Global stability of two-species mutualism model with proportional harvesting

Ahmad, Rosmaini

doi:10.21833/ijaas.2017.07.011

Cited by 2 publications

(2 citation statements)

References 11 publications

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“…In the symbiosis model, two populations include the symbiotic commensalism model (Prasad & Ramacharyulu, 2012), (Sun, G. C & Sun, 2013), (B. Ravindra Reddy, 2013), (XIE et al, 2015), (Wu et al, 2016), (Chen, Jinghuang & Wu, 2017), (Chen, 2018a), (Chen, 2018b), (Lin, 2018), (Zhao et al, 2018), (Chen, 2019), amensalism symbiotic model (Xie et al, 2016), (Chen, 2018c), (Liu et al, 2018), (Wu, 2018), (Guan & Chen, 2019), (Su & Chen, 2019), (Wei et al, 2020) and a mutualism symbiotic model (Ahmad, 2017). Some of these studies include harvesting in one (Chen, 2019) or both populations (Chen, Jinghuang & Wu, 2017), (Chen, 2018c), (Lin, 2018), (Su & Chen, 2019), (Ahmad, 2017). In the symbiosis model, there are three populations, which discusses predatorprey with symbiosis of commensalism (Kumar, N. P. & Ramacharyulu, 2010).…”

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Dynamic Analysis of the Symbiotic Model of Commensalism and Parasitism with Harvesting in Commensal Populations

Puspitasari¹,

Kusumawinahyu²,

Trisilowati³

2021

JTAM

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This article discussed about a dynamic analysis of the symbiotic model of commensalism and parasitism with harvesting in the commensal population. This model is obtained from a modification of the symbiosis commensalism model. This modification is by adding a new population, namely the parasite population. Furthermore, it will be investigated that the three populations can coexist. The analysis carried out includes the determination of all equilibrium points along with their existence and local stability along with their stability requirements. From this model, it is obtained eight equilibrium points, namely three population extinction points, two population extinction points, one population extinction point and three extinction points can coexist. Of the eight points, only two points are asymptotically stable if they meet certain conditions. Next, a numerical simulation will be performed to illustrate the model’s behavior. In this article, a numerical simulation was carried out using the RK-4 method. The simulation results obtained support the results of the dynamic analysis that has been done previously.This article discussed about a dynamic analysis of the symbiotic model of The dynamics of the symbiotic model of commensalism and parasitism with harvesting in the commensal population. is the main focus of this study. This model is obtained from a modification of the symbiosis commensalism model. This modification is by adding a new population, namely the parasite population. Furthermore, it will be investigated that the three populations can coexist. The analysis carried out includes the determination begins by identifying the conditions for the existence of all equilibrium points along with their existence and local stability along with their stability requirements. From this model, it is obtained eight equilibrium points, namely three population extinction points, two population extinction points, one population extinction point and three extinction points can coexist. Of the eight points, only two points are asymptotically stable if they meet certain conditions. Next, a numerical simulation will be performed to illustrate the model’s behavior. In this article, a numerical simulation was carried out using the RK-4 method. The simulation results obtained support the results of the dynamic analysis that has been done previously.[VM1] [VM1]To add a mathematical effect to the article. There can be added mathematical models produced in the study at the end of this section.

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Dynamic Analysis of the Symbiotic Model of Commensalism and Parasitism with Harvesting in Commensal Populations

Puspitasari¹,

Kusumawinahyu²,

Trisilowati³

2021

JTAM

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“…The existing mutualistic interaction model of two species population in which both population are benefited from each other according to type I functional response or linear way and both populations are harvested with density dependent function or proportionally harvested can be expressed by the following system of equations [18]:…”

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Modeling and Simulation Study of Mutuality Interactions with Type II functional Response and Harvesting

Tolcha¹

2018

AJAM

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This paper deals with the study of mutuality interactions between two species population with type II functional response and also with the inclusion of harvesting. Harvesting functions are introduced to express the rate of reductions of the species separately. Mathematical model have been constructed and considered for the analysis and results. In this model, the first population species benefited according to type II functional response and the second species benefited from the first according to type I functional response and also harvested proportional to its density. It is shown that the model has positive and bounded solutions. Stability analysis is carried out. The local and global stability of biologically interested equilibrium point are considered and analyzed. Numerical examples supporting theoretical results such as phase plane and simulation study using DSolver are also included. Assumptions and results are presented and discussed lucidly in the text of the paper.

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Global stability of two-species mutualism model with proportional harvesting

Cited by 2 publications

References 11 publications

Dynamic Analysis of the Symbiotic Model of Commensalism and Parasitism with Harvesting in Commensal Populations

Dynamic Analysis of the Symbiotic Model of Commensalism and Parasitism with Harvesting in Commensal Populations

Modeling and Simulation Study of Mutuality Interactions with Type II functional Response and Harvesting

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