Dynamics of populations with two sexes

2015 ◽  
Vol 08 (04) ◽  
pp. 1550049
Author(s):  
M. Cecilia Pérez ◽  
E. Adriana Saavedra ◽  
Mariano A. Ferrari
Keyword(s):  
Mathematical Model ◽  
Local Stability ◽  
Elephant Seal ◽  
Southern Elephant Seal ◽  
Real Population ◽  
Proposed Model ◽  
Males And Females ◽  
Direct Applicability ◽  
State Existence ◽  
Dynamics Of Populations

A mathematical model is presented in order to describe the dynamics of polygamous populations, bearing in mind single individuals of both sexes and the development of reproductive groups. In this context, the description leads us to consider positive homogeneous dynamical systems, establishing conditions for the stationary state existence and its local stability. A fourth pre-reproductive stage was considered, i.e. males and females spend part of their lives before being in condition to reproduce, as a first step to consider more general models. Finally, we parametrized the proposed model using southern elephant seal data, to analyze the direct applicability to a real population.

scholarly journals The Dynamics of a Single Species in a Polluted Environment

2020 ◽  
pp. 1-12
Author(s):  
Raid Kamel Naji ◽  
Mona Ghassan Younis ◽  
Mohammad Naeemullah
Keyword(s):  
Mathematical Model ◽  
Equilibrium Point ◽  
Local Stability ◽  
Single Species ◽  
Global Dynamics ◽  
Polluted Environment ◽  
Nonlinear Mathematical Model ◽  
Proposed Model

This article proposed and analysed a nonlinear mathematical model that consist of a single species in a polluted environment (PE). The proposed model was also discussed in terms of its uniqueness, existence, and boundedness of the solution. Also, each possible equilibrium point was analysed for local stability, followed by investigation of the global dynamics of the system using the Lypanov functions. The effects of the presence of toxicants on the dynamics of a single species in the PE was numerically investigated

scholarly journals Mathematical Model for Coronavirus Disease 2019 (COVID-19) Containing Isolation Class

2020 ◽  
Vol 2020 ◽  
pp. 1-7 ◽  
Author(s):  
Anwar Zeb ◽  
Ebraheem Alzahrani ◽  
Vedat Suat Erturk ◽  
Gul Zaman
Keyword(s):  
Mathematical Model ◽  
Finite Difference ◽  
Local Stability ◽  
Dynamical Behavior ◽  
Order Method ◽  
Human Contact ◽  
Proposed Model ◽  
Fourth Order Method ◽  
Nsfd Scheme ◽  
Nonstandard Finite Difference

The deadly coronavirus continues to spread across the globe, and mathematical models can be used to show suspected, recovered, and deceased coronavirus patients, as well as how many people have been tested. Researchers still do not know definitively whether surviving a COVID-19 infection means you gain long-lasting immunity and, if so, for how long? In order to understand, we think that this study may lead to better guessing the spread of this pandemic in future. We develop a mathematical model to present the dynamical behavior of COVID-19 infection by incorporating isolation class. First, the formulation of model is proposed; then, positivity of the model is discussed. The local stability and global stability of proposed model are presented, which depended on the basic reproductive. For the numerical solution of the proposed model, the nonstandard finite difference (NSFD) scheme and Runge-Kutta fourth order method are used. Finally, some graphical results are presented. Our findings show that human to human contact is the potential cause of outbreaks of COVID-19. Therefore, isolation of the infected human overall can reduce the risk of future COVID-19 spread.

Effects on prey–predator with different functional responses

2017 ◽  
Vol 10 (08) ◽  
pp. 1750113 ◽  
Author(s):  
Banani Roy ◽  
Sankar Kumar Roy ◽  
M. H. A. Biswas
Keyword(s):  
Mathematical Model ◽  
Local Stability ◽  
Generalist Predator ◽  
Functional Responses ◽  
Interior Equilibrium ◽  
Density Dependent Mortality ◽  
Proposed Model ◽  
Different Types ◽  
The Mathematical Model ◽  
Dependent Mortality

In this paper, we investigate the effects on prey of two predators which are also related in terms of prey–predator relationship. Different types of functional responses are considered to formulate the mathematical model for predator and generalist predator of our proposed model. Harvesting effort for the generalist predator is considered and the density-dependent mortality rate for predator and generalist predator is incorporated in our proposed model. Local stability as well as global stability for the system is discussed. We analyze the different bifurcation parameters to evaluate Hopf bifurcation in the neighborhood of interior equilibrium point. Finally, some numerical simulations and graphical figures are provided to verify our analytical results with the help of different sets of parameters.

