Modeling the Effects of Insects and Insecticides with External Efforts on Agricultural Crops
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Modeling the Effects of Insects and Insecticides with External Efforts on Agricultural Crops A. K. Misra1 · Navnit Jha2 · Rahul Patel1 Accepted: 30 September 2020 © Foundation for Scientific Research and Technological Innovation 2020
Abstract In this paper, we propose a continuous dynamical model along with its discretized system to increase the agricultural crop production using some external efforts in presence of insects and insecticides. It is assumed that agricultural crops grow logistically and its growth deplete due to insect population, which is wholly dependent on crops. Farmers use insecticides to kill insects to protect the crop and its excessive use is hazardous to human health and therefore it is assumed that insecticides are used proportional to the density of insects. To increase field’s growth potential, we presumed that some efforts (e.g. seed selection, use of fertilizers, proper water drainage, etc.) are applied proportional to the difference between carrying capacity and actual production. The quantitative features of the nonlinear crop production model is examined by a coherent non-standard finite difference scheme (NSFDS) in the absence of theoretical solution values. This scheme is formulated by discretizing the model system and renormalizing the denominator of derivatives of continuous system. Convergence analysis of the new NSFD scheme is described in detail. A graphical layout by computer-assisted numerical results is introduced to observe the effects of external efforts on production of agricultural crops. Keywords Mathematical model · Agricultural crops · Insect population · Insecticides · External efforts · Stability · Non-standard finite difference scheme
Introduction Agricultural production plays a crucial role to fulfill not only the basic needs of livelihood but also the demand of raw materials to the industries, which strengths the economy of the country. Due to continuous increase in human population (projected about 10 billion by 2050), it is requisite to increase crop production. Since the cultivation area is limited, so the demand for additional crop production can be fulfilled by enhancing the productivity of * Rahul Patel [email protected] 1
Department of Mathematics, Institute of Science, Banaras Hindu University, Varanasi 221005, India
2
Faculty of Mathematics and Computer Science, South Asian University, Chanakyapuri, New Delhi 110021, India
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Vol.:(0123456789)
Differential Equations and Dynamical Systems
the crop. Farmers adopt different types of irrigation techniques, mechanical technologies, and high-yielding varieties of seeds to enhance the production. Despite advances in the agricultural sector, food insecurity remains to be a serious issue for the human population. According to the Food and agricultural organization report-2019 on food crises, 113 million people experienced food insecurity across 53 countries in 2018 [1]. It may be noted that there are some insects, such as leaf folder in rice, capitulum borer in sunflower, fruits borer in
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