A RESOURCE-DEPENDENT COMPETITION MODEL: EFFECTS OF POPULATION PRESSURE AUGMENTED INDUSTRIALIZATION

2012 ◽  
Vol 03 (02) ◽  
pp. 1250003 ◽  
Author(s):  
MANJU AGARWAL ◽  
SAPNA DEVI
Keyword(s):  
Mathematical Model ◽  
Growth Rate ◽  
Numerical Simulations ◽  
Carrying Capacity ◽  
Rate Coefficient ◽  
Population Pressure ◽  
Equilibrium Density ◽  
Nonlinear Mathematical Model ◽  
Competing Species ◽  
Increase With Increase

In this paper, a nonlinear mathematical model is proposed and analyzed to study the effects of population pressure augmented industrialization on the survival of competing species dependent on resource. It is assumed that the growths of competing species are logistic and carrying capacities increase with increase in the density of resource biomass. Further, it is assumed that the resource biomass too is growing logistically in the environment and its carrying capacity decreases with the increase in densities of competing species and industrialization. The growth rate of population pressure is assumed to be proportional to the densities of competing species. Stabilities of all equilibria and conditions which influence the permanence of the system are carried out using theory of differential equations. Numerical simulations are performed to accomplish our analytical findings. It is shown that the equilibrium density of resource biomass decreases as (i) the growth rate coefficient of population pressure increases (ii) the growth rate coefficient of industrialization due to population pressure increases and (iii) the growth rate coefficient of industrialization due to resource biomass increases. It is found that the competitive outcome alters with increase in the growth rate coefficient of population pressure. Decrease in the equilibrium densities of competing species is also noted with increase in the growth rate coefficient of industrialization due to resource biomass.

A mathematical model to achieve sustainable forest management

2015 ◽  
Vol 06 (04) ◽  
pp. 1550040 ◽  
Author(s):  
A. K. Misra ◽  
Kusum Lata
Keyword(s):  
Mathematical Model ◽  
Sustainable Forest Management ◽  
Forest Products ◽  
Model System ◽  
Forest Resources ◽  
Genetically Engineered ◽  
Population Pressure ◽  
Nonlinear Mathematical Model ◽  
Modeling Process ◽  
Genetically Engineered Plants

Forest resources are important natural resources for all living beings but they are continuously depleting due to overgrowth of human population and their development activities. Therefore, conservation of forest resources is an important problem for sustainable development. In view of this, in this paper, we have proposed and analyzed a nonlinear mathematical model to study the effects of economic and technological efforts on the conservation of forest resources. In the modeling process, it is assumed that due to increase in population size, the demand of population (population pressure) for forest products, lands, etc., increases and to reduce this population pressure, economic efforts are employed proportional to the population pressure. Further, it is assumed that technological efforts in the form of genetically engineered plants are applied proportional to the depleted level of forest resources to conserve them. Model analysis reveals that increase in economic and technological efforts increases the density of forest resources but further increase in these efforts destabilizes the system. Numerical simulation is carried out to verify analytical findings and explore the effect of different parameters on the dynamics of model system.

scholarly journals Asymptotic Properties of One Mathematical Model in Food Engineering under Stochastic Perturbations

Mathematics ◽  
2021 ◽  
Vol 9 (23) ◽  
pp. 3013
Author(s):  
Leonid Shaikhet
Keyword(s):  
Mathematical Model ◽  
Mathematical Models ◽  
Numerical Simulations ◽  
Wide Class ◽  
Asymptotic Properties ◽  
Nonlinear Mathematical Model ◽  
Simple Criterion ◽  
Stochastic Perturbations ◽  
Food Engineering ◽  
Nonlinear Mathematical Models

For the example of one nonlinear mathematical model in food engineering with several equilibria and stochastic perturbations, a simple criterion for determining a stable or unstable equilibrium is reported. The obtained analytical results are illustrated by detailed numerical simulations of solutions of the considered Ito stochastic differential equations. The proposed criterion can be used for a wide class of nonlinear mathematical models in different applications.

