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- W2093560571 abstract "We reconsider the dynamics of pulse-coupled integrate-and-fire neurons analyzed by Mirollo and Strogatz [SIAM J. Appl. Math., 50 (1990), pp. 1645--1662]. Lifting their restriction to identical oscillators, we study the case of different intrinsic frequencies and thresholds of the neurons as well as different but positive couplings. For nonleaky neurons, we prove that generically the dynamics becomes fully synchronous for any initial conditions if the intrinsic frequencies, the thresholds, and the couplings are not too different. For the case of linear evolution functions, this confirms Peskin's conjecture (1975) according to which nearly identical pulse-coupled oscillators, in general, synchronize. It also shows that the requirement of concave evolution functions imposed by Mirollo and Strogatz to ensure global synchronization is not necessary." @default.
- W2093560571 created "2016-06-24" @default.
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- W2093560571 date "2001-01-01" @default.
- W2093560571 modified "2023-09-24" @default.
- W2093560571 title "Similar NonLeaky Integrate-and-Fire Neurons with Instantaneous Couplings Always Synchronize" @default.
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- W2093560571 doi "https://doi.org/10.1137/s0036139998346038" @default.
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