A group of Professor Kenji Sakai (Department of Agricultural Environmental Engineering) of the Graduate School of Agriculture, Tokyo University of Agriculture and Technology has been investigating the fruiting situation of zelkova trees in Fuchu City, Tokyo since 2002, and zelkova trees in front of the Tokyo Metropolitan Government since 2003. Together with a group of Professor Yoshinobu (Department of Natural Environment Conservation) and others, these 15-year observation data revealed that the two populations are completely synchronized on a three-year cycle basis.
Professor Sakai and his colleagues are conducting interdisciplinary research on various chaos synchronization phenomena, including the fertility phenomenon of perennial plants, in collaboration with Associate Professor Prasad, a nonlinear physicist in the Department of Astronomy and Physics, University of Delhi, India.
When plotting the fruiting level of zelkova individuals every year, most of them are individuals with a three-year cycle in both Fuchu and Shinjuku.Furthermore, in this study, the Hilbert transform was used to plot the phase (which phase of the cycle) of the moment (yearly) on the circumference of all zelkova individuals.As a result, it was found that the fertility of Fuchu and Shinjuku as a population was the same in all years.
Next, I investigated why the synchronization is a three-year cycle.When plotting the amount of substance accumulated in the tree of the current year and the amount of substance accumulated in the tree three years after the current year, it touches a straight line of 3 degrees at three points.This state is called "island of period 3 floating in the sea of chaos", "window of period 45", etc., and Li-Yorke's theorem "period 3 means chaos" which can be said to be the basis of chaos theory: Period three implies chaos. "Is said to indicate that it holds true even in a row of zelkova trees.
Furthermore, this study also showed that the mechanism governing the synchronization of the zelkova population is equivalent to the switching circuit of the AC-DC converter.It became clear that a common mathematics lurks behind completely different research subjects of nonlinear physics and conservation ecology.
In the future, he says that he will continue to demonstrate the unified theory of fertility synchronization of other major fruit trees and forest trees, and develop research into the relationship between the emergence of wild animals and fertility synchronization.
Paper information:[Scientific Reports] Period-3 dominant phase synchronization of Zelkova serrata: border-collision bifurcation observed in a plant population
