A Three-Species Food Chain System with Two Types of Functional Responses
In recent decades, many researchers have investigated the ecological models with three and more species to understand complex dynamical behaviors of ecological systems in nature. However, when they studied the models with three species, they have just considered the functional responses between prey...
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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Wiley
2011-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2011/934569 |
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| author | Younghae Do Hunki Baek Yongdo Lim Dongkyu Lim |
| author_facet | Younghae Do Hunki Baek Yongdo Lim Dongkyu Lim |
| author_sort | Younghae Do |
| collection | DOAJ |
| description | In recent decades, many researchers have investigated the ecological models with three and more species to understand complex dynamical behaviors of ecological systems in nature. However,
when they studied the models with three species, they have just considered the functional responses between prey and mid-predator and between mid-predator and top predator as the same type. However, in the paper, in order to describe more realistic ecological world, a three-species food chain system with two types of functional response, Holling type and Beddington-DeAngelis type, is considered. It is shown that this system is dissipative. Also, the local and global stability
of equilibrium points of the system is established. In addition, conditions for the persistence of
the system are found according to the existence of limit cycles. Some numerical examples are
given to substantiate our theoretical results. Moreover, we provide numerical evidence of the existence
of chaotic phenomena by illustrating bifurcation diagrams of system and by calculating
the largest Lyapunov exponent. |
| format | Article |
| id | doaj-art-23a32a2b7f9847b7a608b04221c3f3e1 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2011-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-23a32a2b7f9847b7a608b04221c3f3e12025-02-03T01:22:44ZengWileyAbstract and Applied Analysis1085-33751687-04092011-01-01201110.1155/2011/934569934569A Three-Species Food Chain System with Two Types of Functional ResponsesYounghae Do0Hunki Baek1Yongdo Lim2Dongkyu Lim3Department of Mathematics, Kyungpook National University, Daegu 702-701, Republic of KoreaDepartment of Mathematics Education, Catholic University of Daegu, Gyeongsan-si, Gyeongbuk 712-702, Republic of KoreaDepartment of Mathematics, Kyungpook National University, Daegu 702-701, Republic of KoreaDepartment of Mathematics, Kyungpook National University, Daegu 702-701, Republic of KoreaIn recent decades, many researchers have investigated the ecological models with three and more species to understand complex dynamical behaviors of ecological systems in nature. However, when they studied the models with three species, they have just considered the functional responses between prey and mid-predator and between mid-predator and top predator as the same type. However, in the paper, in order to describe more realistic ecological world, a three-species food chain system with two types of functional response, Holling type and Beddington-DeAngelis type, is considered. It is shown that this system is dissipative. Also, the local and global stability of equilibrium points of the system is established. In addition, conditions for the persistence of the system are found according to the existence of limit cycles. Some numerical examples are given to substantiate our theoretical results. Moreover, we provide numerical evidence of the existence of chaotic phenomena by illustrating bifurcation diagrams of system and by calculating the largest Lyapunov exponent.http://dx.doi.org/10.1155/2011/934569 |
| spellingShingle | Younghae Do Hunki Baek Yongdo Lim Dongkyu Lim A Three-Species Food Chain System with Two Types of Functional Responses Abstract and Applied Analysis |
| title | A Three-Species Food Chain System with Two Types of Functional Responses |
| title_full | A Three-Species Food Chain System with Two Types of Functional Responses |
| title_fullStr | A Three-Species Food Chain System with Two Types of Functional Responses |
| title_full_unstemmed | A Three-Species Food Chain System with Two Types of Functional Responses |
| title_short | A Three-Species Food Chain System with Two Types of Functional Responses |
| title_sort | three species food chain system with two types of functional responses |
| url | http://dx.doi.org/10.1155/2011/934569 |
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