EFFECT OF AWARENESS PROGRAMS IN CONTROLLING THE PREVALENCE OF AN EPIDEMIC WITH TIME DELAY

2011 ◽  
Vol 19 (02) ◽  
pp. 389-402 ◽  
Author(s):  
A. K. MISRA ◽  
ANUPAMA SHARMA ◽  
VISHAL SINGH
Keyword(s):  
Mathematical Model ◽  
Hopf Bifurcation ◽  
Time Delay ◽  
Numerical Simulations ◽  
Periodic Solutions ◽  
Stability Theory ◽  
Direct Contact ◽  
Behavioral Changes ◽  
Nonlinear Mathematical Model ◽  
Awareness Programs

A nonlinear mathematical model with delay to capture the dynamics of effect of awareness programs on the prevalence of any epidemic is proposed and analyzed. It is assumed that pathogens are transmitted via direct contact between susceptibles and infectives. It is assumed further that cumulative density of awareness programs increases at a rate proportional to the number of infectives. It is considered that awareness programs are capable of inducing behavioral changes in susceptibles, which result in the isolation of aware population. The model is analyzed using stability theory of differential equations and numerical simulations. The model analysis shows that, though awareness programs cannot eradicate infection, they help in controlling the prevalence of disease. It is also found that time delay in execution of awareness programs destabilizes the system and periodic solutions may arise through Hopf-bifurcation.

A MATHEMATICAL MODEL FOR THE DEPLETION OF FORESTRY RESOURCES DUE TO POPULATION AND POPULATION PRESSURE AUGMENTED INDUSTRIALIZATION

2013 ◽  
Vol 05 (01) ◽  
pp. 1350022 ◽  
Author(s):  
A. K. MISRA ◽  
KUSUM LATA ◽  
J. B. SHUKLA
Keyword(s):  
Mathematical Model ◽  
Logistic Models ◽  
Model Analysis ◽  
Population Pressure ◽  
Nonlinear Mathematical Model ◽  
Biomass Density ◽  
Modeling Process ◽  
Forestry Resources

In this paper, a nonlinear mathematical model is proposed and analyzed to study the depletion of forestry resources caused simultaneously by population and population pressure augmented industrialization. The control of population pressure, using economic efforts is also considered in the modeling process. It is assumed that cumulative biomass density of forestry resources and the density of population follow logistic models. It is further assumed that the density of population and the level of industrialization increase as the cumulative biomass density of forestry resources increases. The cumulative density of economic efforts, which are applied to control the population pressure, is considered to be proportional to the population pressure. The model analysis shows that as the population pressure increases, the level of industrialization increases leading to decrease in the cumulative biomass density of forestry resources. It is found that if population pressure is controlled by using some economic efforts, the decrease in cumulative biomass density of forestry resources can be made much less than the case when no control is applied. It is also noted that if the population pressure augmented industrialization increases without control, the forestry resources may become extinct.

scholarly journals A Mathematical Model to Examination the Behavior of Two Competing Biological Species under the Effect of a Toxicant

2019 ◽  
Vol 8 (2S10) ◽  
pp. 673-677
Keyword(s):  
Mathematical Model ◽  
Carrying Capacity ◽  
Biological Species ◽  
Competing Species ◽  
Biological Population ◽  
Long Run ◽  
Common Resource ◽  
The Mind

It is well known that the toxicants present in the environment affect the growth of any biological population living in that habitat. It also affects the carrying capacity of the environment with respect to that biological population. In this paper we are considering two logistically growing biological populations competing for a common resource under the effect of a toxicant and we’ve assumed that the first population discharges toxicant which is harmful to the second population only. Since, condition of the population and their habitat are limited therefore, keeping the above in the mind, here we’ve proposed a mathematical model to study the behaviour of the two competing population and observed that one species dies away as the time lapses due to the effect of the toxicants. It has been shown further that under certain conditions both the competing species can coexist in a long run

scholarly journals Analytical and Approximate Solutions of a Novel Nervous Stomach Mathematical Model

2020 ◽  
Vol 2020 ◽  
pp. 1-9 ◽  
Author(s):  
Yolanda Guerrero Sánchez ◽  
Zulqurnain Sabir ◽  
Hatıra Günerhan ◽  
Haci Mehmet Baskonus
Keyword(s):  
Mathematical Model ◽  
Numerical Simulations ◽  
Death Rate ◽  
Approximate Solutions ◽  
Mathematical Form ◽  
Nonlinear Mathematical Model ◽  
Transformation Technique ◽  
Differential Transformation ◽  
Sleep Factor

The stomach is usually considered as a hollow muscular sac, which initiates the second segment of digestion. It is the most sophisticated endocrine structure having unique biochemistry, physiology, microbiology, and immunology. The pivotal aim of the present study is to propose the nonlinear mathematical model of the nervous stomach system based on three compartments namely, tension (T), food (F), and medicine (M). The detailed description of each compartment is provided along with the mathematical form and different rates/factors, such as sleep factor, food rate, tension rate, medicine term, and death rate. The solution of the designed model is presented numerically by using the well-known differential transformation technique. The behavior of the obtained solution has been captured with respect to time as well as presentations of the numerical simulations.

