scholarly journals Psi-Caputo Logistic Population Growth Model

2021 ◽  
Vol 2021 ◽  
pp. 1-9
Author(s):  
Muath Awadalla ◽  
Yves Yannick Yameni Noupoue ◽  
Kinda Abu Asbeh
Keyword(s):  
Population Growth ◽  
Fractional Derivative ◽  
Carrying Capacity ◽  
Chinese Population ◽  
Logistic Model ◽  
Logistic Equation ◽  
Logistic Growth ◽  
Growth Equation ◽  
Uniqueness Of The Solution ◽  
Better Than

This article studies modeling of a population growth by logistic equation when the population carrying capacity K tends to infinity. Results are obtained using fractional calculus theories. A fractional derivative known as psi-Caputo plays a substantial role in the study. We proved existence and uniqueness of the solution to the problem using the psi-Caputo fractional derivative. The Chinese population, whose carrying capacity, K, tends to infinity, is used as evidence to prove that the proposed approach is appropriate and performs better than the usual logistic growth equation for a population with a large carrying capacity. A psi-Caputo logistic model with the kernel function x + 1 performed the best as it minimized the error rate to 3.20% with a fractional order of derivative α  = 1.6455.

scholarly journals An Improved Logistic Model Illustrating Microcystis aeruginosa Growth Under Different Turbulent Mixing Conditions

Water ◽  
2019 ◽  
Vol 11 (4) ◽  
pp. 669
Author(s):  
Haiping Zhang ◽  
Fan Huang ◽  
Feipeng Li ◽  
Zhujun Gu ◽  
Ruihong Chen ◽  
...  
Keyword(s):  
Microcystis Aeruginosa ◽  
Growth Model ◽  
Turbulent Mixing ◽  
Logistic Model ◽  
Logistic Equation ◽  
Logistic Growth ◽  
Turbulence Mixing ◽  
Population Dynamics Models ◽  
Dynamics Models ◽  
Relationship Of

To overcome the limitations of the normal logistic equation, we aimed to improve the logistic model under hydrodynamic conditions for the examination of the responses of cyanobacterium, coupled turbulence mixing, and growth of cyanobacterium in population dynamics models. Selecting Microcystis aeruginosa and experimenting with the ideal conditions in a laboratory beaker, the chlorophyll-a concentration reached the corresponding maximum under each turbulent condition compared with the control. According to the experiment results, the theory of mass transfer, turbulence mixing, and the logistic equation are organically combined. The improved logistic growth model of Microcystis aeruginosa and competition growth model in the symbiont Scenedesmus quadricauda under turbulent conditions were established. Using the MATLAB multi-parameter surface fitting device, both models produced good fitting effects, with R > 0.95, proving that the results fit the models, and demonstrating the relationship of the unity of nutrient transfer and algae growth affected by turbulence mixing. With continuous increases in turbulent mixing, the fitted curve became smoother and steadier. Algae stimulated by turbulence accelerate reproduction and fission to achieve population dominance. The improved logistic model quantitatively explains the Microcystis aeruginosa response to turbulence and provides a basis to represent ecological and biogeochemical processes in enclosed eutrophic water bodies.

scholarly journals Analysis of logistic equation pertaining to a new fractional derivative with non-singular kernel

2017 ◽  
Vol 9 (2) ◽  
pp. 168781401769006 ◽  
Author(s):  
Devendra Kumar ◽  
Jagdev Singh ◽  
Maysaa Al Qurashi ◽  
Dumitru Baleanu
Keyword(s):  
Numerical Simulation ◽  
Fixed Point ◽  
Fractional Derivative ◽  
Fractional Order ◽  
Existence And Uniqueness ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Logistic Equation ◽  
Iterative Technique ◽  
Uniqueness Of The Solution

In this work, we aim to analyze the logistic equation with a new derivative of fractional order termed in Caputo–Fabrizio sense. The logistic equation describes the population growth of species. The existence of the solution is shown with the help of the fixed-point theory. A deep analysis of the existence and uniqueness of the solution is discussed. The numerical simulation is conducted with the help of the iterative technique. Some numerical simulations are also given graphically to observe the effects of the fractional order derivative on the growth of population.

scholarly journals Population prediction of purwanegara village, Indonesia using modified logistic model with migration factor

2018 ◽  
Vol 7 (3) ◽  
pp. 1962
Author(s):  
Diandra Chika Fransisca ◽  
Padosroha Marbun
Keyword(s):  
Population Growth ◽  
Equilibrium Point ◽  
Growth Model ◽  
Carrying Capacity ◽  
Logistic Model ◽  
Central Java ◽  
Migration Factor ◽  
Central Java Province ◽  
Population Prediction ◽  
Birth Death

