Generic behavior of master-stability functions in coupled nonlinear dynamical systems

Liang Huang, Qingfei Chen, Ying-Cheng Lai, Louis M. Pecora

Research output: Contribution to journalArticlepeer-review

224 Citations (Scopus)


Master-stability functions (MSFs) are fundamental to the study of synchronization in complex dynamical systems. For example, for a coupled oscillator network, a necessary condition for synchronization to occur is that the MSF at the corresponding normalized coupling parameters be negative. To understand the typical behaviors of the MSF for various chaotic oscillators is key to predicting the collective dynamics of a network of these oscillators. We address this issue by examining, systematically, MSFs for known chaotic oscillators. Our computations and analysis indicate that it is generic for MSFs being negative in a finite interval of a normalized coupling parameter. A general scheme is proposed to classify the typical behaviors of MSFs into four categories. These results are verified by direct simulations of synchronous dynamics on networks of actual coupled oscillators.

Original languageEnglish
Article number036204
Number of pages11
JournalPhysical Review. E, Statistical, Nonlinear and Soft Matter Physics
Issue number3
Publication statusPublished - Sept 2009


  • chaos
  • nonlinear dynamical systems
  • oscillators
  • synchronisation
  • chaotic systems
  • synchronization
  • networks


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