大熊猫保护的种群动力学机理研究
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摘要
该文主要运用种群生态学理论来研究大熊猫种群,利用动力学建模方法建立大熊猫种群与环境之间、局域种群与种群之间关系的数学模型,通过运用脉冲微分方程理论、时滞微分方程理论等数学理论方法和数值模拟对所建立的微分系统的动力学行为进行探索,从而对大熊猫种群在区域内的持续生存进行预测和推断,为大熊猫种群保护研究提供理论依据。具体研究内容和结果如下：
(1)建立大熊猫与两种主食竹之间关系的两次脉冲微分系统,研究当大熊猫栖息地仅有两种主食竹时主食竹开花对大熊猫种群生存的影响,并结合卧龙自然保护区五一棚地区的调查研究数据,用数值模拟的方法讨论了五一棚地区大熊猫与两种主食竹拐棍竹和冷箭竹之间的关系。该章所建模型及研究方法可以用来预测某一区域内主食竹开花是否会对大熊猫的生存造成影响,研究结论可为开花竹林的人工复壮更新和人工造竹林提供理论依据。
(2)从数学的角度建立描述“乔木-竹子-大熊猫”之间关系的微分方程数学模型。通过对带有时滞和阶段结构的变系数微分系统的分析,得到了系统持续生存的条件,从理论上验证了李俊清等提出的森林、主食竹、大熊猫三位一体系统的稳定性维持机制,并进一步分析制约系统稳定发展的因素,为大熊猫栖息地保护提出建议。
(3)建立大熊猫在不同类型的斑块间扩散和迁移的微分系统模型,通过数学分析得到大熊猫在斑块间持续生存和灭绝的条件,并把所得结论用在秦岭大熊猫局域种群中去。研究方法可用来研究大熊猫在各类局域种群中的扩散和迁移,从而预测大熊猫局域种群的未来发展情况。
(4)针对在两个相邻的斑块环境里放归圈养大熊猫的两个方案分别建立了状态反馈脉冲控制数学模型,通过运用半连续系统几何理论,讨论系统在相空间的阶k(k大于等于1的整数)周期解的存在性和稳定性,从而验证了所给出的放归方案的稳定性和合理性。研究结论可为复壮小局域种群野生大熊猫数量和大熊猫历史分布区野生大熊猫的重新引入工作提供理论依据。
In this paper, some differential equation models for describing the development of the giant panda population were established by dynamic modeling methods, and the dynamical behaviors of the differential systems were explored by impulsive differential equations theory, delay differential equations theory and other mathematical theories and numerical simulation methods. The results can be used to predict and infer the persistence of the giant panda population, and also provide theoretical basis for the study of giant panda protection. The results are summarized as follows.
(1) An impulsive differential system on the relation of giant panda and two kinds of staple food bamboo was established, and how the staple food of bamboo flowering impact on the survival of the giant panda was discussed. Based on the investigation data of Wolong nature protection five one shed area, the relation between pandas and two kinds of staple food bamboo (Fargesia robusta and Bashania fargesii) was discussed by using numerical simulation method. The model can be used to consider whether bamboo flowering cause giant pandas to food shortages or not in some areas, and the study also provides a theoretical basis for blossom bamboo artificial regeneration and the artificial forest.
(2) From the view of mathematics, a mathematical delay differential equation model of the relation between the trees, bamboo and giant pandas was established. Through the analysis of the variable coefficient differential systems with time delay and stage structure, the conditions for the permanence of the system were obtained, which can ensure the three populations to develop Corporately. The characteristics of this part are to verify the stability of the forest, bamboo and panda three-in-one system maintenance mechanism which was presented by Juqing Li et al. and to analyze the factors that restrict the stable development of the system, which will provide theoretical basis for the giant panda habitat protection.
(3) An n dimensional differential system was established on the giant panda population dispersal in complex patchy environments. By mathematical analysis of the periodic coefficient diffusion differential system, sufficient conditions for permanence and extinction were obtained. Furthermore, the conclusions were applied to the local population in Qinling Mountains. The research method can be used to predict the future development of the local population of giant pandas.
