Persistent synchronization of heterogeneous networks with time-dependent linear diffusive coupling
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arXiv
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| Format: | Preprint |
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2023
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| _version_ | 1866929552452747264 |
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| author | Jardón-Kojakhmetov, Hildeberto Kuehn, Christian Longo, Iacopo P. |
| author_facet | Jardón-Kojakhmetov, Hildeberto Kuehn, Christian Longo, Iacopo P. |
| contents | We study synchronization for linearly coupled temporal networks of heterogeneous time-dependent nonlinear agents via the convergence of attracting trajectories of each node. The results are obtained by constructing and studying the stability of a suitable linear nonautonomous problem bounding the evolution of the synchronization errors. Both, the case of the entire network and only a cluster, are addressed and the persistence of the obtained synchronization against perturbation is also discussed. Furthermore, a sufficient condition for the existence of attracting trajectories of each node is given. In all cases, the considered dependence on time requires only local integrability, which is a very mild regularity assumption. Moreover, our results mainly depend on the network structure and its properties, and achieve synchronization up to a constant in finite time. Hence they are quite suitable for applications. The applicability of the results is showcased via several examples: coupled van-der-Pol/FitzHugh-Nagumo oscillators, weighted/signed opinion dynamics, and coupled Lorenz systems. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2305_05747 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Persistent synchronization of heterogeneous networks with time-dependent linear diffusive coupling Jardón-Kojakhmetov, Hildeberto Kuehn, Christian Longo, Iacopo P. Dynamical Systems Multiagent Systems 34A34, 37C60, 34A12 We study synchronization for linearly coupled temporal networks of heterogeneous time-dependent nonlinear agents via the convergence of attracting trajectories of each node. The results are obtained by constructing and studying the stability of a suitable linear nonautonomous problem bounding the evolution of the synchronization errors. Both, the case of the entire network and only a cluster, are addressed and the persistence of the obtained synchronization against perturbation is also discussed. Furthermore, a sufficient condition for the existence of attracting trajectories of each node is given. In all cases, the considered dependence on time requires only local integrability, which is a very mild regularity assumption. Moreover, our results mainly depend on the network structure and its properties, and achieve synchronization up to a constant in finite time. Hence they are quite suitable for applications. The applicability of the results is showcased via several examples: coupled van-der-Pol/FitzHugh-Nagumo oscillators, weighted/signed opinion dynamics, and coupled Lorenz systems. |
| title | Persistent synchronization of heterogeneous networks with time-dependent linear diffusive coupling |
| topic | Dynamical Systems Multiagent Systems 34A34, 37C60, 34A12 |
| url | https://arxiv.org/abs/2305.05747 |