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  • 1
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    Relay interlayer synchronisation: invariance and stability conditions (2022)
    In:  Nonlinearity
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    Publication Date: 2022-03-21
    Description: In this paper, the existence (invariance) and stability (locally and globally) of relay interlayer synchronisation (RIS) are investigated in a chain of multiplex networks. The local dynamics of the nodes in the symmetric positions layers on both sides of the non-identical middlemost layer(s) are identical. The local and global stability conditions for this synchronisation state are analytically derived based on the master stability function approach and by constructing a suitable Lyapunov function, respectively. We propose an appropriate demultiplexing process for the existence of the RIS state. Then the variational equation transverse to the RIS manifold for demultiplexed networks is derived. In numerical simulations, the impact of interlayer and intralayer coupling strengths, variations of the system parameter in the relay layers and demultiplexing on the emergence of RIS in triplex and pentaplex networks are explored. Interestingly, in this multiplex network, enhancement of RIS is observed when a type of impurity via parameter mismatch in the local dynamics of the nodes is introduced in the middlemost layer. A common time-lag with small amplitude shift between the symmetric positions and central layers plays an important role for the enhancing of relay interlayer synchrony. This analysis improves our understanding of synchronisation states in multiplex networks with nonidentical layers.
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  • 2
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    Blinking coupling enhances network synchronization (2022)
    In:  Physical Review E
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    Publication Date: 2023-01-13
    Description: This paper studies the synchronization of a network with linear diffusive coupling, which blinks between the variables periodically. The synchronization of the blinking network in the case of sufficiently fast blinking is analyzed by showing that the stability of the synchronous solution depends only on the averaged coupling and not on the instantaneous coupling. To illustrate the effect of the blinking period on the network synchronization, the Hindmarsh-Rose model is used as the dynamics of nodes. The synchronization is investigated by considering constant single-variable coupling, averaged coupling, and blinking coupling through a linear stability analysis. It is observed that by decreasing the blinking period, the required coupling strength for synchrony is reduced. It equals that of the averaged coupling model times the number of variables. However, in the averaged coupling, all variables participate in the coupling, while in the blinking model only one variable is coupled at any time. Therefore, the blinking coupling leads to an enhanced synchronization in comparison with the single-variable coupling. Numerical simulations of the average synchronization error of the network confirm the results obtained from the linear stability analysis.
    Language: English
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  • 3
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    Converting high-dimensional complex networks to lower-dimensional ones preserving synchronization features (2022)
    In:  EPL (Europhysics Letters)
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    Publication Date: 2023-01-17
    Description: Studying the stability of synchronization of coupled oscillators is one of the prominent topics in network science. However, in most cases, the computational cost of complex network analysis is challenging because they consist of a large number of nodes. This study includes overcoming this obstacle by presenting a method for reducing the dimension of a large-scale network, while keeping the complete region of stable synchronization unchanged. To this aim, the first and last non-zero eigenvalues of the Laplacian matrix of a large network are preserved using the eigen-decomposition method and Gram-Schmidt orthogonalization. The method is only applicable to undirected networks and the result is a weighted undirected network with smaller size. The reduction method is studied in a large-scale a small-world network of Sprott-B oscillators. The results show that the trend of the synchronization error is well maintained after node reduction for different coupling schemes.
    Language: English
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  • 4
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    Equivalent synchronization patterns in chaotic jerk systems (2022)
    In:  EPL (Europhysics Letters)
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    Publication Date: 2023-01-17
    Description: Jerk systems are some of the simplest dynamical systems that can exhibit chaotic dynamics. This paper investigates the synchronization of coupled jerk systems with coupling in single variables. We apply the well-known approach for synchronization analysis, the master stability function, which determines the stability of the synchronization manifold. It is shown that a jerk system in which the jerk equation is not dependent on the acceleration has similar master stability functions when coupled in velocity or acceleration variables. Therefore, the system has the same synchronization behavior in these two coupling configurations. Such an equivalence has not been reported in the literature.
    Language: English
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  • 5
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    Similar Master Stability Functions for Different Coupling Schemes in Basic Chaotic Systems (2023)
    In:  International Journal of Bifurcation and Chaos
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    Publication Date: 2023-11-16
    Description: Tools Share Recommend to Library Abstract Synchronization is a prominent phenomenon in coupled chaotic systems. The master stability function (MSF) is an approach that offers the prerequisites for the stability of complete synchronization, which is dependent on the coupling configuration. In this paper, some basic chaotic systems with the general form of the Sprott-A, Sprott-B, Sprott-D, Sprott-F, Sprott-G, Sprott-O, and Jerk systems are considered. For each system, their parametric form is designed, and constraints required to have similar MSFs in different coupling schemes are determined. Then, the parameters of the designed chaotic systems are found through an exhaustive computer search seeking chaotic solutions. The simplest cases found in this way are introduced, and similar synchronization patterns are confirmed numerically.
    Language: English
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  • 6
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    Optimal time-varying coupling function can enhance synchronization in complex networks (2023)
    In:  Chaos
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    Publication Date: 2024-03-26
    Description: In this paper, we propose a time-varying coupling function that results in enhanced synchronization in complex networks of oscillators. The stability of synchronization can be analyzed by applying the master stability approach, which considers the largest Lyapunov exponent of the linearized variational equations as a function of the network eigenvalues as the master stability function. Here, it is assumed that the oscillators have diffusive single-variable coupling. All possible single-variable couplings are studied for each time interval, and the one with the smallest local Lyapunov exponent is selected. The obtained coupling function leads to a decrease in the critical coupling parameter, resulting in enhanced synchronization. Moreover, synchronization is achieved faster, and its robustness is increased. For illustration, the optimum coupling function is found for three networks of chaotic Rössler, Chen, and Chua systems, revealing enhanced synchronization.
    Language: English
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