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Entropy
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Synchronization in Complex Networks of Nonlinear Dynamical Systems
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Synchronization in Complex Networks of Nonlinear Dynamical Systems

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

Deadline for manuscript submissions: closed (30 April 2023) | Viewed by 9279

Special Issue Editors

Dr. Ralf Toenjes

E-Mail Website
Guest Editor
Institute of Physics and Astronomy, Potsdam University, 14476 Potsdam-Golm, Germany
Interests: synchronization; stochastic processes; networks
Dr. Igor Franović

E-Mail Website
Guest Editor
Scientific Computing Laboratory, Center for the Study of Complex Systems, Institute of Physics Belgrade, University of Belgrade, Pregrevica 118, Belgrade 11080, Serbia
Interests: nonlinear dynamics; stochastic processes; dynamics of complex networks

Special Issue Information

Dear Colleagues,

The mathematical abstraction of networks is a hugely successful tool for describing the structure of complex systems through the relations of their parts. When the parts of a complex system evolve with characteristic intrinsic frequencies, interaction through a network can lead to alterations in frequencies, phases and amplitudes. These effects, broadly studied under the topic of synchronization, are essential for the function, i.e., the global behavior, of complex systems. Recent years have seen a push to generalize networks to non-binary interactions and characterize new effects specific to higher-order interactions. This Special Issue of Entropy aims to present new results on the interplay of network structure, including network motifs, and dynamics.

Dr. Ralf Toenjes
Dr. Igor Franović
Guest Editors

Manuscript Submission Information

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Keywords

  • synchronization
  • remote synchronization
  • control of synchronization
  • network motifs
  • networks
  • complex networks
  • networks of networks
  • generalized networks
  • non-pairwise interaction
  • dynamics of networks

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Published Papers (6 papers)

