The analytical solutions of the harvesting Verhulst’s evolution equation

Miškinis, Paulius; Vasiliauskienė, Vaida

doi:10.1016/j.ecolmodel.2017.06.021

Cited by 5 publications

(6 citation statements)

References 16 publications

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“…(3) where f(P; t) is a function of P and t. Miskinis and Vasilliauskiene studied a special case of the environment called the influence of harvesting of the population where the Verhulst equation is given by Eq. ( 4) [10].…”

Section: The Proposed Modelmentioning

confidence: 99%

“…Where the new coefficient now are given by Θ(t) =r(t)-c(t) and Γ(t)=r(t)/K, respectively. It is clear, if the growth rate a constant then this yields the Miskinis and Vasilliauskiene model [10], i.e., Eq (4). The equation is the focus of the study.…”

Section: (6)mentioning

confidence: 99%

“…Otherwise, if the variation is greater, then we fit the solution with the effect of the environment taken into account. To further study the environmental effect, let us use the same simulation parameters as in Miskinis et al [10] where K = 52.0 mm, r = 3.19×10 -2 h -1 , ϵ is about 0.1, and then initial condition P 0 is 0.27 mm and c=0.015 h -1 . We simulate the solution for four scenarios.…”

Section: (15)mentioning

confidence: 99%

“…Although the equation has been known for a long time, many studies are still conducted to examine its general properties. Further investigation is carried out by considering the effect of the environment on growth [9] [10].…”

Section: Introductionmentioning

confidence: 99%

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Analytic Solution to The Inhomogeneous Verhulst Equation Using Multiple Expansion Methods

Salim¹,

Sulaiman²,

Kenji³

2023

J. Multidiscip. Appl. Nat. Sci.

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The present study aims to obtain an analytic solution for the inhomogeneous Verhults equation using multiple expansion methods. This study identifies the external factors represented by the inhomogeneous term that determine optimal variable conditions for ecosystem population growth. The simulation involves scenarios that utilize constant growth rates, periodic growth rates, constant external factors, and periodic external factors. It is found that external factors increase population growth, whereas constant external factors prevent growth under saturation conditions. Periodic external factors cause fluctuations in the amplitude of growth regions. The present study will highlight and discuss the development and application of the solution.

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Section: The Proposed Modelmentioning

confidence: 99%

Section: (6)mentioning

confidence: 99%

Section: (15)mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Analytic Solution to The Inhomogeneous Verhulst Equation Using Multiple Expansion Methods

Salim¹,

Sulaiman²,

Kenji³

2023

J. Multidiscip. Appl. Nat. Sci.

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“…In general, for any parameter v the solution of the thermodepth model (1) is obtained using only numerical computational methods. However, when v = 1 in the case of non-homogeneous Verhulst equation, there is a precise analytical solution [20]:…”

Section: Termodepth Model Solutionsmentioning

confidence: 99%

Peculiarities of the Vertical Thermal Regime of Lake Tapeliai

Miškinis¹,

Moisejenkova²,

Jukna³

et al. 2019

Pol. J. Environ. Stud.

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One of the basic parameters of lake water is temperature [1, 2]. The willingness to determine the thermal structure theoretically applicable to the biggest variety of lakes drives professionals to create quite complex software packages taking into account all possible internal and external factors that determine lake water temperature changes [3-5]. Mathematically, such software packages comprise 9-15 nonlinear differential equations with partial derivatives and border and initial conditions of the same amount. The model has about 10 free parameters, which in principle give a good coincidence with experimental data (see [4-6]). Determining the lake thermal structure belongs to the classical limnology area and is under investigation up to now (see, e.g., [28, 29] and the references therein). Continuous thermodynamic, hydrophysical and other processes allow us to group lakes under selected criteria. Usually, they are classified according to the origin of water sources, water chemical structure, slope, water quality, water level, water circulation intensity, etc. [7-10]. Many works have recently analyzed the

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Forecasting of the Development of Fixed-Line Broadband Internet

Anikin

2020

Artificial Intelligence: Anthropogenic Nature vs. Social Origin

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The analytical solutions of the harvesting Verhulst’s evolution equation

Cited by 5 publications

References 16 publications

Analytic Solution to The Inhomogeneous Verhulst Equation Using Multiple Expansion Methods

Analytic Solution to The Inhomogeneous Verhulst Equation Using Multiple Expansion Methods

Peculiarities of the Vertical Thermal Regime of Lake Tapeliai

Forecasting of the Development of Fixed-Line Broadband Internet

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