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Entropy
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Advances in Nonlinear Dynamical Systems and Chaos
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Advances in Nonlinear Dynamical Systems and Chaos

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

Deadline for manuscript submissions: 15 July 2024 | Viewed by 2961

Special Issue Editor

Dr. Sadataka Furui

E-Mail Website
Guest Editor
Faculty of Science and Engineering, Teikyo University, Utsunomiya 320-8551, Japan
Interests: nonlinear differential equation; bifurcation; Chua’s nonlinear circuit; lattice simulation; soliton
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

Nonlinear differential equations cause periodic or nonperiodic oscillations, bifurcations to other oscillation modes, and unstable or chaotic oscillations. To analyze these phenomena mathematically, the topological degree approach, through introducing differentiable stable manifolds and unstable manifolds immersed in a system of diffeomorphic mapping, was successful.

A set of solutions of the partial differential equation ψ(x,t) may describe the evolution of a spatially extended system in the vicinity of a Hopf bifurcation, and spatiotemporal chaos described by an ordinary differential equation could appear.

Phenomenologically, the time dependence of electronic current and voltage revealed an interesting pattern of bifurcation and chaotic oscillations. Pinched hysteresis loops in current–voltage space characterize the nonlinear properties of a memristor.

When an analytical solution of a differential equation is difficult, the topological properties of a discretized lattice calculation can be analyzed in neural networks via using a machine learning technique.

This Special Issue aims to shed light on the old problems of nonlinear dynamics, such as bifurcation and chaos from mathematically well-defined frameworks, and discuss new experimental results.

Dr. Sadataka Furui
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. 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 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

  • topological degree approach
  • Hopf bifurcation
  • chaos
  • hysteresis
  • memristor

Published Papers (3 papers)

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Research

17 pages, 2848 KiB  
Article
A Nonlinear Local Approximation Approach for Catchment Classification
by Shakera K. Khan and Bellie Sivakumar
Entropy 2024, 26(3), 218; https://doi.org/10.3390/e26030218 - 29 Feb 2024
Viewed by 906
Abstract
Catchment classification plays an important role in many applications associated with water resources and environment. In recent years, several studies have applied the concepts of nonlinear dynamics and chaos for catchment classification, mainly using dimensionality measures. The present study explores prediction as a [...] Read more.
Catchment classification plays an important role in many applications associated with water resources and environment. In recent years, several studies have applied the concepts of nonlinear dynamics and chaos for catchment classification, mainly using dimensionality measures. The present study explores prediction as a measure for catchment classification, through application of a nonlinear local approximation prediction method. The method uses the concept of phase-space reconstruction of a time series to represent the underlying system dynamics and identifies nearest neighbors in the phase space for system evolution and prediction. The prediction accuracy measures, as well as the optimum values of the parameters involved in the method (e.g., phase space or embedding dimension, number of neighbors), are used for classification. For implementation, the method is applied to daily streamflow data from 218 catchments in Australia, and predictions are made for different embedding dimensions and number of neighbors. The prediction results suggest that phase-space reconstruction using streamflow alone can provide good predictions. The results also indicate that better predictions are achieved for lower embedding dimensions and smaller numbers of neighbors, suggesting possible low dimensionality of the streamflow dynamics. The classification results based on prediction accuracy are found to be useful for identification of regions/stations with higher predictability, which has important implications for interpolation or extrapolation of streamflow data. Full article
(This article belongs to the Special Issue Advances in Nonlinear Dynamical Systems and Chaos)
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14 pages, 440 KiB  
Article
Distributed Dynamic Event-Triggered Control to Leader-Following Consensus of Nonlinear Multi-Agent Systems with Directed Graphs
by Jia-Cheng Guan, Hong-Wei Ren and Guo-Liang Tan
Entropy 2024, 26(2), 113; https://doi.org/10.3390/e26020113 - 26 Jan 2024
Viewed by 789
Abstract
This paper investigates achieving leader-following consensus in a class of multi-agent systems with nonlinear dynamics. Initially, it introduces a dynamic event-triggered strategy designed to effectively alleviate the strain on the system’s communication resources. Subsequently, a distributed control strategy is proposed and implemented in [...] Read more.
This paper investigates achieving leader-following consensus in a class of multi-agent systems with nonlinear dynamics. Initially, it introduces a dynamic event-triggered strategy designed to effectively alleviate the strain on the system’s communication resources. Subsequently, a distributed control strategy is proposed and implemented in the nonlinear leader-follower system using the dynamic event-triggered mechanism, aiming to ensure synchronization across all nodes at an exponential convergence speed. Thirdly, the research shows that under the dynamic event-triggered strategy the minimum event interval of any two consecutive triggers guarantees the elimination of Zeno behavior. Lastly, the validity of the calculation results is verified by a simulation example. Full article
(This article belongs to the Special Issue Advances in Nonlinear Dynamical Systems and Chaos)
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12 pages, 471 KiB  
Article
A Note on Stronger Forms of Sensitivity for Non-Autonomous Dynamical Systems on Uniform Spaces
by Lixin Jiao, Heyong Wang, Lidong Wang and Nan Wang
Entropy 2024, 26(1), 47; https://doi.org/10.3390/e26010047 - 02 Jan 2024
Viewed by 791
Abstract
This paper introduces the notion of multi-sensitivity with respect to a vector within the context of non-autonomous dynamical systems on uniform spaces and provides insightful results regarding N-sensitivity and strongly multi-sensitivity, along with their behaviors under various conditions. The main results established [...] Read more.
This paper introduces the notion of multi-sensitivity with respect to a vector within the context of non-autonomous dynamical systems on uniform spaces and provides insightful results regarding N-sensitivity and strongly multi-sensitivity, along with their behaviors under various conditions. The main results established are as follows: (1) For a k-periodic nonautonomous dynamical system on a Hausdorff uniform space (S,U), the system (S,fk∘⋯∘f1) exhibits N-sensitivity (or strongly multi-sensitivity) if and only if the system (S,f1,∞) displays N-sensitivity (or strongly multi-sensitivity). (2) Consider a finitely generated family of surjective maps on uniform space (S,U). If the system (S,f1,∞) is N-sensitive, then the system (S,fk,∞) is also N-sensitive. When the family f1,∞ is feebly open, the converse statement holds true as well. (3) Within a finitely generated family on uniform space (S,U), N-sensitivity (and strongly multi-sensitivity) persists under iteration. (4) We present a sufficient condition under which an nonautonomous dynamical system on infinite Hausdorff uniform space demonstrates N-sensitivity. Full article
(This article belongs to the Special Issue Advances in Nonlinear Dynamical Systems and Chaos)
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