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Axioms
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Nonautonomous and Random Dynamical Systems
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Nonautonomous and Random Dynamical Systems

A special issue of Axioms (ISSN 2075-1680).

Deadline for manuscript submissions: closed (31 October 2022) | Viewed by 9334

Special Issue Editor

Dr. Davor Dragicevic

E-Mail Website
Guest Editor
Department of Mathematics, University of Rijeka, Radmile Matejčić 2, 51000 Rijeka, Croatia
Interests: ergodic theory; hyperbolic dynamical systems; difference equations; ordinary differential equations

Special Issue Information

Dear Colleagues,

The theory of dynamical systems is concerned with the study of the asymptotic behaviour (of both qualitative and quantitative nature) of complex systems modelling real life phenomena. In the last couple of decades, dynamical systems have emerged as one of the most active and impactful areas of modern mathematics, with spectacular applications to other branches of mathematics as well as to other natural sciences such as biology, chemistry, and physics.

In particular, it is of central importance to study nonautonomous and random dynamical systems because those are used to model transport in complex environments (such as in the atmosphere or in the ocean), where the rules of dynamics are not static but rather exhibit various types of changes.

The aim of this Special Issue is to stimulate the study of nonautonomous and random dynamical systems as well as to explore new directions.

All research papers concerned with the qualitative and asymptotic behavior of nonautonomous or random dynamical systems are welcome, with particular emphasis on those dealing with various concepts of stability or hyperbolicity. In addition, we particularly welcome research papers dealing with the quantitative properties of random dynamical systems such as various limit laws.

Finally, we also plan to publish carefully selected survey papers describing recent major advancements in the previously mentioned research areas.

Dr. Davor Dragicevic
Guest Editor

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

  • Hyperbolicity
  • Stability
  • Random dynamical systems
  • Nonautonomous dynamical systems
  • Ergodic theory
  • Limit laws

Published Papers (5 papers)

