Degradation and subsequent regeneration of a forestry resource: A mathematical model

Dynamical analysis of a modified Leslie-Gower Holling-type II predator-prey stochastic model in polluted environments with interspecific competition and impulsive toxicant input

In this paper, we use a mean-reverting Ornstein-Uhlenbeck process to simulate the stochastic perturbations in the environment, and then a modified Leslie-Gower Holling-type II predator-prey stochastic model in a polluted environment with interspecific competition and pulse toxicant input is proposed. Through constructing V-function and applying Ito^'s formula, the sharp sufficient conditions including strongly persistent in the mean, persistent in the mean and extinction are established. In addition, the theoretical results are verified by numerical simulation.

A MATHEMATICAL MODEL TO STUDY THE IMPACT OF MINING ACTIVITIES AND POLLUTION ON FOREST RESOURCES AND WILDLIFE POPULATION

In this paper, we develop a nonlinear mathematical model that investigates the impact of mining activities and pollution on forest resources and wildlife population. It is assumed that concentration of pollutants grows in the environment at a constant rate and also augments due to different mining activities prevailing in the forest area. The model is formulated in terms of differential equations and analyzed using elements of stability theory and numerical simulation. The obtained results depict that both forest resources as well as wildlife population get very much affected, either directly or indirectly, due to mining activities and environmental pollution. It is being concluded that, in order to save forests, an ecological balance is required to be maintained among forest resources, forest-dependent wildlife population, mining activities and environmental pollution.

Stability and Bionomic Analysis of Fuzzy Prey-Predator Harvesting Model in Presence of Toxicity: A Dynamic Approach

This paper deals with a prey-predator model in which both the species are infected by some toxicants which are released by some other species or source with fuzzy biological parameters. The application of fuzzy differential equation in the modeling of prey-predator populations with the effect of toxicants is presented. The dynamical behavior and harvesting of the fuzzy exploited system are studied by using the utility function method. Sufficient conditions for the local stability of the positive equilibrium are obtained by analyzing the characteristic equation. Furthermore, the possibility of the existence of bionomic equilibrium is studied under imprecise biological parameters. The study of the presence of toxic substance and harvesting in the modeling system can have significant impact on the existence of both the species, which is in line with reality. Numerical simulation results are presented to validate the theoretical analysis.

A RESOURCE DEPENDENT FISHERY MODEL WITH OPTIMAL HARVESTING POLICY

A dynamic model for a single-species fishery, which depends partially on a logistically growing resource with functional response, is proposed using taxation as control instrument to protect fish population from overexploitation. The analysis of the model shows that both the equilibrium density of fish population as well as the maximum sustainable yield increase as resource biomass density increases. The optimal harvesting policy is also discussed with the help of Pontryagin's Maximum Principle. It is found that for the optimum equilibrium value of resource biomass density, the total user's cost of harvest per unit effort must be equal to the discounted value of future price at the steady state.

A MODEL FOR THE EFFECT OF POLLUTANT ON HUMAN POPULATION DEPENDENT ON A RESOURCE WITH ENVIRONMENTAL AND HEALTH POLICY

In this paper, a nonlinear mathematical model to study the effect of environmental pollution on resource biomass and human populations is proposed and analyzed. In modeling the system, it is considered that there is a limited budget to be spent on environmental cleanup and health policies. An optimal investment policy is also discussed using Pontryagin's Maximum Principle.

Depletion of forestry resource biomass due to industrialization pressure: a ratio-dependent mathematical model

A model for interactions between forestry biomass, wildlife population and industrialization pressure is proposed and analysed. Here, the functional responses are assumed to be ratio-dependent type. The effect of forestry biomass depletion in a forested habitat caused by industrialization pressure on the survival of the forestry biomass dependent wildlife species is studied. The behaviours of the system near all ecological feasible equilibria are analysed.

Models for the effect of toxicant in single-species and predator-prey systems

Models of single-species and predator-prey systems in a polluted closed environment are developed and partially analyzed. Three cases are considered: a single influx of toxicant, a constant influx of toxicant, and a periodic pollution of the environment. In the case of single-species growth we are able to determine some local and global dynamics. In the case of predator-prey systems, we investigate the existence of steady states for a small constant influx of toxicant.