Constant Production in an Orchard: An interaction-based approach

Alternate bearing, the cyclic pattern of heavy and light fruit crops in fruit species, is a complex phenomenon influenced by both internal and external influences in an orchard. The impact of direct interactions practically realized through grafting and indirect interactions, which would be practically realized through pollination between two plants using the resource budget model was introduced in Prasad et al. (2017). We have observed a fascinating phenomenon in our study, where the introduction of mixed interaction (direct and indirect) within a coupled map lattice not only fosters intricate dynamics but also gives rise to the intriguing concept of anti-synchronization. This remarkable phenomenon entails a synchronized pattern among paired plants, wherein one plant yields a crop in a given year while the other plant in the subsequent year. In an orchard comprising 2L2 trees, grafting, and pollination result in a distinct temporal pattern. Specifically, during a given period, approximately L2 trees undergo an on-year, while the remaining trees experience an off-year. This cyclic alternation enables the total production of 2L2 trees to remain constant each year. We utilized two coupled tent map systems to derive the condition for the stability of the onset of the anti-synchronization state analytically. Our findings demonstrate that the strength of interaction plays a significant role in the occurrence of anti-synchronization thereby controlling alternate bearing. In general, our results provide insights into the interactions involved in the phenomenon of alternate bearing in an orchard and may have practical implications for sustainable and efficient crop production.