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Research

17 pages, 2150 KiB  
Article
Synchronization Induced by Layer Mismatch in Multiplex Networks
by Md Sayeed Anwar, Sarbendu Rakshit, Jürgen Kurths and Dibakar Ghosh
Entropy 2023, 25(7), 1083; https://doi.org/10.3390/e25071083 - 19 Jul 2023
Cited by 3 | Viewed by 1359
Abstract
Heterogeneity among interacting units plays an important role in numerous biological and man-made complex systems. While the impacts of heterogeneity on synchronization, in terms of structural mismatch of the layers in multiplex networks, has been studied thoroughly, its influence on intralayer synchronization, in [...] Read more.
Heterogeneity among interacting units plays an important role in numerous biological and man-made complex systems. While the impacts of heterogeneity on synchronization, in terms of structural mismatch of the layers in multiplex networks, has been studied thoroughly, its influence on intralayer synchronization, in terms of parameter mismatch among the layers, has not been adequately investigated. Here, we study the intralayer synchrony in multiplex networks, where the layers are different from one other, due to parameter mismatch in their local dynamics. In such a multiplex network, the intralayer coupling strength for the emergence of intralayer synchronization decreases upon the introduction of impurity among the layers, which is caused by a parameter mismatch in their local dynamics. Furthermore, the area of occurrence of intralayer synchronization also widens with increasing mismatch. We analytically derive a condition under which the intralayer synchronous solution exists, and we even sustain its stability. We also prove that, in spite of the mismatch among the layers, all the layers of the multiplex network synchronize simultaneously. Our results indicate that a multiplex network with mismatched layers can induce synchrony more easily than a multiplex network with identical layers. Full article
(This article belongs to the Special Issue Synchronization in Complex Networks of Nonlinear Dynamical Systems)
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11 pages, 614 KiB  
Article
Unveiling the Connectivity of Complex Networks Using Ordinal Transition Methods
by Juan A. Almendral, I. Leyva and Irene Sendiña-Nadal
Entropy 2023, 25(7), 1079; https://doi.org/10.3390/e25071079 - 18 Jul 2023
Cited by 2 | Viewed by 1108
Abstract
Ordinal measures provide a valuable collection of tools for analyzing correlated data series. However, using these methods to understand information interchange in the networks of dynamical systems, and uncover the interplay between dynamics and structure during the synchronization process, remains relatively unexplored. Here, [...] Read more.
Ordinal measures provide a valuable collection of tools for analyzing correlated data series. However, using these methods to understand information interchange in the networks of dynamical systems, and uncover the interplay between dynamics and structure during the synchronization process, remains relatively unexplored. Here, we compare the ordinal permutation entropy, a standard complexity measure in the literature, and the permutation entropy of the ordinal transition probability matrix that describes the transitions between the ordinal patterns derived from a time series. We find that the permutation entropy based on the ordinal transition matrix outperforms the rest of the tested measures in discriminating the topological role of networked chaotic Rössler systems. Since the method is based on permutation entropy measures, it can be applied to arbitrary real-world time series exhibiting correlations originating from an existing underlying unknown network structure. In particular, we show the effectiveness of our method using experimental datasets of networks of nonlinear oscillators. Full article
(This article belongs to the Special Issue Synchronization in Complex Networks of Nonlinear Dynamical Systems)
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11 pages, 797 KiB  
Article
Exponentially Long Transient Time to Synchronization of Coupled Chaotic Circle Maps in Dense Random Networks
by Hans Muller Mendonca, Ralf Tönjes and Tiago Pereira
Entropy 2023, 25(7), 983; https://doi.org/10.3390/e25070983 - 27 Jun 2023
Cited by 4 | Viewed by 1327
Abstract
We study the transition to synchronization in large, dense networks of chaotic circle maps, where an exact solution of the mean-field dynamics in the infinite network and all-to-all coupling limit is known. In dense networks of finite size and link probability of smaller [...] Read more.
We study the transition to synchronization in large, dense networks of chaotic circle maps, where an exact solution of the mean-field dynamics in the infinite network and all-to-all coupling limit is known. In dense networks of finite size and link probability of smaller than one, the incoherent state is meta-stable for coupling strengths that are larger than the mean-field critical coupling. We observe chaotic transients with exponentially distributed escape times and study the scaling behavior of the mean time to synchronization. Full article
(This article belongs to the Special Issue Synchronization in Complex Networks of Nonlinear Dynamical Systems)
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17 pages, 3095 KiB  
Article
Transient Phase Clusters in a Two-Population Network of Kuramoto Oscillators with Heterogeneous Adaptive Interaction
by Dmitry V. Kasatkin and Vladimir I. Nekorkin
Entropy 2023, 25(6), 913; https://doi.org/10.3390/e25060913 - 9 Jun 2023
Cited by 2 | Viewed by 1087
Abstract
Adaptive interactions are an important property of many real-word network systems. A feature of such networks is the change in their connectivity depending on the current states of the interacting elements. In this work, we study the question of how the heterogeneous character [...] Read more.
Adaptive interactions are an important property of many real-word network systems. A feature of such networks is the change in their connectivity depending on the current states of the interacting elements. In this work, we study the question of how the heterogeneous character of adaptive couplings influences the emergence of new scenarios in the collective behavior of networks. Within the framework of a two-population network of coupled phase oscillators, we analyze the role of various factors of heterogeneous interaction, such as the rules of coupling adaptation and the rate of their change in the formation of various types of coherent behavior of the network. We show that various schemes of heterogeneous adaptation lead to the formation of transient phase clusters of various types. Full article
(This article belongs to the Special Issue Synchronization in Complex Networks of Nonlinear Dynamical Systems)
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38 pages, 6107 KiB  
Article
Global Existence and Fixed-Time Synchronization of a Hyperchaotic Financial System Governed by Semi-Linear Parabolic Partial Differential Equations Equipped with the Homogeneous Neumann Boundary Condition
by Chengqiang Wang, Xiangqing Zhao, Yulin Zhang and Zhiwei Lv
Entropy 2023, 25(2), 359; https://doi.org/10.3390/e25020359 - 15 Feb 2023
Cited by 7 | Viewed by 1664
Abstract
Chaotic nonlinear dynamical systems, in which the generated time series exhibit high entropy values, have been extensively used and play essential roles in tracking accurately the complex fluctuations of the real-world financial markets. We are concerned with a system of semi-linear parabolic partial [...] Read more.
Chaotic nonlinear dynamical systems, in which the generated time series exhibit high entropy values, have been extensively used and play essential roles in tracking accurately the complex fluctuations of the real-world financial markets. We are concerned with a system of semi-linear parabolic partial differential equations supplemented by the homogeneous Neumann boundary condition, which governs a financial system comprising the labor force, the stock, the money, and the production sub-blocks distributed in a certain line segment or planar region. The system derived by removing the terms involved with partial derivatives with respect to space variables from our concerned system was demonstrated to be hyperchaotic. We firstly prove, via Galerkin’s method and establishing a priori inequalities, that the initial-boundary value problem for the concerned partial differential equations is globally well posed in Hadamard’s sense. Secondly, we design controls for the response system to our concerned financial system, prove under some additional conditions that our concerned system and its controlled response system achieve drive-response fixed-time synchronization, and provide an estimate on the settling time. Several modified energy functionals (i.e., Lyapunov functionals) are constructed to demonstrate the global well-posedness and the fixed-time synchronizability. Finally, we perform several numerical simulations to validate our synchronization theoretical results. Full article
(This article belongs to the Special Issue Synchronization in Complex Networks of Nonlinear Dynamical Systems)
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18 pages, 3845 KiB  
Article
Dominant Attractor in Coupled Non-Identical Chaotic Systems
by Dorsa Nezhad Hajian, Sriram Parthasarathy, Fatemeh Parastesh, Karthikeyan Rajagopal and Sajad Jafari
Entropy 2022, 24(12), 1807; https://doi.org/10.3390/e24121807 - 11 Dec 2022
Cited by 2 | Viewed by 1697
Abstract
The dynamical interplay of coupled non-identical chaotic oscillators gives rise to diverse scenarios. The incoherent dynamics of these oscillators lead to the structural impairment of attractors in phase space. This paper investigates the couplings of Lorenz–Rössler, Lorenz–HR, and Rössler–HR to identify the dominant [...] Read more.
The dynamical interplay of coupled non-identical chaotic oscillators gives rise to diverse scenarios. The incoherent dynamics of these oscillators lead to the structural impairment of attractors in phase space. This paper investigates the couplings of Lorenz–Rössler, Lorenz–HR, and Rössler–HR to identify the dominant attractor. By dominant attractor, we mean the attractor that is less changed by coupling. For comparison and similarity detection, a cost function based on the return map of the coupled systems is used. The possible effects of frequency and amplitude differences between the systems on the results are also examined. Finally, the inherent chaotic characteristic of systems is compared by computing the largest Lyapunov exponent. The results suggest that in each coupling case, the attractor with the greater largest Lyapunov exponent is dominant. Full article
(This article belongs to the Special Issue Synchronization in Complex Networks of Nonlinear Dynamical Systems)
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