Pattern and waves on 2D-Kuramoto model with many-body interactions

Luo, Hao-jie; Xue, Yu; Huang, Mu-yang; Zhang, Qiang; Zhang, Kun

doi:10.1016/j.chaos.2023.114402

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2024

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“…(i) In the existing research, various network systems with R-Ds have been extensively studied, (but not for DCDNs systems). For example, inertial neural networks (INNs) [18][19][20][21][22], memristor neural networks (MNNs) [23][24][25][26][27][28][29][30], fuzzy systems [31][32][33][34], and Kuramoto model [35,36]. (ii) There are also many results on the dynamical behavior of R-D networks.…”

Section: Introductionmentioning

confidence: 99%

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Edge-Based Synchronization Control Criteria of Complex Dynamical Networks with Reaction–Diffusions

Xie,

Zhang,

Xiong

2024

Mathematics

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This research investigates the edge-based asymptotic synchronization of delayed complex dynamical networks with reaction–diffusions and by an edge-based adaptive pinning control technique. Sufficient conditions for reaction–diffusion networks to realize synchronization are provided by Green’s formula, Wirtinger inequality, inequality analysis techniques, and contradiction methods. The results show that network synchronization can be achieved by pinning any edge of the network (the choice of edge is arbitrary), which greatly reduces the difficulty of control. Lastly, a series of numerical examples illustrating the theoretical findings is provided.

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Section: Introductionmentioning

confidence: 99%

“…A control method, the edge-based adaptive pinning control, is adopted. It combines the advantages of adaptive control [26,32,36] and pinning control [4,11,20,25,30,33]. Further using the coupling effect of the network edge structure, the network synchronization can be realized only by pinning one edge of the networks, and this edge is arbitrarily selected.…”

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confidence: 99%