Synchronization or cluster synchronization in coupled Van der Pol oscillators networks with different topological types

Wang, Shuai; Li, Yong

doi:10.1088/1402-4896/ac46f3

Cited by 6 publications

(2 citation statements)

References 23 publications

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“…The mathematical principles behind complex networks can be better understood from the perspective of network dynamics. As the most common collective behavior in network dynamics, synchronization plays an important role in systems engineering [4], ecology [5], and other fields [6][7][8]. Therefore, it is critical to study the intrinsic mechanisms of synchronization phenomena, both in theory and in practice.…”

Section: Introductionmentioning

confidence: 99%

Stochastic synchronization of Kuramoto-oscillator network with pinning control

Zhu,

Li,

Sun

et al. 2024

Phys. Scr.

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The issue of time cost for the Kuramoto-oscillator network synchronization has received widespread attention. However, there is no relevant research on the stochastic synchronization of the Kuramoto-oscillator network with partial uncontrollable oscillators. This article investigates the synchronization problem of the Kuramoto-oscillator network in noisy environments using the pinning control strategy and multilayer distributed control. Previous research requires control of all oscillators, which implies a great control cost. To reduce the control cost, the ﬁnite/ﬁxed time controllers with pinning control are designed to provide the conditions for synchronization in noisy environments, and then the upper bounds on the convergence time of the network are estimated. Finally, numerical simulations are performed to justify the theoretical conclusions.

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Section: Introductionmentioning

confidence: 99%

Stochastic synchronization of Kuramoto-oscillator network with pinning control

Zhu,

Li,

Sun

et al. 2024

Phys. Scr.

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“…It is widely recognized that the communication topology of CDNs is often subject to dynamic changes over time. These changes can also significantly impact the network's behavior and performance [9,10]. The Markovian switch is a commonly used switching mechanism to describe the randomly changing topology of CDNs.…”

Section: Introductionmentioning

confidence: 99%

Mean-square asymptotic synchronization of complex dynamical networks subject to communication delay and switching topology

Wang,

Qin,

et al. 2023

Phys. Scr.

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This paper addresses the issue of mean-square asymptotic synchronization (MSAS) of complex dynamical networks with communication delay and switching topology. The communication delay is assumed to be time-variant and bounded, and the switching topology is governed by a semi-Markovian process and allowed to be asymmetric. A distributed control law based on state feedback is presented. Two criteria for the MSAS are derived using a mode-dependent Lyapunov-Krasovskii functional, the Bessel-Legendre integral inequality, and a parameter-dependent convex combination inequality, for the asymmetric and symmetric topology cases, respectively. The scenario of fixed topology is also considered, for which two asymptotic synchronization criteria are proposed. Two simulation examples are provided to illustrate the effectiveness and reduced conservatism of the proposed theoretical results.

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Multi-type synchronization for coupled van der Pol oscillator systems with multiple coupling modes

Wang,

Yang

2024

Chaos: An Interdisciplinary Journal of Nonlinear Science

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In this paper, we investigate synchronous solutions of coupled van der Pol oscillator systems with multiple coupling modes using the theory of rotating periodic solutions. Multiple coupling modes refer to two or three types of coupling modes in van der Pol oscillator networks, namely, position, velocity, and acceleration. Rotating periodic solutions can represent various types of synchronous solutions corresponding to different phase differences of coupled oscillators. When matrices representing the topology of different coupling modes have symmetry, the overall symmetry of the oscillator system depends on the intersection of the symmetries of the different topologies, determining the type of synchronous solutions for the coupled oscillator network. When matrices representing the topology of different coupling modes lack symmetry, if the adjacency matrices representing different coupling modes can be simplified into structurally identical quotient graphs (where weights can be proportional) through the same external equitable partition, the symmetry of the quotient graph determines the synchronization type of the original system. All these results are consistent with multi-layer networks where connections between different layers are one-to-one.

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Synchronization or cluster synchronization in coupled Van der Pol oscillators networks with different topological types

Cited by 6 publications

References 23 publications

Stochastic synchronization of Kuramoto-oscillator network with pinning control

Stochastic synchronization of Kuramoto-oscillator network with pinning control

Mean-square asymptotic synchronization of complex dynamical networks subject to communication delay and switching topology

Multi-type synchronization for coupled van der Pol oscillator systems with multiple coupling modes

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