Chaos emerging in soil failure patterns observed during tillage: Normalized deterministic nonlinear prediction (NDNP) and its application.

Real-world processes are often combinations of deterministic and stochastic processes. Soil failure observed during farm tillage is one example of this phenomenon. In this paper, we investigated the nonlinear features of soil failure patterns in a farm tillage process. We demonstrate emerging determinism in soil failure patterns from stochastic processes under specific soil conditions. We normalized the deterministic nonlinear prediction considering autocorrelation and propose it as a robust way of extracting a nonlinear dynamical system from noise contaminated motion. Soil is a typical granular material. The results obtained here are expected to be applicable to granular materials in general. From a global scale to nano scale, the granular material is featured in seismology, geotechnology, soil mechanics, and particle technology. The results and discussions presented here are applicable in these wide research areas. The proposed method and our findings are useful with respect to the application of nonlinear dynamics to investigate complex motions generated from granular materials.

Understanding the alternate bearing phenomenon: Resource budget model.

We consider here the resource budget model of plant energy resources, which characterizes the ecological alternate bearing phenomenon in fruit crops, in which high and low yields occur in alternate years. The resource budget model is a tent-type map, which we study in detail. An infinite number of chaotic bands are observed in this map, which are separated by periodic unstable fixed points. These m bands chaotic attractors become m/2 bands when the period-m unstable fixed points simultaneously collide with the chaotic bands. The distance between two sets of coexisting chaotic bands that are separated by a period-1 unstable fixed point is discussed. We explore the effects of varying a range of parameters of the model. The presented results explain the characteristic behavior of the alternate bearing estimated from the real field data. Effects of noise are also explored. The significance of these results to ecological perspectives of the alternate bearing phenomenon is highlighted.

Limited and time-delayed internal resource allocation generates oscillations and chaos in the dynamics of citrus crops.

Alternate bearing or masting is a yield variability phenomenon in perennial crops. The complex dynamics in this phenomenon have stimulated much ecological research. Motivated by data from an eight-year experiment with forty-eight individual trees, we explored the mechanism inherent to these dynamics in Satsuma mandarin (Citrus unshiu Marc.). By integrating high-resolution imaging technology, we found that the canopy structure and reproduction output of individual citrus crops are mutually dependent on each other. Furthermore, it was revealed that the mature leaves in early season contribute their energy to the fruiting of the current growing season, whereas the younger leaves show a delayed contribution to the next growing season. We thus hypothesized that the annual yield variability might be caused by the limited and time-delayed resource allocation in individual plants. A novel lattice model based on this hypothesis demonstrates that this pattern of resource allocation will generate oscillations and chaos in citrus yield.

Delayed feedback control for chaotic vibration in nonlinear impact dynamics of bouncing agricultural tractor.

Agricultural tractors often lose contact and recollide with the ground surface while driving on narrow paddy fields and bumpy farm roads owing to excessive vibrations. These nonlinear impact dynamics can cause chaotic vibrations during tractor operation. Chaotic vibrations are random complex motions that can deteriorate tractor stability and lead to tractor overturning accidents, causing damage to machinery and risk of injury to the operator. This study investigates the theoretical feasibility of chaos control to eliminate chaotic vibrations in tractor dynamics. Delayed feedback (DF) control is employed to eliminate complex vibrations in tractor dynamics. First, the frequency response, bifurcation diagram, and largest Lyapunov exponent are obtained to investigate the nonlinear dynamics of the tractor and identify the parametric region in which chaotic vibrations occur. Subsequently, the DF control is designed based on the trial-and-error method and applied to the tractor dynamics as the driving force control input. The numerical results demonstrate that the DF control can successfully eliminate chaotic vibration and reduce the vibration level. Therefore, this study is expected to contribute to improving the tractor safety by reducing the risk of overturning.

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

Trees produce pollen during specific times of the year. Pollen can induce pollinosis, a type of allergic rhinitis, in humans. In Japan, allergenic pollen is mainly dispersed from February to May. Using data collected at 120 observation sites managed by the Japanese Ministry of the Environment, we studied the annual patterns of airborne allergenic pollen. The allergenic pollen showed an alternating ON-OFF cycle, but the length of the cycle differed among regions. We used an in-phase/out-of-phase analysis to quantify two characteristic features of the synchronisation. The degrees of phase synchronisation were strong in eastern and weak in western Japan. The pattern of allergenic pollen dispersal throughout Japan is typical intermittent synchronisation. This is the first study to evaluate allergenic pollen's distribution from a phase synchronisation viewpoint.

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

The population synchrony of tree seed production has attracted widespread attention in agriculture, forestry and ecosystem management. Oaks usually show synchronisation of irregular or intermittent sequences of acorn production, which is termed 'masting'. Tree crops such as citrus and pistachio show a clear two-year cycle (period-2) termed 'alternate bearing'. We identified period-3 dominant phase synchronisation in a population of Zelkova serrata. As 'period-3' is known to provide evidence to imply chaos in nonlinear science, the observed period-3 phase synchronisation of Zelkova serrata is an attractive real-world phenomenon that warrants investigation in terms of nonlinear dynamics. Using the Hilbert transform, we proposed a procedure to determine the fractions of periods underlying the survey data and distinguished the on-year (high yield year) and the off-year (low yield year) of the masting. We quantified the effects of pollen coupling, common environmental noise and individual variability on the phase synchronisation and demonstrated how the period-3 synchronisation emerges through a border-collision bifurcation process. In this paper, we propose a model that can describe diverse behaviours of seed production observed in many different tree species by changing its parameters.

Transition of chaotic motion to a limit cycle by intervention of economic policy: an empirical analysis in agriculture.

This paper investigates the transition of dynamics observed in an actual real agricultural economic dataset. Lyapunov spectrum analysis is conducted on the data to distinguish deterministic chaos and the limit cycle. Chaotic and periodic oscillation were identified before and after the second oil crisis, respectively. The statitonarity of the time series is investigated using recurrence plots. This shows that government intervention might reduce market instability by removing a chaotic market's long-term unpredictability.

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

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.