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Fireflies Synchronicity Essay

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Synchronicity In Chaos A study of how a population of fireflies with different frequencies synchronise their frequencies over time Ananya Kaushik BSc. Mathematics 3rd Year SNU ID- AAA0625 Introduction I have picked the topic synchronization in chaos, more specifically I am a studying synchronicity in fireflies. A phenomenon observed by Mirollo and Strogatz [1]in their paper ‘Synchronization of Pulse- Coupled Biological Oscillators’ is that when we see a swarm of fireflies, which start out with different frequencies of blinking, after a period of time, their frequencies get synchronized, ie, they all start blinking or glowing together. In Strogatz paper, he has discussed various applications of this …show more content…

Instead of a line, I considered them to be on a circle so the frequency of the last firefly was updated with the frequency of the first firefly and the cycle could continue for any number of iterations till the frequencies of all the fireflies had very little difference between them. It was made clear in the book that there is a threshold for which synchronization would occur and if the difference was greater than this, the adjacent firefly would fail to catch up and synchronization would not occur. The last paper I studied, generalized this for an even larger number of fireflies and the updation scheme was such that the frequency of one chosen firefly was not only dependent on its neighbor but a number of neighbours on a grid. The program is not finished and is still under construction to make it as efficient and effective as possible. I have attached the draft of the program. Future work- As suggested at the end of Strogatz paper and as done in the paper by Pan-jun Kim, I would like to find out what happens in a lattice of fireflies of any number n. I would also like to understand what would happen if an acceleration term was added to the updation

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