A Mathematical Model with Pulse Effect for Three Populations of the Giant Panda and Two Kinds of Bamboo
A mathematical model for the relationship between the populations of giant pandas and two kinds of bamboo is established. We use the impulsive perturbations to take into account the effect of a sudden collapse of bamboo as a food source. We show that this system is uniformly bounded. Using the Floqu...
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| Format: | Article |
| Language: | English |
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Wiley
2013-01-01
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| Series: | The Scientific World Journal |
| Online Access: | http://dx.doi.org/10.1155/2013/137384 |
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| _version_ | 1849413355232559104 |
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| author | Xiang-yun Shi Guo-hua Song |
| author_facet | Xiang-yun Shi Guo-hua Song |
| author_sort | Xiang-yun Shi |
| collection | DOAJ |
| description | A mathematical model for the relationship between the populations of giant pandas and two kinds of bamboo is established. We use the impulsive perturbations to take into account the effect of a sudden collapse of bamboo as a food source. We show that this system is uniformly bounded. Using the Floquet theory and comparison techniques of impulsive equations, we find conditions for the local and global stabilities of the giant panda-free periodic solution. Moreover, we obtain sufficient conditions for the system to be permanent. The results provide a theoretical basis for giant panda habitat protection. |
| format | Article |
| id | doaj-art-6c87a2a85d95472d82a5e1a427c7ded7 |
| institution | Kabale University |
| issn | 1537-744X |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | The Scientific World Journal |
| spelling | doaj-art-6c87a2a85d95472d82a5e1a427c7ded72025-08-20T03:34:09ZengWileyThe Scientific World Journal1537-744X2013-01-01201310.1155/2013/137384137384A Mathematical Model with Pulse Effect for Three Populations of the Giant Panda and Two Kinds of BambooXiang-yun Shi0Guo-hua Song1College of Forestry, Beijing Forestry University, Beijing 100083, ChinaCollege of Forestry, Beijing Forestry University, Beijing 100083, ChinaA mathematical model for the relationship between the populations of giant pandas and two kinds of bamboo is established. We use the impulsive perturbations to take into account the effect of a sudden collapse of bamboo as a food source. We show that this system is uniformly bounded. Using the Floquet theory and comparison techniques of impulsive equations, we find conditions for the local and global stabilities of the giant panda-free periodic solution. Moreover, we obtain sufficient conditions for the system to be permanent. The results provide a theoretical basis for giant panda habitat protection.http://dx.doi.org/10.1155/2013/137384 |
| spellingShingle | Xiang-yun Shi Guo-hua Song A Mathematical Model with Pulse Effect for Three Populations of the Giant Panda and Two Kinds of Bamboo The Scientific World Journal |
| title | A Mathematical Model with Pulse Effect for Three Populations of the Giant Panda and Two Kinds of Bamboo |
| title_full | A Mathematical Model with Pulse Effect for Three Populations of the Giant Panda and Two Kinds of Bamboo |
| title_fullStr | A Mathematical Model with Pulse Effect for Three Populations of the Giant Panda and Two Kinds of Bamboo |
| title_full_unstemmed | A Mathematical Model with Pulse Effect for Three Populations of the Giant Panda and Two Kinds of Bamboo |
| title_short | A Mathematical Model with Pulse Effect for Three Populations of the Giant Panda and Two Kinds of Bamboo |
| title_sort | mathematical model with pulse effect for three populations of the giant panda and two kinds of bamboo |
| url | http://dx.doi.org/10.1155/2013/137384 |
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