Takuji Kousaka, Tetsushi Ueta, Hiroshi Kawakami, Synchronization of Electric Fireflies by using Square Wave Generators, Institute of Electronics, Information and Communication Engineers, IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences, Vol.E81-A, No.5, pp.656-663, Apr. 1998.
Abstract: In this article, we propose a square wave generator whose switching threshold values are switched by external inputs. This circuit is designed to simulate the synchronized luminescence of coupled fireflies. We investigate the behavior of the solutions in two coupled oscillators. The dynamics are demonstrated by a linear autonomous equation piecewisely, therefore, a one-dimensional return map is derived. We also prove the existence of stable in-phase synchronization in the coupled oscillator by using the return map, and we show the existence of regions of periodic solutions within a parameter space. Some theoretical results are confirmed by laboratory measurements.