Synchronous/asynchronous patterns in three-cell networks with multiple time delays

Yuan Yuan, Lei Li

Research output: Contribution to journalArticlepeer-review


Some patterns of synchrony/asynchrony in the dynamics of coupled cell systems can be predicted by symmetry. However, in the system without symmetry, the different patterns of periodic solutions may exist as well. We consider a general model including three cells with multiple time delays that connect in any possible manner. Our approach is based on the analytic construction by using a perturbation procedure together with the Fredholm alternative theory. Then we employ the PoincaréLindstedt series expansion to compute the Floquet exponents which determine the stability. Finally, we resort to numerical computation to get some insights about the leading term in the Floquet exponents, and the numerical simulations are given to confirm the theoretical results.
Original languageEnglish
Pages (from-to)1701-1718
Number of pages18
JournalInternational Journal of Bifurcation and Chaos in Applied Sciences and Engineering
Issue number6
Publication statusPublished - 2011
Externally publishedYes


  • asynchronous
  • Floquet theory
  • mirror-reflecting solutions
  • Neural networks
  • phase-locked solutions
  • standing wave solutions


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