Search for Articles:
Title / Keyword
Author / Affiliation / Email
Journal
Article Type
 
 
Advanced Search
 
Section
Special Issue
Volume
Issue
Number
Page
 
4.0
2.3
Journals
Mathematics
Special Issues
Advances in Chaos Theory and Dynamical Systems
share announcement

Advances in Chaos Theory and Dynamical Systems

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "Dynamical Systems".

Deadline for manuscript submissions: closed (31 December 2023) | Viewed by 5407

Special Issue Editors

Dr. Chris G. Antonopoulos

E-Mail Website
Guest Editor
School of Mathematics, Statistics and Actuarial Science (SMSAS), University of Essex, Wivenhoe Park, Colchester CO4 3SQ, UK
Interests: dynamical systems; nonlinear dynamics; chaos theory; mathematical modelling; complex behaviour; complex systems; complex networks; synchronisation and applications
Dr. Thanos Manos

E-Mail Website
Guest Editor
Department of Mathematics, Laboratoire de Physique Théorique et Modélisation, CY Cergy Paris Université, CNRS, UMR 8089, CEDEX, 95302 Cergy-Pontoise, France
Interests: nonlinear dynamical systems; classical and quantum chaos; mathematical modeling of biological systems; neuromodulation; whole brain dynamical modelling

Special Issue Information

Dear Colleagues,

We are pleased to announce a Special Issue of the journal Mathematics entitled “Advances in Chaos Theory and Dynamical Systems”.

Many problems in life and sciences can be described by dynamical systems, i.e., by systems whose states evolve with time over a state space according to deterministic fixed rules. They can model a vast range of phenomena in nature, society and sciences and can bring together different fields in maths to support interdisciplinary approaches to understand the world around us. Chaos theory started developing in the early 1960s by E. Lorenz and focuses on the study of unpredictable behaviour in dynamical systems governed by deterministic laws. 

The goal is to analyse and better understand processes in different fields in science or applications, such as in maths, physics, biology, epidemiology, ecology, complex systems, complex networks, synchronisation phenomena, mechanics, etc. Dynamical systems and chaos theory can help develop common approaches to tackle problems that might look unrelated at first sight. Combined can offer unique and powerful theoretical and numerical approaches to study those problems and better understand them, providing us with the opportunity to improve our understanding of nature, our lives and well-being.

This Special Issue welcomes original research articles, short communications, and review papers on the forefront of advances in chaos theory and dynamical systems. Potential topics include theoretical and numerical studies as well as analyses of applied models related to a vast range of fields, cited below.

Dr. Chris G. Antonopoulos
Dr. Thanos Manos
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. Mathematics is an international peer-reviewed open access semimonthly 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 2600 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

  • dynamical systems
  • nonlinear dynamics
  • nonlinear systems
  • chaotic systems
  • Hamiltonian systems
  • dissipative systems
  • complex systems
  • chaotic indicators
  • bifurcation analysis
  • symbolic dynamics
  • control theory
  • networks
  • synchronisation phenomena
  • chimera states
  • statistical mechanics
  • Boltzmann-Gibbs entropy
  • Tsallis entropy

Benefits of Publishing in a Special Issue

  • Ease of navigation: Grouping papers by topic helps scholars navigate broad scope journals more efficiently.
  • Greater discoverability: Special Issues support the reach and impact of scientific research. Articles in Special Issues are more discoverable and cited more frequently.
  • Expansion of research network: Special Issues facilitate connections among authors, fostering scientific collaborations.
  • External promotion: Articles in Special Issues are often promoted through the journal's social media, increasing their visibility.
  • e-Book format: Special Issues with more than 10 articles can be published as dedicated e-books, ensuring wide and rapid dissemination.

Further information on MDPI's Special Issue polices can be found here.

Published Papers (3 papers)

Download All Papers
Order results
Result details
Show export options expand_more Show export options expand_less
Select all
Export citation of selected articles as:

Research

29 pages, 757 KiB  
Article
The Solution of the Extended 16th Hilbert Problem for Some Classes of Piecewise Differential Systems
by Louiza Baymout, Rebiha Benterki and Jaume Llibre
Mathematics 2024, 12(3), 464; https://doi.org/10.3390/math12030464 - 31 Jan 2024
Viewed by 1076
Abstract
The limit cycles have a main role in understanding the dynamics of planar differential systems, but their study is generally challenging. In the last few years, there has been a growing interest in researching the limit cycles of certain classes of piecewise differential [...] Read more.
The limit cycles have a main role in understanding the dynamics of planar differential systems, but their study is generally challenging. In the last few years, there has been a growing interest in researching the limit cycles of certain classes of piecewise differential systems due to their wide uses in modeling many natural phenomena. In this paper, we provide the upper bounds for the maximum number of crossing limit cycles of certain classes of discontinuous piecewise differential systems (simply PDS) separated by a straight line and consequently formed by two differential systems. A linear plus cubic polynomial forms six families of Hamiltonian nilpotent centers. First, we study the crossing limit cycles of the PDS formed by a linear center and one arbitrary of the six Hamiltonian nilpotent centers. These six classes of PDS have at most one crossing limit cycle, and there are systems in each class with precisely one limit cycle. Second, we study the crossing limit cycles of the PDS formed by two of the six Hamiltonian nilpotent centers. There are systems in each of these 21 classes of PDS that have exactly four crossing limit cycles. Full article
(This article belongs to the Special Issue Advances in Chaos Theory and Dynamical Systems)
►▼ Show Figures

Figure 1

19 pages, 735 KiB  
Article
The New Four-Dimensional Fractional Chaotic Map with Constant and Variable-Order: Chaos, Control and Synchronization
by Tareq Hamadneh, Souad Bensid Ahmed, Hassan Al-Tarawneh, Omar Alsayyed, Gharib Mousa Gharib, Maha S. Al Soudi, Abderrahmane Abbes and Adel Ouannas
Mathematics 2023, 11(20), 4332; https://doi.org/10.3390/math11204332 - 18 Oct 2023
Cited by 3 | Viewed by 1237
Abstract
Using fractional difference equations to describe fractional and variable-order maps, this manuscript discusses the dynamics of the discrete 4D sinusoidal feedback sine iterative chaotic map with infinite collapse (ICMIC) modulation map (SF-SIMM) with fractional-order. Also, it presents a novel variable-order version of SF-SIMM [...] Read more.
Using fractional difference equations to describe fractional and variable-order maps, this manuscript discusses the dynamics of the discrete 4D sinusoidal feedback sine iterative chaotic map with infinite collapse (ICMIC) modulation map (SF-SIMM) with fractional-order. Also, it presents a novel variable-order version of SF-SIMM and discusses their chaotic dynamic behavior by employing a distinct function for the variable fractional-order. To establish the existence of chaos in the suggested discrete SF-SIMM, some numerical methods such as phase plots, bifurcation and largest Lyapunov exponent diagrams, C0 complexity and 0–1 test are utilized. After that, two different control schemes are used for the conceived discrete system. The states are stabilized and asymptotically forced towards zero by the first controller. The second controller is used to synchronize a pair of maps with non–identical parameters. Finally, MATLAB simulations will be executed to confirm the results provided. Full article
(This article belongs to the Special Issue Advances in Chaos Theory and Dynamical Systems)
►▼ Show Figures

Figure 1

15 pages, 865 KiB  
Article
The Ergodicity and Sensitivity of Nonautonomous Discrete Dynamical Systems
by Risong Li, Tianxiu Lu, Hongqing Wang, Jie Zhou, Xianfeng Ding and Yongjiang Li
Mathematics 2023, 11(6), 1384; https://doi.org/10.3390/math11061384 - 13 Mar 2023
Cited by 2 | Viewed by 1418
Abstract
Let (E,h1,∞) be a nonautonomous discrete dynamical system (briefly, N.D.D.S.) that is defined by a sequence (hj)j=1∞ of continuous maps hj:E→E over a nontrivial [...] Read more.
Let (E,h1,∞) be a nonautonomous discrete dynamical system (briefly, N.D.D.S.) that is defined by a sequence (hj)j=1∞ of continuous maps hj:E→E over a nontrivial metric space (E,d). This paper defines and discusses some forms of ergodicity and sensitivity for the system (E,h1,∞) by upper density, lower density, density, and a sequence of positive integers. Under some conditions, if the rate of convergence at which (hj)j=1∞ converges to the limit map h is “fast enough” with respect to a sequence of positive integers with a density of one, it is shown that several sensitivity properties for the N.D.D.S. (E,h1,∞) are the same as those properties of the system (E,h). Some sufficient conditions for the N.D.D.S. (E,h1,∞) to have stronger sensitivity properties are also presented. The conditions in our results are less restrictive than those in some existing works, and the conclusions of all the theorems in this paper improve upon those of previous studies. Thus, these results are extensions of the existing ones. Full article
(This article belongs to the Special Issue Advances in Chaos Theory and Dynamical Systems)
►▼ Show Figures

Figure 1

Show export options expand_more Show export options expand_less
Select all
Export citation of selected articles as:
 
Displaying articles 1-3
Back to TopTop