic differential equations;

Integral equations.

Prof. Dr. Ravi P. Agarwal
Prof. Dr. Maria Alessandra Ragusa
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 papers will be 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. Entropy 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 1800 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 (8 papers)

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Research

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Article
Some Integral Inequalities Involving Metrics
Entropy 2021, 23(7), 871; https://0-doi-org.brum.beds.ac.uk/10.3390/e23070871 - 08 Jul 2021
Viewed by 515
Abstract
In this work, we establish some integral inequalities involving metrics. Moreover, some applications to partial metric spaces are given. Our results are extension of previous obtained metric inequalities in the discrete case. Full article
(This article belongs to the Special Issue Nonlinear Dynamics and Analysis)
Article
Existence of a Unique Solution to a Fractional Partial Differential Equation and Its Continuous Dependence on Parameters
Entropy 2021, 23(7), 851; https://0-doi-org.brum.beds.ac.uk/10.3390/e23070851 - 01 Jul 2021
Viewed by 526
Abstract
In the present paper we give conditions under which there exists a unique weak solution for a nonlocal equation driven by the integrodifferential operator of fractional Laplacian type. We argue for the optimality of some assumptions. Some Lyapunov-type inequalities are given. We also [...] Read more.
In the present paper we give conditions under which there exists a unique weak solution for a nonlocal equation driven by the integrodifferential operator of fractional Laplacian type. We argue for the optimality of some assumptions. Some Lyapunov-type inequalities are given. We also study the continuous dependence of the solution on parameters. In proofs we use monotonicity and variational methods. Full article
(This article belongs to the Special Issue Nonlinear Dynamics and Analysis)
Article
SUPG-Stabilized Virtual Element Method for Optimal Control Problem Governed by a Convection Dominated Diffusion Equation
Entropy 2021, 23(6), 723; https://0-doi-org.brum.beds.ac.uk/10.3390/e23060723 - 05 Jun 2021
Viewed by 681
Abstract
In this paper, the streamline upwind/Petrov Galerkin (SUPG) stabilized virtual element method (VEM) for optimal control problem governed by a convection dominated diffusion equation is investigated. The virtual element discrete scheme is constructed based on the first-optimize-then-discretize strategy and SUPG stabilized virtual element [...] Read more.
In this paper, the streamline upwind/Petrov Galerkin (SUPG) stabilized virtual element method (VEM) for optimal control problem governed by a convection dominated diffusion equation is investigated. The virtual element discrete scheme is constructed based on the first-optimize-then-discretize strategy and SUPG stabilized virtual element approximation of the state equation and adjoint state equation. An a priori error estimate is derived for both the state, adjoint state, and the control. Numerical experiments are carried out to illustrate the theoretical findings. Full article
(This article belongs to the Special Issue Nonlinear Dynamics and Analysis)
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Article
Stability of Non-Linear Dirichlet Problems with ϕ-Laplacian
Entropy 2021, 23(6), 647; https://0-doi-org.brum.beds.ac.uk/10.3390/e23060647 - 22 May 2021
Viewed by 549
Abstract
We study the stability and the solvability of a family of problems (ϕ(x))=g(t,x,x,u)+f* with Dirichlet boundary conditions, where ϕ, [...] Read more.
We study the stability and the solvability of a family of problems (ϕ(x))=g(t,x,x,u)+f* with Dirichlet boundary conditions, where ϕ, u, f* are allowed to vary as well. Applications for boundary value problems involving the p-Laplacian operator are highlighted. Full article
(This article belongs to the Special Issue Nonlinear Dynamics and Analysis)
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Article
Hybrid Control of Digital Baker Map with Application to Pseudo-Random Number Generator
Entropy 2021, 23(5), 578; https://0-doi-org.brum.beds.ac.uk/10.3390/e23050578 - 08 May 2021
Cited by 1 | Viewed by 495
Abstract
Dynamical degradation occurs when chaotic systems are implemented on digital devices, which seriously threatens the security of chaos-based cryptosystems. The existing solutions mainly focus on the compensation of dynamical properties rather than on the elimination of the inherent biases of chaotic systems. In [...] Read more.
