메뉴 건너뛰기




Volumn 54, Issue 3, 1996, Pages 2334-2350

Synchronization of integrate and fire oscillators with global coupling

Author keywords

[No Author keywords available]

Indexed keywords


EID: 0001671620     PISSN: 1063651X     EISSN: None     Source Type: Journal    
DOI: 10.1103/physreve.54.2334     Document Type: Article
Times cited : (35)

References (66)
  • 13
    • 0009747213 scopus 로고
    • edited by Simon A. Levin, Lecture Notes in Biomathematics Springer, Berlin
    • S. Strogatz, in Frontiers in Mathematical Biology, edited by Simon A. Levin, Lecture Notes in Biomathematics Vol. 100 (Springer, Berlin, 1993).
    • (1993) Frontiers in Mathematical Biology , vol.100
    • Strogatz, S.1
  • 15
    • 0000254372 scopus 로고
    • T. Walker, Science 166, 891 (1969).
    • (1969) Science , vol.166 , pp. 891
    • Walker, T.1
  • 34
    • 0010160412 scopus 로고
    • H. Smith, Science 82, 151 (1935).
    • (1935) Science , vol.82 , pp. 151
    • Smith, H.1
  • 35
    • 0003913214 scopus 로고
    • Courant Institute of Mathematical Sciences, New York University, New York
    • C. Peskin, Mathematical Aspects of Heart Physiology, Courant Institute of Mathematical Sciences, New York University, New York, 1975.
    • (1975) Mathematical Aspects of Heart Physiology
    • Peskin, C.1
  • 55
    • 5544312572 scopus 로고
    • Ph.D. thesis, University of Aarhus, Denmark
    • K. Christensen, Ph.D. thesis, University of Aarhus, Denmark, 1992, p.49.
    • (1992) , pp. 49
    • Christensen, K.1
  • 61
    • 5544241047 scopus 로고    scopus 로고
    • note
    • In [36], Mirollo and Strogatz speak of positive feedback but this effect plays no role in the demonstration of their theorem. This is why the case of linear oscillators seemed to be excluded from synchronization by their theorem.
  • 63
    • 5544258719 scopus 로고    scopus 로고
    • note
    • In [36] Mirollo and Strogatz explicitly state the absorption rule but only for a system with numerous oscillators. Since their proof of synchronization is inductive with the system of two oscillators as anchor it is important to realize that absorption is actually necessary for synchronization also for a pair of oscillators.
  • 64
    • 85087580292 scopus 로고    scopus 로고
    • In [55], Christensen concluded also that synchronization requires
    • c≥1/N.
    • c≥1/N
  • 65
    • 5544280667 scopus 로고    scopus 로고
    • note
    • By adaptation of the frequencies we mean as in [12] a "learning" mechanism, where the oscillators are allowed to modify their intrinsic frequencies in order to match with an exterior periodic stimulus.
  • 66
    • 5544230069 scopus 로고    scopus 로고
    • note
    • Synchronization with a general shape E(φ) has been also recently proven by Corral et al. [38] in the case of oscillators with adequate response function to pulses. A response function chosen so that the phase advance caused by a pulse gets larger towards the threshold is equivalent to a convex E(φ).


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.