Direct coupling: a possible strategy to control fruit production in alternate bearing

Abstract

We investigated the theoretical possibility of applying phenomenon of synchronization of coupled nonlinear oscillators to control alternate bearing in citrus. The alternate bearing of fruit crops is a phenomenon in which a year of heavy yield is followed by an extremely light one. This phenomenon has been modeled previously by the resource budget model, which describes a typical nonlinear oscillator of the tent map type. We have demonstrated how direct coupling, which could be practically realized through grafting, contributes to the nonlinear dynamics of alternate bearing, especially phase synchronization. Our results show enhancement of out-of-phase synchronization in production, which depends on initial conditions obtained under the given system parameters. Based on these numerical experiments, we propose a new method to control alternate bearing, say in citrus, thereby enabling stable fruit production. The feasibility of validating the current results through field experimentation is also discussed.

Dispersal of allergenic pollen from Cryptomeria japonica and Chamaecyparis obtusa: characteristic annual fluctuation patterns caused by intermittent phase synchronisations

“…Prasad et al . 28 expressed phase differences as in-phase and out-of-phase to quantify the extent of phase synchronisation. Fist, is defined as follows;…”

Period-3 dominant phase synchronisation of Zelkova serrata: border-collision bifurcation observed in a plant population

“…Given that we focused on the phase synchronisation, we employed the notion of in-phase and out-of-phase analysis 22 . The fraction of in-phase in a population { x i ( t ); i = 1, 2, …, N , t = 1, 2…, T } is also used 22 to measure the phase synchronisation of a population of trees. If the arbitrary pair of x i ( t ) and x j ( t ) show in-phase behaviour between year t and year t + 1, then…”

“…In nonlinear physics, the synchronisation of ensembles of oscillators is known to be caused by mutual coupling or common identical noise 20,21 . Many types of coupling, such as indirect global and local coupling 16–19 and direct coupling 22 , have been investigated. The common noise-induced synchrony 23–27 is known as the Moran effect in population ecology.…”

Density Dependent Resource Budget Model for Alternate Bearing

“…The Resource Budget Model belongs to the cat-51 egory of tent maps for which there is no stable period-2 so-52 lution at the level of individual tree (except at the bifurcation 53 point). Systems of two trees do have an in-phase period-2 so-54 lution, but it is only stable if the trees are coupled via indirect 55 (mean-field) coupling, as with pollination, and not for trees 56 coupled directly (diffusively) through local interactions like 57 root grafting (Prasad et al, 2017). Together, these features 58 make the Resource Budget Model a simple and successful 59 Figure 1: The orbit diagram of the Resource Budget Model shows that the dynamics of the system goes from a stable fixed point for the depletion coefficient, < 1, to period-four oscillation for a very small range of and then quickly leading to chaos.…”

“…The trees planted in proximity to one another 350 interact in complex ways including exchanging their carbon 351 through root grafts (Klein et al, 2016). Grafting is known as 352 direct interaction or diffusive coupling (Prasad et al, 2017). 353 Trees also interact through pollination via external agents 354 (e.g.…”