THE DEVELOPMENT OF THE MATHEMATICAL MODEL OF PREDICTING THE INDICATORS OF ACCREDITATION OF TECHNICAL UNIVERSITIES IN THE RUSSIAN FEDERATION

2017 ◽  
pp. 27-38
Author(s):  
Olga Mikhaylovna Tikhonova ◽  
Alexander Fedorovich Rezchikov ◽  
Vladimir Andreevich Ivashchenko ◽  
Vadim Alekseevich Kushnikov
Keyword(s):  
Mathematical Model ◽  
System Dynamics ◽  
Regression Model ◽  
Oriented Graph ◽  
Real Data ◽  
Educational Process ◽  
Proposed Model ◽  
Linear Differential ◽  
The University ◽  
The Mathematical Model

The paper presents the system of predicting the indicators of accreditation of technical universities based on J. Forrester mechanism of system dynamics. According to analysis of cause-and-effect relationships between selected variables of the system (indicators of accreditation of the university) there was built the oriented graph. The complex of mathematical models developed to control the quality of training engineers in Russian higher educational institutions is based on this graph. The article presents an algorithm for constructing a model using one of the simulated variables as an example. The model is a system of non-linear differential equations, the modelling characteristics of the educational process being determined according to the solution of this system. The proposed algorithm for calculating these indicators is based on the system dynamics model and the regression model. The mathematical model is constructed on the basis of the model of system dynamics, which is further tested for compliance with real data using the regression model. The regression model is built on the available statistical data accumulated during the period of the university's work. The proposed approach is aimed at solving complex problems of managing the educational process in universities. The structure of the proposed model repeats the structure of cause-effect relationships in the system, and also provides the person responsible for managing quality control with the ability to quickly and adequately assess the performance of the system.

A Mathematical Model for the Anaerobic Digestion Process Applied to a Mixture of Night Soil and Septic Tank Sludge

1986 ◽  
Vol 18 (7-8) ◽  
pp. 239-248 ◽  
Author(s):  
Sung Ryong Ha ◽  
Dwang Ho Lee ◽  
Sang Eun Lee
Keyword(s):  
Mathematical Model ◽  
Anaerobic Digestion ◽  
Biomass Concentration ◽  
Gas Production ◽  
Septic Tank ◽  
Volatile Acid ◽  
Hydraulic Residence Time ◽  
Anaerobic Digestion Process ◽  
Digestion Process ◽  
Proposed Model

Laboratory scale experiments were conducted to develop a mathematical model for the anaerobic digestion of a mixture of night soil and septic tank sludge. The optimum mixing ratio by volume between night soil and septic tank sludge was found to be 7:3. Due to the high solids content in the influent waste, mixed-liquor volatile suspended solids (MLVSS) was not considered to be a proper parameter for biomass concentration, therefore, the active biomass concentration was estimated based on deoxyribonucleic acid (DNA) concentration in the reactor. The weight ratio between acidogenic bacteria and methanogenic bacteria in the mixed culture of a well-operated anaerobic digester was approximately 3:2. The proposed model indicates that the amount of volatile acid produced and the gas production rate can be expressed as a function of hydraulic residence time (HRT). The kinetic constants of the two phases of the anaerobic digestion process were determined, and a computer was used to simulate results using the proposed model for the various operating parameters, such as BOD5 and volatile acid concentrations in effluent, biomass concentrations and gas production rates. These were consistent with the experimental data.

scholarly journals On the Dragging Trajectory of Anchors in Clay for Merchant Ships

2021 ◽  
Vol 9 (2) ◽  
pp. 118
Author(s):  
Xinqing Zhuang ◽  
Keliang Yan ◽  
Pan Gao ◽  
Yihua Liu
Keyword(s):  
Mathematical Model ◽  
Structural Integrity ◽  
Indirect Measurement ◽  
Test System ◽  
Flow Rule ◽  
Burial Depth ◽  
Proposed Model ◽  
Depth Increase ◽  
Two Parameters ◽  
The Mathematical Model

Anchor dragging is a major threat to the structural integrity of submarine pipelines. A mathematical model in which the mechanical model of chain and the bearing model of anchor were coupled together. Based on the associated flow rule, an incremental procedure was proposed to solve the spatial state of anchor until it reaches the ultimate embedding depth. With an indirect measurement method for the anchor trajectory, a model test system was established. The mathematical model was validated against some model tests, and the effects of two parameters were studied. It was found that both the ultimate embedding depth of a dragging anchor and the distance it takes to reach the ultimate depth increase with the shank-fluke pivot angle, but decrease as the undrained shear strength of clay increases. The proposed model is supposed to be useful for the embedding depth calculation and guiding the design of the pipeline burial depth.