EXISTENCE AND SURVIVAL OF TWO COMPETING SPECIES IN A POLLUTED ENVIRONMENT: A MATHEMATICAL MODEL

2001 ◽  
Vol 09 (02) ◽  
pp. 89-103 ◽  
Author(s):  
J. B. SHUKLA ◽  
A. K. AGRAWAL ◽  
B. DUBEY ◽  
P. SINHA
Keyword(s):  
Mathematical Model ◽  
Growth Rate ◽  
Emission Rate ◽  
Biological Species ◽  
Rate Coefficients ◽  
Washout Rate ◽  
Polluted Environment ◽  
Nonlinear Mathematical Model ◽  
Model Study ◽  
External Sources

In this paper, a nonlinear mathematical model to study the effect of a toxicant emitted into the environment from external sources on two competing biological species is proposed and analyzed. The cases of constant emission and instantaneous spill of a toxicant are considered in the model study. In the case of constant emission, it is shown that four usual outcomes of competition between two species may be altered under appropriate conditions which are mainly dependent on emission rate of toxicant into the environment, uptake concentrations of toxicant by the two species and their growth rate coefficients and carrying capacities. However, in the case of instantaneous spill, it is found that if the washout rate of toxicant is large, then the four outcomes of competition exist under usual conditions. It is also pointed out that the survival of the competitors, coexisting in absence of the toxicant, may be threatened if the constant emission of toxicant into their environment continues unabatedly.

scholarly journals Numerical simulations and analysis for mathematical model of avascular tumor growth using Gompertz growth rate function

2021 ◽  
Vol 60 (4) ◽  
pp. 3731-3740
Author(s):  
Akhtar Ali ◽  
Majid Hussain ◽  
Abdul Ghaffar ◽  
Zafar Ali ◽  
Kottakkaran Sooppy Nisar ◽  
...  
Keyword(s):  
Mathematical Model ◽  
Growth Rate ◽  
Tumor Growth ◽  
Numerical Simulations ◽  
Rate Function ◽  
Growth Rate Function ◽  
Avascular Tumor

Saturation mechanism and generated viscosity in gravito-turbulent accretion disks

2020 ◽  
Vol 640 ◽  
pp. A53
Author(s):  
L. Löhnert ◽  
S. Krätschmer ◽  
A. G. Peeters
Keyword(s):  
Growth Rate ◽  
Numerical Simulations ◽  
Accretion Disks ◽  
Gravitational Instability ◽  
Turbulent Viscosity ◽  
Radial Distance ◽  
Maximum Growth ◽  
Wave Number ◽  
Radiative Cooling ◽  
Mixing Length

Here, we address the turbulent dynamics of the gravitational instability in accretion disks, retaining both radiative cooling and irradiation. Due to radiative cooling, the disk is unstable for all values of the Toomre parameter, and an accurate estimate of the maximum growth rate is derived analytically. A detailed study of the turbulent spectra shows a rapid decay with an azimuthal wave number stronger than ky−3, whereas the spectrum is more broad in the radial direction and shows a scaling in the range kx−3 to kx−2. The radial component of the radial velocity profile consists of a superposition of shocks of different heights, and is similar to that found in Burgers’ turbulence. Assuming saturation occurs through nonlinear wave steepening leading to shock formation, we developed a mixing-length model in which the typical length scale is related to the average radial distance between shocks. Furthermore, since the numerical simulations show that linear drive is necessary in order to sustain turbulence, we used the growth rate of the most unstable mode to estimate the typical timescale. The mixing-length model that was obtained agrees well with numerical simulations. The model gives an analytic expression for the turbulent viscosity as a function of the Toomre parameter and cooling time. It predicts that relevant values of α = 10−3 can be obtained in disks that have a Toomre parameter as high as Q ≈ 10.

scholarly journals Volterra–Lyapunov Stability Analysis of the Solutions of Babesiosis Disease Model

Symmetry ◽  
2021 ◽  
Vol 13 (7) ◽  
pp. 1272
Author(s):  
Fengsheng Chien ◽  
Stanford Shateyi
Keyword(s):  
Mathematical Model ◽  
Stability Analysis ◽  
Global Stability ◽  
Numerical Simulations ◽  
Lyapunov Stability ◽  
Disease Model ◽  
Transmission Dynamics ◽  
Global Stability Analysis ◽  
Lyapunov Stability Analysis ◽  
Disease Free

This paper studies the global stability analysis of a mathematical model on Babesiosis transmission dynamics on bovines and ticks populations as proposed by Dang et al. First, the global stability analysis of disease-free equilibrium (DFE) is presented. Furthermore, using the properties of Volterra–Lyapunov matrices, we show that it is possible to prove the global stability of the endemic equilibrium. The property of symmetry in the structure of Volterra–Lyapunov matrices plays an important role in achieving this goal. Furthermore, numerical simulations are used to verify the result presented.

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