局部耦合的累積和發射的五個振盪器之網路的同步化現象

Abstract

局部耦合的累積和發射的n個振盪器之網路同步化現象的問題，最早被 Mirollo和Strogatz [SIAM J. Appl. Math., 50,1645-1662(1990)]提出。而第一個關於這個問題的部分答案則是被Hung和Juang完成[ Degree of Master,Department of Applied Mathematics in National Chiao Tung University, June(2008)]，他們解決了n=4的問題。在討論n=4和n ≥ 5時，最大的差異之一在於：討論n ≤ 4時，初值中零的個數將滿足一些單調性，但n ≥ 5卻沒有這樣好的性質。而此篇論文將完整討論n=5的情形。

The synchronization problem of the system of n integrate-and-fire oscillators bring locally coupled was first raised by Mirollo and Strogatz [SIAM J.Appl.Math.,50,1645-1662(1990)]. The first work toward solving this studied the problem is done by Hung and Juang, in which they studied the problem for n=4. One of major difference between n=4 and n ≥ 5 is that for n ≤ 4, the number of zeros in its initial states would satisfy some monotonicity property after the case. However, for n ≥ 5such monotonicity property will no longer hold. In this thesis, we are able to solve the case n=5 completely.