arXiv subjects

Rui Kato

Publications and source records attributed to Rui Kato.

3 recordsLinked to original sources

arXiv2025

Cluster Synchronization and Phase Cohesiveness of Kuramoto Oscillators via Mean-phase Feedback Control and Pacemakers

Brain networks typically exhibit characteristic synchronization patterns where several synchronized clusters coexist. On the other hand, neurological disorders are considered to be related to pathological synchronization such as excessive synchronization of large populations of neurons. Motivated by these phenomena, this paper presents two approaches to control the cluster synchronization and the cluster phase cohesiveness of Kuramoto oscillators. One is based on feeding back the mean phases to the clusters, and the other is based on the use of pacemakers. First, we show conditions on the feedback gains and the pacemaker weights for the network to achieve cluster synchronization. Then, we propose a method to find optimal feedback gains through convex optimization. Second, we show conditions on the feedback gains and the pacemaker weights for the network to achieve cluster phase cohesiveness. A numerical example demonstrates the effectiveness of the proposed methods.

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arXiv2022

Cluster Synchronization of Kuramoto Oscillators and the Method of Averaging

Rigorous conditions for cluster synchronization of Kuramoto oscillators are presented. The method of averaging plays an important role in stability analysis, but the standard Lyapunov's second method is not applicable due to the lack of uniform continuity. This paper contributes to overcoming this difficulty with the help of nonmonotonic Lyapunov functions. Our extensions of averaging in stability theory are key to derive the two interrelated cluster synchronization conditions: (i) the coupling strengths between clusters are sufficiently weak and/or (ii) the natural frequencies are largely different between clusters. Cluster phase cohesiveness in the absence of network partitions ensuring the existence of invariant manifolds is also investigated. Moreover, we apply our theoretical findings to brain networks and exhibit certain relations among network parameters and functional connectivity.

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arXiv2020

Linearization-Based Quantized Stabilization of Nonlinear Systems Under DoS Attacks

Motivated by recent security issues in cyber-physical systems, this technical note studies the stabilization problem of networked control systems under Denial-of-Service (DoS) attacks. In particular, we consider to stabilize a nonlinear system with limited data rate via linearization. We employ a deterministic DoS attack model constrained in terms of attacks' frequency and duration, allowing us to cover a large class of potential attacks. To achieve asymptotic stabilization, we propose a resilient dynamic quantizer in the sense that it does not saturate in the presence of packet losses caused by DoS attacks. A sufficient condition for stability is derived by restricting the average DoS frequency and duration. In addition, because of the locality of linearization, we explicitly investigate an estimate of the region of attraction, which can be expected to be reduced depending on the strength of DoS attacks. A simulation example is presented for demonstration of our results.

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