Synchronization of pulse-coupled oscillators to a global pacemaker

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• 作者：Felipe Nú ; ñ ; ez^a ; ^b ; ^{fenunez@ing.puc.cl" class="auth_mail" title="E-mail the corresponding author} ; Yongqiang Wang^c ; ^{yongqiw@clemson.edu" class="auth_mail" title="E-mail the corresponding author} ; Andrew R. Teel^a ; ^{teel@ece.ucsb.edu" class="auth_mail" title="E-mail the corresponding author} ; Francis J. Doyle III^a ; ^d ; ^{frank_doyle@seas.harvard.edu" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Pulse-coupled oscillators ; Synchronization ; Phase models ; Phase response curve
• 刊名：Systems & Control Letters
• 出版年：2016
• 出版时间：February 2016
• 年：2016
• 卷：88
• 期：Complete
• 页码：75-80
• 全文大小：1605 K

文摘

Pulse-coupled oscillators (PCOs) are limit cycle oscillators coupled by exchanging pulses at discrete time instants. Their importance in biology and engineering has motivated numerous studies aiming to understand the basic synchronization properties of a network of PCOs. In this work, we study synchronization of PCOs subject to a global pacemaker (or global cue) and local interactions between slave oscillators. We characterize solutions and give synchronization conditions using the phase response curve (PRC) as the design element, which is restricted to be of the delay type in the first half of the cycle, interval class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0167691115002431&_mathId=si13.gif&_user=111111111&_pii=S0167691115002431&_rdoc=1&_issn=01676911&md5=3512b907ffd78a43bd59a68448cb0193" title="Click to view the MathML source">(0,π)class="mathContainer hidden">class="mathCode">$(0,\pi )$, and of the advance type in the second half of the cycle, interval class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0167691115002431&_mathId=si14.gif&_user=111111111&_pii=S0167691115002431&_rdoc=1&_issn=01676911&md5=699c1be091f97a126301391a71cd7a47" title="Click to view the MathML source">(π,2π)class="mathContainer hidden">class="mathCode">$(\pi ,2\pi )$. It is shown that global synchronization is feasible when using an advance-delay PRC if the influence of the global cue is strong enough. Numerical examples are provided to illustrate the analytical findings.