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Research

24 pages, 319 KiB  
Article
Controllability Results for First Order Impulsive Fuzzy Differential Systems
by Rui Liu, Michal Fečkan, Donal O’Regan and Jinrong Wang
Axioms 2022, 11(9), 471; https://0-doi-org.brum.beds.ac.uk/10.3390/axioms11090471 - 14 Sep 2022
Cited by 1 | Viewed by 1177
Abstract
In this paper, we investigate the controllability of first-order impulsive fuzzy differential equations. Using the direct construction method, the controllability of first-order linear impulsive fuzzy differential equations is considered with a<0, the (c1) solution, and a<0 [...] Read more.
In this paper, we investigate the controllability of first-order impulsive fuzzy differential equations. Using the direct construction method, the controllability of first-order linear impulsive fuzzy differential equations is considered with a<0, the (c1) solution, and a<0, the (c2) solution, respectively.In addition, by employing the Banach fixed-point theorem, the controllability of first-order nonlinear impulsive fuzzy differential equations is studied. Finally, examples are presented to illustrate our theoretical results. Full article
(This article belongs to the Special Issue Nonautonomous and Random Dynamical Systems)
20 pages, 481 KiB  
Article
Local and Global Stability of Certain Mixed Monotone Fractional Second Order Difference Equation with Quadratic Terms
by Mirela Garić-Demirović, Sabina Hrustić and Zehra Nurkanović
Axioms 2021, 10(4), 288; https://0-doi-org.brum.beds.ac.uk/10.3390/axioms10040288 - 01 Nov 2021
Cited by 1 | Viewed by 1329
Abstract
This paper investigates the local and global character of the unique positive equilibrium of a mixed monotone fractional second-order difference equation with quadratic terms. The corresponding associated map of the equation decreases in the first variable, and it can be either decreasing or [...] Read more.
This paper investigates the local and global character of the unique positive equilibrium of a mixed monotone fractional second-order difference equation with quadratic terms. The corresponding associated map of the equation decreases in the first variable, and it can be either decreasing or increasing in the second variable depending on the corresponding parametric values. We use the theory of monotone maps to study global dynamics. For local stability, we use the center manifold theory in the case of the non-hyperbolic equilibrium point. We show that the observed equation exhibits three types of global behavior characterized by the existence of the unique positive equilibrium, which can be locally stable, non-hyperbolic when there also exist infinitely many non-hyperbolic and stable minimal period-two solutions, and a saddle. Numerical simulations are carried out to better illustrate the results. Full article
(This article belongs to the Special Issue Nonautonomous and Random Dynamical Systems)
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12 pages, 266 KiB  
Article
Integral Characterizations for Uniform Stability with Growth Rates in Banach Spaces
by Rovana Boruga (Toma), Mihail Megan and Daniela Maria-Magdalena Toth
Axioms 2021, 10(3), 235; https://0-doi-org.brum.beds.ac.uk/10.3390/axioms10030235 - 21 Sep 2021
Cited by 5 | Viewed by 1583
Abstract
The aim of this paper is to present some integral characterizations for the concept of uniform stability with growth rates in Banach spaces. In this sense, we prove necessary and sufficient conditions (of Barbashin and Datko type) for an evolution operator to be [...] Read more.
The aim of this paper is to present some integral characterizations for the concept of uniform stability with growth rates in Banach spaces. In this sense, we prove necessary and sufficient conditions (of Barbashin and Datko type) for an evolution operator to be uniform h- stable. As particular cases of this notion, we obtain four characterizations for uniform exponential stability and two characterizations for uniform polynomial stability. Full article
(This article belongs to the Special Issue Nonautonomous and Random Dynamical Systems)
11 pages, 255 KiB  
Article
On Uniform Stability with Growth Rates of Stochastic Skew-Evolution Semiflows in Banach Spaces
by Tímea Melinda Személy Fülöp, Mihail Megan and Diana Ioana Borlea(Pătraşcu)
Axioms 2021, 10(3), 182; https://0-doi-org.brum.beds.ac.uk/10.3390/axioms10030182 - 08 Aug 2021
Cited by 1 | Viewed by 1485
Abstract
The main purpose of this paper is to study a more general concept of uniform stability in mean in which the uniform behavior in the classical sense is replaced by a weaker requirement with respect to some probability measure. This concept includes, as [...] Read more.
The main purpose of this paper is to study a more general concept of uniform stability in mean in which the uniform behavior in the classical sense is replaced by a weaker requirement with respect to some probability measure. This concept includes, as particular cases, the concepts of uniform exponential stability in mean and uniform polynomial stability in mean. Extending techniques employed in the deterministic case, we obtain variants of some results for the general cases of uniform stability in mean for stochastic skew-evolution semiflows in Banach spaces. Full article
(This article belongs to the Special Issue Nonautonomous and Random Dynamical Systems)
14 pages, 257 KiB  
Article
Smooth Stable Manifold for Delay Differential Equations with Arbitrary Growth Rate
by Lokesh Singh and Dhirendra Bahuguna
Axioms 2021, 10(2), 105; https://0-doi-org.brum.beds.ac.uk/10.3390/axioms10020105 - 25 May 2021
Cited by 1 | Viewed by 1864
Abstract
In this article, we construct a C1 stable invariant manifold for the delay differential equation x′=Ax(t)+Lxt+f(t,xt) assuming the ρ-nonuniform exponential dichotomy for [...] Read more.
In this article, we construct a C1 stable invariant manifold for the delay differential equation x′=Ax(t)+Lxt+f(t,xt) assuming the ρ-nonuniform exponential dichotomy for the corresponding solution operator. We also assume that the C1 perturbation, f(t,xt), and its derivative are sufficiently small and satisfy smoothness conditions. To obtain the invariant manifold, we follow the method developed by Lyapunov and Perron. We also show the dependence of invariant manifold on the perturbation f(t,xt). Full article
(This article belongs to the Special Issue Nonautonomous and Random Dynamical Systems)
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