Spatial phase synchronisation of pistachio alternate bearing: Common-noise-induced synchronisation of coupled chaotic oscillators

Abstract

The collective dynamics of chaotic oscillators has drawn considerable attention in numerous fields, including agriculture and forestry. The alternate bearing of tree crops is a phenomenon in which a year of heavy yield is followed by a year of light yield. This phenomenon has been conventionally investigated using a tent map known as a resource budget model. Alternate fruiting is caused by strong synchronisation among trees in an orchard and is a major problem in fruit growing. To develop control methods for alternate fruiting, it is essential to understand the strength of synchronisation at the individual and population levels of trees in orchards and the mechanism of alternate fruiting. In this study, in-phase/out-of-phase analysis was applied to the yield data of a 9562 pistachio (Pistacia vera L.) population, and the phase transitions and mode-locking in the orchard were revealed. Using a developed network model consisting of diffusively coupled chaotic oscillators on which common noise was imposed identically, the phase transitions, mode-locking, and 1/3 power-law scaling spatial correlation were confirmed mathematically. Furthermore, the manner in which three essential factors, i.e. common noise, direct coupling, and the cropping coefficient gradient, explain the spatial synchrony of the orchard was elucidated. The proposed methodology based on nonlinear dynamics would be useful for pomology, forestry, and ecosystem management.