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.

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.

Modeling the effects of environmental pollution intensified by urbanization on human population

2016 ◽  
Vol 07 (03) ◽  
pp. 1650013 ◽  
Author(s):  
Abhinav Tandon ◽  
Kumari Jyotsna
Keyword(s):  
Mathematical Model ◽  
Environmental Pollution ◽  
Human Population ◽  
Model Analysis ◽  
Population Pressure ◽  
Long Run ◽  
Constant Rate ◽  
Growing Population

A mathematical model is presented here to investigate the effects of environmental pollution, intensified by urbanization, on the density of human population. Here, urbanization is assumed to grow with constant rate and also, induced through growing population and the corresponding population pressure. The model analysis, qualitatively and numerically, show that though the growth of population or population pressure is responsible for the growing urbanization, but for very large increase of urbanization, the population may not survive in the long run due to environmental pollution driven by urbanization.

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.

scholarly journals Mathematical Modeling of the Spread of Alcoholism Among Colombian College Students

2020 ◽  
Vol 16 (32) ◽  
pp. 195-223
Author(s):  
Edgardo Pérez
Keyword(s):  
Mathematical Modeling ◽  
College Students ◽  
Mathematical Model ◽  
Drinking Behavior ◽  
Preventive Measure ◽  
Nonlinear Mathematical Model ◽  
Consumption Behavior ◽  
Existence And Stability ◽  
Drugs And Crime ◽  
The Impact

In this paper, we present a nonlinear mathematical model, describing the spread of high-risk alcohol consumption behavior among college students in Colombia. We proved the existence and stability of the alcohol-free and drinking state equilibrium by means of Lyapunov function and LaSalle’s invariance principle. Also, we apply optimal control to study the impact of a preventive measure on the spread of drinking behavior among college students. Finally, we use numerical simulations and available data provided by the United Nations Office on Drugs and Crime (UNODC) and the Colombian Ministry of Justice to validate the obtained mathematical model.

A Nonlinear Mathematical Model for Ship Turning Circle Simulation in Waves

2005 ◽  
Vol 49 (02) ◽  
pp. 69-79 ◽  
Author(s):  
Ming-Chung Fang ◽  
Jhih-Hong Luo ◽  
Ming-Ling Lee
Keyword(s):  
Mathematical Model ◽  
Degrees Of Freedom ◽  
Regular Waves ◽  
Nonlinear Mathematical Model ◽  
Ship Maneuvering ◽  
Sea Trial ◽  
Six Degrees Of Freedom ◽  
Strip Theory ◽  
Calm Water ◽  
Maneuvering Motion

In the paper, a simplified six degrees of freedom mathematical model encompassing calm water maneuvering and traditional seakeeping theories is developed to simulate the ship turning circle test in regular waves. A coordinate system called the horizontal body axes system is used to present equations of maneuvering motion in waves. All corresponding hydrodynamic forces and coefficients for seakeeping are time varying and calculated by strip theory. For simplification, the added mass and damping coefficients are calculated using the constant draft but vary with encounter frequency. The nonlinear mathematical model developed here is successful in simulating the turning circle of a containership in sea trial conditions and can be extended to make the further simulation for the ship maneuvering under control in waves. Manuscript received at SNAME headquarters February 19, 2003; revised manuscript received January 27, 2004.

Information dualism of the problem of optimum terminal control of dynamic object

2021 ◽  
pp. 85-90
Author(s):  
V.P. Ivanov
Keyword(s):  
Mathematical Model ◽  
Optimal Control ◽  
Control Law ◽  
Computational Algorithms ◽  
Terminal Control ◽  
Dynamic Object ◽  
Nonlinear Mathematical Model ◽  
Dynamical Object

The article deals with the problem of synthesis of terminal control. A functional, a nonlinear mathematical model of a dynamic object, restrictions on the maximum permissible values of control are given. The control law is synthesized. The following statement is proved: the synthesis of the optimal control is carried out using the entire initial mathematical model of the dynamical object, but to calculate the control at any particular moment of time, it is possible to use a reduced (truncated) model, which simplifies the computational algorithms. Thus, there is an informational dualism of the manage- ment task. The approach is an extension of the principle of information redefinition of Yu.B. Germeier to the area of optimal terminal control.

Optimizing Series Repairable Systems with Imperfect Repair

2013 ◽  
pp. 83-93
Author(s):  
Mohammed Hajeeh
Keyword(s):  
Mathematical Model ◽  
Closed Form ◽  
Optimal Solution ◽  
Closed Form Expression ◽  
Repairable Systems ◽  
Nonlinear Mathematical Model ◽  
Repair Rate ◽  
Imperfect Repair ◽  
Repair Models ◽  
Minimum Costs

Repairable systems are either repaired perfectly to a state of as good as new or imperfectly. In this work, a system which undergoes imperfect repair is investigated. A nonlinear mathematical model is formulated for a system with the objective of finding the optimum failure and repair rate with the minimum costs subject to attaining a pre-specified performance level. Two imperfect repair models are examined. In the first model, the system is replaced by a new one after several failures. In the second model, the system is either replaced with a specific probability (1-p) or is imperfectly repaired after each failure with probability p. The optimal solution is presented in a closed form expression.

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