scholarly journals Content Dependent Representation Selection Model for Systems Based on MPEG DASH

Electronics ◽  
2021 ◽  
Vol 10 (15) ◽  
pp. 1843
Author(s):  
Jelena Vlaović ◽  
Snježana Rimac-Drlje ◽  
Drago Žagar
Keyword(s):  
Mathematical Model ◽  
Spatial Information ◽  
Relevant Literature ◽  
Video Quality ◽  
Similarity Index ◽  
Video Encoding ◽  
Adaptation Algorithm ◽  
Subjective Testing ◽  
Proposed Model ◽  
The Mathematical Model

A standard called MPEG Dynamic Adaptive Streaming over HTTP (MPEG DASH) ensures the interoperability between different streaming services and the highest possible video quality in changing network conditions. The solutions described in the available literature that focus on video segmentation are mostly proprietary, use a high amount of computational power, lack the methodology, model notation, information needed for reproduction, or do not consider the spatial and temporal activity of video sequences. This paper presents a new model for selecting optimal parameters and number of representations for video encoding and segmentation, based on a measure of the spatial and temporal activity of the video content. The model was developed for the H.264 encoder, using Structural Similarity Index Measure (SSIM) objective metrics as well as Spatial Information (SI) and Temporal Information (TI) as measures of video spatial and temporal activity. The methodology that we used to develop the mathematical model is also presented in detail so that it can be applied to adapt the mathematical model to another type of an encoder or a set of encoding parameters. The efficiency of the segmentation made by the proposed model was tested using the Basic Adaptation algorithm (BAA) and Segment Aware Rate Adaptation (SARA) algorithm as well as two different network scenarios. In comparison to the segmentation available in the relevant literature, the segmentation based on the proposed model obtains better SSIM values in 92% of cases and subjective testing showed that it achieves better results in 83.3% of cases.

The Generation Principle and Mathematical Models of Double-Enveloping Internal Gear Pairs

2015 ◽  
Author(s):  
Xuan Li ◽  
Bingkui Chen ◽  
Yawen Wang ◽  
Guohua Sun ◽  
Teik C. Lim
Keyword(s):  
Mathematical Model ◽  
Load Capacity ◽  
Geometrical Shape ◽  
Gear Pair ◽  
Numerical Examples ◽  
Proposed Model ◽  
General Mathematical Model ◽  
Meshing Characteristics ◽  
Internal Gear ◽  
Tooth Pair

In this paper, the planar double-enveloping method is presented for the generation of tooth profiles of the internal gear pair for various applications, such as gerotors and gear reducers. The main characteristic of this method is the existence of double contact between one tooth pair such that the sealing property, the load capacity and the transmission precision can be significantly improved as compared to the conventional configuration by the single-enveloping theory. Firstly, the generation principle of the planar double-enveloping method is introduced. Based on the coordinate transformation and the envelope theory, the general mathematical model of the double-enveloping internal gear pair is presented. By using this model, users can directly design different geometrical shape profiles to obtain a double-enveloping internal gear pair with better meshing characteristics. Secondly, to validate the effectiveness of the proposed model, specific mathematical formulations of three double-enveloping internal gear pairs which apply circular, parabolic and elliptical curves as the generating curves are given. The equations of tooth profiles and meshing are derived and the composition of tooth profiles is analyzed. Finally, numerical examples are provided for an illustration.

scholarly journals An Optimized Mathematical Model for Items Supplies Planning of a Logistic System

2016 ◽  
Vol 10 (10) ◽  
pp. 133
Author(s):  
Mohammad Ali Nasiri Khalili ◽  
Mostafa Kafaei Razavi ◽  
Morteza Kafaee Razavi
Keyword(s):  
Mathematical Model ◽  
Mixed Integer ◽  
Logistics System ◽  
Proposed Model ◽  
Multiple Objective Decision Making ◽  
System Requirements ◽  
Purchasing Logistics ◽  
The Cost ◽  
The Mathematical Model ◽  
First Time

Items supplies planning of a logistic system is one of the major issue in operations research. In this article the aim is to determine how much of each item per month from each supplier logistics system requirements must be provided. To do this, a novel multi objective mixed integer programming mathematical model is offered for the first time. Since in logistics system, delivery on time is very important, the first objective is minimization of time in delivery on time costs (including lack and maintenance costs) and the cost of purchasing logistics system. The second objective function is minimization of the transportation supplier costs. Solving the mathematical model shows how to use the Multiple Objective Decision Making (MODM) can provide the ensuring policy and transportation logistics needed items. This model is solved with CPLEX and computational results show the effectiveness of the proposed model.

Sign in / Sign up

Export Citation Format

Share Document