In this paper, a non-linear mathematical model is proposed and analyzed to study the effects of mitigation options on the control of methane emissions in the atmosphere caused by rice paddies and livestock populations to reduce global warming. In the modeling process, it is assumed that the cumulative biomass density of rice paddies and the density of livestock populations follow logistic models with their respective growth rates and carrying capacities. The growth rate of concentration of methane in the atmosphere is assumed to be directly proportional to the cumulative density of various processes involved in the production of rice paddies as well as the cumulative density of various processes used in the farming of livestock populations. This growth rate is also assumed to increase with natural factors such as wetlands but it decreases with the cumulative density of mitigation options, considered to be proportional to the increased level of methane concentration in the atmosphere. The non-linear model is analyzed by using the stability theory of differential equations and computer simulation. The analysis shows that mitigation options can control the methane emissions in the atmosphere caused by rice paddies and livestock populations considerably. The computer simulation of the model confirms this analytical result. The data from model prediction is compared with actual methane data in the atmosphere and found to be very satisfactory.

中文翻译：

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减缓措施对控制稻田和牲畜造成的甲烷排放以减少全球变暖的影响：建模研究和与环境数据的比较

在本文中，提出并分析了一个非线性数学模型，以研究减缓方案对控制稻田和牲畜种群造成的大气中甲烷排放的影响，以减少全球变暖。在建模过程中，假设稻田的累积生物量密度和牲畜种群密度遵循逻辑模型及其各自的增长率和承载能力。假设大气中甲烷浓度的增长率与稻田生产中各种过程的累积密度以及牲畜养殖中使用的各种过程的累积密度成正比。还假设这种增长率会随着湿地等自然因素而增加，但随着缓解方案的累积密度而降低，这被认为与大气中甲烷浓度的增加水平成正比。利用微分方程的稳定性理论和计算机模拟对非线性模型进行了分析。分析表明，缓解方案可以显着控制稻田和牲畜种群造成的大气中的甲烷排放。模型的计算机模拟证实了这一分析结果。模型预测的数据与大气中的实际甲烷数据进行了比较，发现非常令人满意。利用微分方程的稳定性理论和计算机模拟对非线性模型进行了分析。分析表明，缓解方案可以显着控制稻田和牲畜种群造成的大气中的甲烷排放。模型的计算机模拟证实了这一分析结果。模型预测的数据与大气中的实际甲烷数据进行了比较，发现非常令人满意。利用微分方程的稳定性理论和计算机模拟对非线性模型进行了分析。分析表明，缓解方案可以显着控制稻田和牲畜种群造成的大气中的甲烷排放。模型的计算机模拟证实了这一分析结果。模型预测的数据与大气中的实际甲烷数据进行了比较，发现非常令人满意。