Nonlinear Dynamics

, Volume 95, Issue 3, pp 2093–2102 | Cite as

Amplitude death islands in globally delay-coupled fractional-order oscillators

  • Rui Xiao
  • Zhongkui SunEmail author
  • Xiaoli Yang
  • Wei Xu
Original Paper


In this paper, amplitude death (AD) is investigated theoretically and numerically in N globally delay-coupled fractional-order oscillators. Due to the presence of fractional-order derivative and coupling delay, Laplace transform method has been utilized to obtain the characteristic equations. Then, based on Lyapunov stability, we theoretically get the boundaries and number of death islands. It has been found that with the introduction of the fractional-order derivative, many more death islands emerge, and the oscillation quenching dynamics are facilitated. We find AD only occurs between two critical fractional-order derivatives \(\alpha _c^ - \) (lower-bounded value) and \(\alpha _c^ + \) (upper-bounded value) which are affected by natural frequency and system size. With the increment of system size, the oscillation quenching dynamics are weakened. The number of death islands is closely geared to the fractional-order derivative and the system size. Furthermore, the results from numerical simulations best confirm the theoretical analyses.


Coupled oscillators Fractional-order derivative Coupling delay Amplitude death islands 



This work was supported by the National Natural Science Foundation of China (Grant Nos. 11772254, 11742013) and the NPU Foundation for Fundamental Research.

Compliances with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest, with respect to the research, authorship and publication.


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© Springer Nature B.V. 2018

Authors and Affiliations

  1. 1.Department of Applied MathematicsNorthwestern Polytechnical UniversityXi’anPeople’s Republic of China
  2. 2.College of Mathematics and Information ScienceShaan’xi Normal UniversityXi’anPeople’s Republic of China

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