Mathematical modelling of Fish Resources Harvesting with Predator at Maximum Sustainable Yield
Kinfe Hailemariam Hntsaa, Zenebe Taka Mengesha (PhD)b*
aDepartment of Mathematics, Aksum University, Axum, Ethiopia, kinfhail@gmail.com
bDepartment of Biology, Aksum University, Axum, Ethiopia, zenebeteka2007@gmail.com
In this study, the population dynamic of fish is considered following Logistic model with the inclusion of harvesting. The prey-predator interaction is also considered with an assumption that the predator population which is completely theoretical and not physically defined has a little effect on the growth of prey population provided that there are no limiting factors other than the predators. This is to say that the prey-predator cycle remains stable as far as other factors are constant in the natural environment. The growth function of the predator population is constructed corresponding to the prey population, and its results showed that the predator population size is either convergent to a finite positive limit, zero or diverges to positive infinity; while the fish population size follows Logistic function and grows to an upper asymptote. Furthermore, the prey-predator interaction is considered with the assumption that the predator population has an effect on the growth of the prey population and the predator population has intra-specific competition for a limited environmental resource. Its result showed that the predator population size did not go to infinity without bound. In both cases the maximum sustainable yield is obtained, numerical simulation and stability analysis of the model are included.
Possehl heeft als gespecialiseerde aannemer ruim 25 jaar internationale ervaring met het onderhouden en repareren van start- en landingsbanen, verkeerswegen en beton in burger- & utiliteitsbouw en GWW.
Dagelijks staan we met veel plezier onze klanten bij in het oplossen van technische vraagstukken.
We gaan ver voor onze klanten en hechten veel waarde aan een duurzame relatie. Zonder overdrijven mogen we ons na meer dan een kwart eeuw ervaring "experts in toplagen" noemen.
Mathematical modelling of Fish Resources Harvesting with Predator at Maximum Sustainable Yield
Kinfe Hailemariam Hntsaa, Zenebe Taka Mengesha (PhD)b*
aDepartment of Mathematics, Aksum University, Axum, Ethiopia, kinfhail@gmail.com
bDepartment of Biology, Aksum University, Axum, Ethiopia, zenebeteka2007@gmail.com
In this study, the population dynamic of fish is considered following Logistic model with the inclusion of harvesting. The prey-predator interaction is also considered with an assumption that the predator population which is completely theoretical and not physically defined has a little effect on the growth of prey population provided that there are no limiting factors other than the predators. This is to say that the prey-predator cycle remains stable as far as other factors are constant in the natural environment. The growth function of the predator population is constructed corresponding to the prey population, and its results showed that the predator population size is either convergent to a finite positive limit, zero or diverges to positive infinity; while the fish population size follows Logistic function and grows to an upper asymptote. Furthermore, the prey-predator interaction is considered with the assumption that the predator population has an effect on the growth of the prey population and the predator population has intra-specific competition for a limited environmental resource. Its result showed that the predator population size did not go to infinity without bound. In both cases the maximum sustainable yield is obtained, numerical simulation and stability analysis of the model are included.
Possehl heeft als gespecialiseerde aannemer ruim 25 jaar internationale ervaring met het onderhouden en repareren van start- en landingsbanen, verkeerswegen en beton in burger- & utiliteitsbouw en GWW.
Dagelijks staan we met veel plezier onze klanten bij in het oplossen van technische vraagstukken.
We gaan ver voor onze klanten en hechten veel waarde aan een duurzame relatie. Zonder overdrijven mogen we ons na meer dan een kwart eeuw ervaring "experts in toplagen" noemen.
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- Linda Leigh Rodgers seeks an administrative position with over 10 years of experience in accounts payable, accounts receivable, payroll, budget management, and project coordination for construction and grant management organizations.
- She has managed over $40 million in state and federal grants with experience ensuring audit compliance.
- Her skills include full-cycle accounts payable and receivable, contract management, budgeting, project cost accounting, and experience with accounting software and Microsoft Office.
Laser Therapy, an Emerging Clinical ParadigmPaul Schwen
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The document provides a resume and portfolio for Ross Pulsford, a photographer and creative director with over 20 years of experience in photography, film, television commercials, and brand development who is seeking new work opportunities that allow travel and working with leading creative teams on large projects. Pulsford has expertise in photography, creative direction, film directing, event production, and software skills. Examples are provided of Pulsford's past clients and projects in print media, television commercials, exhibitions, and corporate branding that achieved successful outcomes.
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- Linda Leigh Rodgers seeks an administrative position with over 10 years of experience in accounts payable, accounts receivable, payroll, budget management, and project coordination for construction and grant management organizations.
- She has managed over $40 million in state and federal grants with experience ensuring audit compliance.
- Her skills include full-cycle accounts payable and receivable, contract management, budgeting, project cost accounting, and experience with accounting software and Microsoft Office.
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Laser therapy emerged in the early 20th century and has since grown as a clinical paradigm. Key developments include Finsen using ultraviolet light to treat diseases in 1882, Einstein proposing the theory of lasers in 1916, and Maiman creating the first working laser in 1960. Laser therapy was used widely in Eastern Europe and Asia from the 1970s onward to treat pain, accelerate healing, and reduce inflammation through photobiostimulation. Higher power lasers above 5 watts became more commonly used and effective in the late 20th century. Laser therapy aims to stimulate cells to enhance healing through absorption of infrared light wavelengths.
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