Dynamical degradation occurs when chaotic systems are implemented on digital devices, which seriously threatens the security of chaos-based cryptosystems. The existing solutions mainly focus on the compensation of dynamical properties rather than on the elimination of the inherent biases of chaotic systems. In this paper, a unidirectional hybrid control method is proposed to improve the dynamical properties and to eliminate the biases of digital chaotic maps. A continuous chaotic system is introduced to provide external feedback control of the given digital chaotic map. Three different control modes are investigated, and the influence of control parameter on the properties of the controlled system is discussed. The experimental results show that the proposed method can not only improve the dynamical degradation of the digital chaotic map but also make the controlled digital system produce outputs with desirable performances. Finally, a pseudorandom number generator (PRNG) is proposed. Statistical analysis shows that the PRNG has good randomness and almost ideal entropy values. Full article
(This article belongs to the Special Issue Nonlinear Dynamics and Analysis)
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Article
New Criteria on Oscillatory and Asymptotic Behavior of Third-Order Nonlinear Dynamic Equations with Nonlinear Neutral Terms
Entropy 2021, 23(2), 227; https://0-doi-org.brum.beds.ac.uk/10.3390/e23020227 - 15 Feb 2021
Cited by 2 | Viewed by 777
Abstract
In the paper, we provide sufficient conditions for the oscillatory and asymptotic behavior of a new type of third-order nonlinear dynamic equations with mixed nonlinear neutral terms. Our theorems not only improve and extend existing theorems in the literature but also provide a [...] Read more.
In the paper, we provide sufficient conditions for the oscillatory and asymptotic behavior of a new type of third-order nonlinear dynamic equations with mixed nonlinear neutral terms. Our theorems not only improve and extend existing theorems in the literature but also provide a new approach as far as the nonlinear neutral terms are concerned. The main results are illustrated by some particular examples. Full article
(This article belongs to the Special Issue Nonlinear Dynamics and Analysis)
Article
Nonlinear Neutral Delay Differential Equations of Fourth-Order: Oscillation of Solutions
Entropy 2021, 23(2), 129; https://0-doi-org.brum.beds.ac.uk/10.3390/e23020129 - 20 Jan 2021
Cited by 28 | Viewed by 761
Abstract
The objective of this paper is to study oscillation of fourth-order neutral differential equation. By using Riccati substitution and comparison technique, new oscillation conditions are obtained which insure that all solutions of the studied equation are oscillatory. Our results complement some known results [...] Read more.
The objective of this paper is to study oscillation of fourth-order neutral differential equation. By using Riccati substitution and comparison technique, new oscillation conditions are obtained which insure that all solutions of the studied equation are oscillatory. Our results complement some known results for neutral differential equations. An illustrative example is included. Full article
(This article belongs to the Special Issue Nonlinear Dynamics and Analysis)

Review

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Review
A Survey of Function Analysis and Applied Dynamic Equations on Hybrid Time Scales
Entropy 2021, 23(4), 450; https://0-doi-org.brum.beds.ac.uk/10.3390/e23040450 - 11 Apr 2021
Viewed by 540
Abstract
As an effective tool to unify discrete and continuous analysis, time scale calculus have been widely applied to study dynamic systems in both theoretical and practical aspects. In addition to such a classical role of unification, the dynamic equations on time scales have [...] Read more.
As an effective tool to unify discrete and continuous analysis, time scale calculus have been widely applied to study dynamic systems in both theoretical and practical aspects. In addition to such a classical role of unification, the dynamic equations on time scales have their own unique features which the difference and differential equations do not possess and these advantages have been highlighted in describing some complicated dynamical behavior in the hybrid time process. In this review article, we conduct a survey of abstract analysis and applied dynamic equations on hybrid time scales, some recent main results and the related developments on hybrid time scales will be reported and the future research related to this research field is discussed. The results presented in this article can be extended and generalized to study both pure mathematical analysis and real applications such as mathematical physics, biological dynamical models and neural networks, etc. Full article
(This article belongs to the Special Issue Nonlinear Dynamics and Analysis)
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