MATHEMATICAL MODEL OF THREE SPECIES FOOD CHAIN WITH INTRASPECIFIC COMPETITION AND HARVESTING ON PREDATOR
This research develops a mathematical model of three species of food chains between prey, predator, and top predator by adding intraspecific competition and harvesting factors. Interaction between prey with predator and interaction between predator with top predator uses the functional response type...
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| Format: | Article |
| Language: | English |
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Universitas Pattimura
2022-06-01
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| Series: | Barekeng |
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| Online Access: | https://ojs3.unpatti.ac.id/index.php/barekeng/article/view/5220 |
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| author | Muhammad Manaqib Suma'inna Suma'inna Amalia Zahra |
| author_facet | Muhammad Manaqib Suma'inna Suma'inna Amalia Zahra |
| author_sort | Muhammad Manaqib |
| collection | DOAJ |
| description | This research develops a mathematical model of three species of food chains between prey, predator, and top predator by adding intraspecific competition and harvesting factors. Interaction between prey with predator and interaction between predator with top predator uses the functional response type II. Model formation begins with creating a diagram food chain of three species compartments. Then a nonlinear differential equation system is formed based on the compartment diagram. Based on this system four equilibrium points are obtained. Analysis of local stability at the equilibrium points by linearization shows that there is one unstable equilibrium point and three asymptotic stable local equilibrium points. Numerical simulations at equilibrium points show the same results as the results of the analysis. Then numerical simulations on several parameter variations show that intraspecific competition has little effect on population changes in predator and top predator. While the harvesting parameter predator affects the population of predator and top predator. |
| format | Article |
| id | doaj-art-f0ce5bb719e240adb1c16f344d76b75c |
| institution | DOAJ |
| issn | 1978-7227 2615-3017 |
| language | English |
| publishDate | 2022-06-01 |
| publisher | Universitas Pattimura |
| record_format | Article |
| series | Barekeng |
| spelling | doaj-art-f0ce5bb719e240adb1c16f344d76b75c2025-08-20T03:05:41ZengUniversitas PattimuraBarekeng1978-72272615-30172022-06-0116255156210.30598/barekengvol16iss2pp551-5625220MATHEMATICAL MODEL OF THREE SPECIES FOOD CHAIN WITH INTRASPECIFIC COMPETITION AND HARVESTING ON PREDATORMuhammad Manaqib0Suma'inna Suma'inna1Amalia Zahra2Department of Mathematics, Faculty of Sciences and Technology, UIN Syarif Hidayatullah JakartaDepartment of Mathematics, Faculty of Sciences and Technology, UIN Syarif Hidayatullah JakartaDepartment of Mathematics, Faculty of Sciences and Technology, UIN Syarif Hidayatullah JakartaThis research develops a mathematical model of three species of food chains between prey, predator, and top predator by adding intraspecific competition and harvesting factors. Interaction between prey with predator and interaction between predator with top predator uses the functional response type II. Model formation begins with creating a diagram food chain of three species compartments. Then a nonlinear differential equation system is formed based on the compartment diagram. Based on this system four equilibrium points are obtained. Analysis of local stability at the equilibrium points by linearization shows that there is one unstable equilibrium point and three asymptotic stable local equilibrium points. Numerical simulations at equilibrium points show the same results as the results of the analysis. Then numerical simulations on several parameter variations show that intraspecific competition has little effect on population changes in predator and top predator. While the harvesting parameter predator affects the population of predator and top predator.https://ojs3.unpatti.ac.id/index.php/barekeng/article/view/5220predator-prey modelfood chain modelequilibrium stabilitynumerical simulation |
| spellingShingle | Muhammad Manaqib Suma'inna Suma'inna Amalia Zahra MATHEMATICAL MODEL OF THREE SPECIES FOOD CHAIN WITH INTRASPECIFIC COMPETITION AND HARVESTING ON PREDATOR Barekeng predator-prey model food chain model equilibrium stability numerical simulation |
| title | MATHEMATICAL MODEL OF THREE SPECIES FOOD CHAIN WITH INTRASPECIFIC COMPETITION AND HARVESTING ON PREDATOR |
| title_full | MATHEMATICAL MODEL OF THREE SPECIES FOOD CHAIN WITH INTRASPECIFIC COMPETITION AND HARVESTING ON PREDATOR |
| title_fullStr | MATHEMATICAL MODEL OF THREE SPECIES FOOD CHAIN WITH INTRASPECIFIC COMPETITION AND HARVESTING ON PREDATOR |
| title_full_unstemmed | MATHEMATICAL MODEL OF THREE SPECIES FOOD CHAIN WITH INTRASPECIFIC COMPETITION AND HARVESTING ON PREDATOR |
| title_short | MATHEMATICAL MODEL OF THREE SPECIES FOOD CHAIN WITH INTRASPECIFIC COMPETITION AND HARVESTING ON PREDATOR |
| title_sort | mathematical model of three species food chain with intraspecific competition and harvesting on predator |
| topic | predator-prey model food chain model equilibrium stability numerical simulation |
| url | https://ojs3.unpatti.ac.id/index.php/barekeng/article/view/5220 |
| work_keys_str_mv | AT muhammadmanaqib mathematicalmodelofthreespeciesfoodchainwithintraspecificcompetitionandharvestingonpredator AT sumainnasumainna mathematicalmodelofthreespeciesfoodchainwithintraspecificcompetitionandharvestingonpredator AT amaliazahra mathematicalmodelofthreespeciesfoodchainwithintraspecificcompetitionandharvestingonpredator |