Abstract
In the paper, we introduce a differential equations model of paddy ecosystems in the fallow season to study the effect of weeds removal from the paddy fields. We found that there is an unstable equilibrium of the extinction of weeds and herbivores in the system. When the intensity of weeds removal meets certain conditions and the intrinsic growth rate of herbivores is higher than their excretion rate, there is a coexistence equilibrium state in the system. By linearizing the system and using the Routh–Hurwitz criterion, we obtained the local asymptotically stable conditions of the coexistence equilibrium state. The critical value formula of the Hopf bifurcation is presented too. The model demonstrates that weeds removal from paddy fields could largely reduce the weeds biomass in the equilibrium state, but it also decreases the herbivore biomass, which probably reduces the content of inorganic fertilizer in the soil. We found a particular intensity of weeds removal that could result in the minimum content of inorganic fertilizer, suggesting weeds removal should be kept away from this intensity.
Highlights
Paddy field fertility is the premise of high quality, high yield, and low energy consumption of rice. e method of increasing rice yield by applying a large amount of chemical fertilizers and pesticides has threatened the sustainable development of grain and the ecological security. erefore, how to use biodiversity in paddy ecosystems to improve the stability and sustainability of agricultural systems has been attracting more and more attention [1,2,3]
Xiang et al found that adding the factor of domesticated animals in a paddy ecosystem in the fallow season could improve the level of nutrient availability in the soil [29], and some new features such as a Hopf bifurcation appear in the system
We only consider the effect of weeds removal on three main components of a paddy ecosystem in fallow season: weeds, inorganic fertilizer, and herbivores. ere is an obvious nutrient-dependent consumption ring among the three: weeds are used as food for farmed animals in paddy fields, weeds are nourished by the effective nutrients in the soil, and the effective nutrients can be transformed from animal manure
Summary
Paddy field fertility is the premise of high quality, high yield, and low energy consumption of rice. e method of increasing rice yield by applying a large amount of chemical fertilizers and pesticides has threatened the sustainable development of grain and the ecological security. erefore, how to use biodiversity in paddy ecosystems to improve the stability and sustainability of agricultural systems has been attracting more and more attention [1,2,3]. Ere are many factors affecting the fertility of a paddy ecosystem, such as soil nutrient availability, light, moisture, weeds, insects, microorganisms, and so on. Xiang et al found that adding the factor of domesticated animals in a paddy ecosystem in the fallow season could improve the level of nutrient availability in the soil [29], and some new features such as a Hopf bifurcation appear in the system. E main purpose of this paper is to analyze the effect of weeds removal in a paddy ecosystem in the fallow season by establishing a differential equations model and find a strategy of weeds removal. The mathematical model of the paddy ecosystem with weeds removal is introduced.
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