Ryusuke Kon
(Kyushu University)

09/3/16, 16:00 - 17:00 at Room 3631 (6th floor of building 3 of the Faculty of Sciences)

An insect is said to be periodical if the life cycle has a fixed length of k years (k>1) and the adults appear synchronously every k-th year. The remarkable examples are 13- and 17-year periodical cicadas inhabiting North America. Using a Leslie matrix model, Bulmer (1977) showed that severe inter-class competition can lead to such temporally synchronous behavior observed in periodical insects. In this talk, I complement his results by constructing an average Liapunov function. This complementary result ensures that the synchronous state, which could include chaotic orbits, is attractive if inter-class competition is sufficiently severe and is repelling if intra-class competition is sufficiently severe.

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