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Synchronization in oscillator networks with time delay and limited non-homogeneous coupling strength

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Abstract

Motivated by the needs of multi-agent systems in the presence of sensing and communication which is delayed, intermittent, and asynchronous, we present a Kuramoto-type model as the delay inherent in such systems is taken into account. First, we have investigated a condition on maximum delay for the frequency entrainment of non-identical Kuramoto oscillators with heterogeneous delays and a constant coupling gain. Our next mission is to investigate the model of delayed coupled Kuramoto oscillators, which are characterized by non-identical natural frequencies and non-homogeneous coupling strength. We assume that the difference between the coupling gains is less than a certain limited value \(M\), and on the basis of Lyapunov stability theorem, we present a strictly positive lower bound for \(M\) to achieve a consensus on the derivatives of the phases. This consensus property is even more surprising because the phases themselves do not necessarily reach a consensus. We apply our results to these oscillators and show that synchronization is guaranteed for appropriate initial conditions.

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Authors and Affiliations

  1. Department of Electrical Engineering, Mashhad Branch, Islamic Azad University, Mashhad, Iran

    M. Tousi & R. Kardehi Moghaddam

  2. Department of Electrical Engineering, Ferdowsi University of Mashhad, Mashhad, Iran

    N. Pariz

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  1. M. Tousi
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  2. R. Kardehi Moghaddam
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  3. N. Pariz
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Correspondence to M. Tousi.

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Tousi, M., Kardehi Moghaddam, R. & Pariz, N. Synchronization in oscillator networks with time delay and limited non-homogeneous coupling strength. Nonlinear Dyn 82, 1–8 (2015). https://doi.org/10.1007/s11071-015-2133-y

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  • DOI: https://doi.org/10.1007/s11071-015-2133-y

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