Population growth model is a widely been used model to do an estimation and forecasting towards the population of peoples, animals, bac-teria and even in economics growth. Many studies have been carried out on population growth model concerning the factors of birth, death and carrying capacity in order to predict the number of population at certain area. From these studies there is only one study involved the constant value factor of migration as an input in the logistic model. Therefore contradicting with the above modified logistic model, in this study logistic model is modified by adding a migration factor as a function of population. This function takes into account the migration and the interaction between peoples that is limited to the carrying capacity of the environment. This model can be solved qualitatively using the analysis of equilibrium point and quantitatively using the separable variables method. This modified logistic model with migration factor has been applied in the population prediction of Purwanegara village in Central Java Province, Indonesia. Throughout the results, the modified logistic model with migration factor as a function of population gives a better result for population prediction of Purwanegara village in Central Java Province, Indonesia compared with logistic model.  

On the Random Non-Autonomous Logistic Equation with Time-Dependent Coefficients

2021 ◽  
pp. 2150038
Author(s):  
J. Calatayud ◽  
J.-C. Cortés ◽  
F. A. Dorini
Keyword(s):  
Carrying Capacity ◽  
Random Variable ◽  
Transformation Method ◽  
Logistic Equation ◽  
Time Dependent ◽  
Logistic Growth ◽  
Model Output ◽  
Intrinsic Growth Rate ◽  
Recorded Data ◽  
Logistic Growth Model

In this paper, we deal with the non-autonomous logistic growth model with time-dependent intrinsic growth rate and carrying capacity. Accounting for errors in recorded data, randomness is incorporated into the equation by assuming that the input parameters are random variables. The uncertainty of the model output is quantified by approximations of the first probability density function via the random variable transformation method. A numerical example illustrates the results.

Time-dependent solution of the logistic model for population growth in random environment

1980 ◽  
Vol 17 (04) ◽  
pp. 1083-1086
Author(s):  
Prajneshu
Keyword(s):  
Population Growth ◽  
Stationary Solution ◽  
Random Environment ◽  
Carrying Capacity ◽  
Logistic Model ◽  
Time Dependent ◽  
Kolmogorov Equation ◽  
Exact Time ◽  
Time Dependent Solution

The exact time-dependent solution as well as the stationary solution of the logistic model for population growth with varying carrying capacity is worked out in both the Stratonovich and Ito calculi by solving the forward Kolmogorov equation.

scholarly journals Density-independent processes decouple component and ensemble density feedbacks

2021 ◽  
Author(s):  
Corey J. A. Bradshaw ◽  
Salvador Herrando-Perez
Keyword(s):  
Population Growth ◽  
Growth Rates ◽  
Carrying Capacity ◽  
Census Data ◽  
Growth Models ◽  
Structured Populations ◽  
Logistic Growth ◽  
Feedback Signal ◽  
Vital Rates ◽  
Population Growth Rates

Analysis of long-term trends in abundance provide insights into population dynamics. Population growth rates are the emergent interplay of fertility, survival, and dispersal, but the density feedbacks on some vital rates (component) can be decoupled from density feedback on population growth rates (ensemble). However, the mechanisms responsible for this decoupling are poorly understood. We simulated component density feedbacks on survival in age-structured populations of long-living vertebrates and quantified how imposed nonstationarity (density-independent mortality and variation in carrying-capacity) modified the ensemble feedback signal estimated from logistic-growth models to the simulated abundance time series. The statistical detection of ensemble density feedback was largely unaffected by density-independent processes, but catastrophic and proportional mortality eroded the effect of density-dependent survival on ensemble-feedback strength more strongly than variation in carrying capacity. Thus, phenomenological models offer a robust approach to capture density feedbacks from nonstationary census data when density-independent mortality is low.

Time-dependent solution of the logistic model for population growth in random environment

1980 ◽  
Vol 17 (4) ◽  
pp. 1083-1086 ◽  
Author(s):  
Prajneshu
Keyword(s):  
Population Growth ◽  
Stationary Solution ◽  
Random Environment ◽  
Carrying Capacity ◽  
Logistic Model ◽  
Time Dependent ◽  
Kolmogorov Equation ◽  
Exact Time ◽  
Time Dependent Solution

The exact time-dependent solution as well as the stationary solution of the logistic model for population growth with varying carrying capacity is worked out in both the Stratonovich and Ito calculi by solving the forward Kolmogorov equation.

scholarly journals Penerapan Persamaan Diferensial Verhulst dalam Menentukan Proyeksi Penduduk di Kabupaten Tulungagung

