Paddy growth is influenced by the amount of inorganic fertilizer in paddy ecosystem in fallow season. To discover the interaction among weed, inorganic fertilizer and her- bivore in the system, we put forward a differ...Paddy growth is influenced by the amount of inorganic fertilizer in paddy ecosystem in fallow season. To discover the interaction among weed, inorganic fertilizer and her- bivore in the system, we put forward a differential equation model and investigate its properties. Results show that the system has a weed and herbivore extinct equilibrium and a herbivore extinct equilibrium. The two equilibria are proven to be unstable using the center manifold method. Under certain conditions, the system also has a positive equilibrium point. We give the stable region and the unstable region of the positive equilibrium point, which are determined by some parameters. We find that the system has the Hopf bifurcation phenomenon, and give the critical value of Hopf bifurcation by taking a system parameter as the bifurcation parameter. By comparing the equilib- rium states between a paddy ecosystem with herbivore and one without herbivore, we find that the content of inorganic fertilizer can be improved by putting herbivore into a paddy field. An example is given to illustrate the feasibility of the results. Numerical simulation shows that Hopf bifurcation phenomena exist in the system.展开更多
The multi-functionality of paddy farming has become a hot issue recently. Paddy farming provides numerous ecosystem services that are crucial to human well-being. However, evaluation of the contribution of paddy farmi...The multi-functionality of paddy farming has become a hot issue recently. Paddy farming provides numerous ecosystem services that are crucial to human well-being. However, evaluation of the contribution of paddy farming to human well-being usually focus on its economic value, while its non-market services are usually ignored. Only evaluating the market profits or market relative benefits cannot reflect comprehensively the contribution of paddy farming to people＇s well-being. This will affect people＇s choices for or against paddy farming activities and people＇s opt for invest or not invest in it. A comprehensive evaluation of paddy farming can provide an important reference for the government and society to conserve the multi-functionality of paddy farming and achieve sustainable development. To this end, this paper reports a case evaluation of paddy farming in Hunan, the largest rice producing as well as rice yield province in China, and uses emergy theory to make a comprehensive evaluation for paddy farming. The emergy evaluation results of the paddy ecosystem in Hunan are as follows： in 2010, the input emergy of the paddy ecosystem in Hunan is 2.51E＋22 sej and the output emergy is 6.31E＋22sej. For the input emergy, the part from natural resources is 1.96E＋21 sej and the part from human society is 2.32E＋22sej; for the output emergy, the part from products is 2.22E＋22 sej, the part from impositive externality is 4.16E＋22 sej and the part from negative externality is –7.41E＋20 sej. Taking the non-market outputs into consideration, the gains from the human economic society＇s 1 $ input in paddy farming, emergy sustainability index（ESI） and emergy profit rate are respectively 2.73 $, 3.53 and 151.31%. If the evaluation leave out the non-market output, the three indexes are only 0.96 $,1.24 and 30.67%. The research results show that non-market services of paddy farming contribute significantly to human well-being. Therefore, in order to protect the multi-functionality of paddy farming and achieve the sustainable management,the government should take reasonable measures and make incentive plans.展开更多
文摘Paddy growth is influenced by the amount of inorganic fertilizer in paddy ecosystem in fallow season. To discover the interaction among weed, inorganic fertilizer and her- bivore in the system, we put forward a differential equation model and investigate its properties. Results show that the system has a weed and herbivore extinct equilibrium and a herbivore extinct equilibrium. The two equilibria are proven to be unstable using the center manifold method. Under certain conditions, the system also has a positive equilibrium point. We give the stable region and the unstable region of the positive equilibrium point, which are determined by some parameters. We find that the system has the Hopf bifurcation phenomenon, and give the critical value of Hopf bifurcation by taking a system parameter as the bifurcation parameter. By comparing the equilib- rium states between a paddy ecosystem with herbivore and one without herbivore, we find that the content of inorganic fertilizer can be improved by putting herbivore into a paddy field. An example is given to illustrate the feasibility of the results. Numerical simulation shows that Hopf bifurcation phenomena exist in the system.
基金supported by the National Social Science Fundation of China (11BJY028)
文摘The multi-functionality of paddy farming has become a hot issue recently. Paddy farming provides numerous ecosystem services that are crucial to human well-being. However, evaluation of the contribution of paddy farming to human well-being usually focus on its economic value, while its non-market services are usually ignored. Only evaluating the market profits or market relative benefits cannot reflect comprehensively the contribution of paddy farming to people＇s well-being. This will affect people＇s choices for or against paddy farming activities and people＇s opt for invest or not invest in it. A comprehensive evaluation of paddy farming can provide an important reference for the government and society to conserve the multi-functionality of paddy farming and achieve sustainable development. To this end, this paper reports a case evaluation of paddy farming in Hunan, the largest rice producing as well as rice yield province in China, and uses emergy theory to make a comprehensive evaluation for paddy farming. The emergy evaluation results of the paddy ecosystem in Hunan are as follows： in 2010, the input emergy of the paddy ecosystem in Hunan is 2.51E＋22 sej and the output emergy is 6.31E＋22sej. For the input emergy, the part from natural resources is 1.96E＋21 sej and the part from human society is 2.32E＋22sej; for the output emergy, the part from products is 2.22E＋22 sej, the part from impositive externality is 4.16E＋22 sej and the part from negative externality is –7.41E＋20 sej. Taking the non-market outputs into consideration, the gains from the human economic society＇s 1 $ input in paddy farming, emergy sustainability index（ESI） and emergy profit rate are respectively 2.73 $, 3.53 and 151.31%. If the evaluation leave out the non-market output, the three indexes are only 0.96 $,1.24 and 30.67%. The research results show that non-market services of paddy farming contribute significantly to human well-being. Therefore, in order to protect the multi-functionality of paddy farming and achieve the sustainable management,the government should take reasonable measures and make incentive plans.