(4) Two mathematical models of release captive giant pandas in patchy environments were established, and the release mode of captive giant pandas was discussed by using state feedback control impulsive differential equations. Using the geometry theory of semi-continuous dynamical system, the existence and stability of order k periodic solutions in the phase space were studied. Thus, a series of release modes of the captive giant pandas were presented, for increasing small isolated pandas in patchy environments. Also, it would reintroduction wild pandas in the history of the giant panda distribution area.
(1)建立大熊猫与两种主食竹之间关系的两次脉冲微分系统,研究当大熊猫栖息地仅有两种主食竹时主食竹开花对大熊猫种群生存的影响,并结合卧龙自然保护区五一棚地区的调查研究数据,用数值模拟的方法讨论了五一棚地区大熊猫与两种主食竹拐棍竹和冷箭竹之间的关系。该章所建模型及研究方法可以用来预测某一区域内主食竹开花是否会对大熊猫的生存造成影响,研究结论可为开花竹林的人工复壮更新和人工造竹林提供理论依据。
(2)从数学的角度建立描述“乔木-竹子-大熊猫”之间关系的微分方程数学模型。通过对带有时滞和阶段结构的变系数微分系统的分析,得到了系统持续生存的条件,从理论上验证了李俊清等提出的森林、主食竹、大熊猫三位一体系统的稳定性维持机制,并进一步分析制约系统稳定发展的因素,为大熊猫栖息地保护提出建议。
(3)建立大熊猫在不同类型的斑块间扩散和迁移的微分系统模型,通过数学分析得到大熊猫在斑块间持续生存和灭绝的条件,并把所得结论用在秦岭大熊猫局域种群中去。研究方法可用来研究大熊猫在各类局域种群中的扩散和迁移,从而预测大熊猫局域种群的未来发展情况。
(4)针对在两个相邻的斑块环境里放归圈养大熊猫的两个方案分别建立了状态反馈脉冲控制数学模型,通过运用半连续系统几何理论,讨论系统在相空间的阶k(k大于等于1的整数)周期解的存在性和稳定性,从而验证了所给出的放归方案的稳定性和合理性。研究结论可为复壮小局域种群野生大熊猫数量和大熊猫历史分布区野生大熊猫的重新引入工作提供理论依据。
In this paper, some differential equation models for describing the development of the giant panda population were established by dynamic modeling methods, and the dynamical behaviors of the differential systems were explored by impulsive differential equations theory, delay differential equations theory and other mathematical theories and numerical simulation methods. The results can be used to predict and infer the persistence of the giant panda population, and also provide theoretical basis for the study of giant panda protection. The results are summarized as follows.
(1) An impulsive differential system on the relation of giant panda and two kinds of staple food bamboo was established, and how the staple food of bamboo flowering impact on the survival of the giant panda was discussed. Based on the investigation data of Wolong nature protection five one shed area, the relation between pandas and two kinds of staple food bamboo (Fargesia robusta and Bashania fargesii) was discussed by using numerical simulation method. The model can be used to consider whether bamboo flowering cause giant pandas to food shortages or not in some areas, and the study also provides a theoretical basis for blossom bamboo artificial regeneration and the artificial forest.
(2) From the view of mathematics, a mathematical delay differential equation model of the relation between the trees, bamboo and giant pandas was established. Through the analysis of the variable coefficient differential systems with time delay and stage structure, the conditions for the permanence of the system were obtained, which can ensure the three populations to develop Corporately. The characteristics of this part are to verify the stability of the forest, bamboo and panda three-in-one system maintenance mechanism which was presented by Juqing Li et al. and to analyze the factors that restrict the stable development of the system, which will provide theoretical basis for the giant panda habitat protection.
(3) An n dimensional differential system was established on the giant panda population dispersal in complex patchy environments. By mathematical analysis of the periodic coefficient diffusion differential system, sufficient conditions for permanence and extinction were obtained. Furthermore, the conclusions were applied to the local population in Qinling Mountains. The research method can be used to predict the future development of the local population of giant pandas.
(4) Two mathematical models of release captive giant pandas in patchy environments were established, and the release mode of captive giant pandas was discussed by using state feedback control impulsive differential equations. Using the geometry theory of semi-continuous dynamical system, the existence and stability of order k periodic solutions in the phase space were studied. Thus, a series of release modes of the captive giant pandas were presented, for increasing small isolated pandas in patchy environments. Also, it would reintroduction wild pandas in the history of the giant panda distribution area.
引文
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