2018 ◽  
Vol 7 (2) ◽  
pp. 87-102
Author(s):  
Dewi Anggreini
Keyword(s):  
Growth Rate ◽  
Population Growth ◽  
Growth Model ◽  
Carrying Capacity ◽  
Applied Mathematics ◽  
Logistic Growth ◽  
Second Stage ◽  
The Subject ◽  
Logistic Growth Model ◽  
To Come

Penelitian ini bertujuan menentukan proyeksi pertumbuhan penduduk di Kabupaten Tulungagung provinsi Jawa Timur dengan model persamaan diferensial Verhulst berdasarkan laju pertumbuhan dan daya tampung (carrying capacity). Target khusus dari hasil penelitian ini adalah model pertumbuhan logistik bisa digunakan sebagai alat untuk mengetahui proyeksi pertumbuhan penduduk berdasarkan laju pertumbuhan dan daya tampung dibeberapa daerah di Indonesia. Metode riset yang digunakan pada tahap pertama adalah menentukan subjek penelitian dan tahap Kedua adalah (1) mengumpulkan data penelitian (2) analisis data dan terakhir menarik kesimpulan. Data penelitian ini diperoleh dari BPS Kabupaten Tulungagung yaitu jumlah penduduk dari tahun 2010-2016. Hasil Penelitian menunjukkan bahwa: 1) Besarnya nilai carrying capacity yang membatasi penduduk di Kabupaten Tulungagung adalah sebesar 1.089.103,3. 2) Laju pertumbuhan intrinsik penduduk di kabupaten Tulungagung dengan menggunakan Model pertumbuhan logistik adalah sebesar r = 0,07480. 3) Jumlah penduduk di Kabupaten Tulungagung pada tahun 2025 dari hasil estimasi menggunakan model pertumbuhan logistik adalah sebesar 1.055.578 jiwa. 4) Proyeksi jumlah penduduk di Kabupaten Tulungagung  lebih tepat menggunakan model logistik I dengan persamaannya . Penelitian ini diharapkan dapat bermanfaat bagi semua pihak khususnya pada bidang matematika terapan serta metode dalam  menghitung pertumbuhan populasi di suatu daerah pada periode yang akan datang. [This study aims to determine the projected population growth in Tulungagung Regency of East Java province with a model of Verhulst differential equations based on growth rate and carrying capacity. The specific target of this research is logistic growth model can be used as a tool to know the projection of population growth based on growth rate and capacity in some regions in Indonesia. Research methods used in the first stage is to determine the subject of research and the second stage is (1) collect research data (2) data analysis and last draw conclusions. The data of this research is obtained from BPS of Tulungagung Regency that is population from 2010-2016. The results showed that: 1) The amount of carrying capacity that limits the population in Tulungagung Regency is equal 1.089.103,3. 2) The intrinsic growth rate of the population in Tulungagung district using the logistic growth model is r = 0,07480 3) The population in Tulungagung District in 2025 from the estimation using the logistic growth model is 1.055.578 soul, 4) The projection of population in Tulungagung is more appropriate using the logistic model I with the equation .  This study is expected to be useful for all parties, especially in the field of applied mathematics and methods in calculating population growth in an area in the period to come.]

Population strategies and random environments

1975 ◽  
Vol 53 (2) ◽  
pp. 160-165 ◽  
Author(s):  
Hugh Barclay
Keyword(s):  
Population Growth ◽  
Stochastic Models ◽  
Carrying Capacity ◽  
Death Rate ◽  
Logistic Model ◽  
Birth Rate ◽  
Environmental Variation ◽  
Random Environments ◽  
Probability Of Extinction ◽  
Established Species

It is shown using several models that r and K selection may result from random environmental variation. Probabilities of extinction are derived for both colonizing and well-established species using stochastic models similar to the logistic model, and it is shown that the probability of extinction of a population can be reduced by increasing the birth rate or the carrying capacity or by decreasing the death rate or the effects of the environmental variation on population growth. It is probable that random environmental variation mainly facilitates r selection.

A Model in Chinese Population Growth Prediction

2014 ◽  
Vol 556-562 ◽  
pp. 6811-6814 ◽  
Author(s):  
Hai Yan Xuan ◽  
An Qi Zhang ◽  
Na Na Yang
Keyword(s):  
Population Growth ◽  
Prediction Model ◽  
Chinese Population ◽  
Logistic Model ◽  
Total Population ◽  
Prediction Models ◽  
Initial Population ◽  
Population Forecast ◽  
Growth Prediction

Firstly, we calculated several statistics relating to the population forecast. Secondly, ba-sed on the Logistic prediction models, against Logistic model defects, we obtained the improved prediction model. Finally, using China's total population in 2004 as the initial population, we predict the total population of China in the next 30 years and in 2050 year by applying the model.

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