| Summary: | 碩士 === 國立臺北科技大學 === 電機工程系所 === 97 === The thesis is devoted to the investigation of flash synchronization for a population of fireflies. Peskin model, namely Integrate-and-Fire model, is the earliest one used to describe the flash behavior of fireflies. Each firefly is assumed that it owns a voltage-like potential, and piles up this variable monotonously. When its voltage passes the threshold, the firefly sends out the flash of light to affect the neighboring fireflies. The flashing process of firefly repeats its period again and again. When many fireflies get together, they will become a network. In Mirollo, Strogatz, and Peskin’s article, the flashings which influence the neighboring fireflies are regarded as a certain amount in all-to-all network; the whole network will only synchronize in the finite time. We think that the fireflies are like a biological system with the self-regulating mechanisms. In its effecting regulation, there are likely two possibilities: hurry up and slow down. If other firefly’s firing (flash) reveals its own potential highly, we hope to increase our value in order to catch up with others’. Conversely, if the potential is in low state, we expect to reduce the accumulating speed which helps others close to us. By this opinion, we could improve the coupling method a little bit. We found out that even in the different network structures, the system will eventually reach the state of synchronization as well. In addition, we also suppose that the coupling strength would be changed according to the different distance, and also verify the two methods as above. The results are shown that our approach still fulfill the synchronization.
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