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1. A Single Species Model with Birth Pulse and Impulsive Toxin Input.

Author

Goel, Anju and Gakkhar, Sunita

Subjects
*ENVIRONMENTAL toxicology research, *SPECIES, *DYNAMICAL systems, *STABILITY theory, *COMPUTER simulation, *BIFURCATION theory, *CHAOS theory, GROWTH research
Abstract

This paper deals with the dynamics of a single biological species with birth pulses in a polluted environment with impulsive toxin input. The biological species is subjected to continuous harvesting. The toxin is absorbed in the organism and affects its growth. The discrete dynamical system determined by stroboscopic map is analyzed. The threshold condition for the stability of semi trivial solution as well as non trivial period-one solution is obtained. Finally, by numerical simulation with MATLAB, the dynamical behavior of the model is found to be complex. Above the threshold level there is a characteristic sequence of bifurcations leading to chaotic dynamics. Route to chaos is found to be period doubling. [ABSTRACT FROM AUTHOR]

Published
2016
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2. Analysis on Bifurcation for a Predator-Prey Model with Beddington-DeAngelis Functional Response and Non-Selective Harvesting.

Author

Wang, Rong and Jia, Yunfeng

Subjects
*BIFURCATION theory, *LOTKA-Volterra equations, *FUNCTIONAL analysis, *HARVESTING, *BIOLOGICAL mathematical modeling, *STABILITY theory, *EXISTENCE theorems
Abstract

The biomathematical model is an important tool in exploring the dynamic behavior of different species. In this paper, we deal with a predator-prey model with Beddington-DeAngelis functional response and non-selective harvesting. We discuss the existence and stability of the local bifurcation solution, which emanates from the semi-trivial solution. Moreover, by using the boundedness of positive solutions and the global bifurcation theory, we find that the local bifurcation branch can be extended to the global bifurcation. [ABSTRACT FROM AUTHOR]

Published
2016
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3. Effects of supplying alternative food in a predator–prey model with harvesting.

Author

Sahoo, Banshidhar and Poria, Swarup

Subjects
*FOOD supply, *PREDATION, *HARVESTING, *MATHEMATICAL models, *STABILITY theory
Abstract

Abstract: In this paper, we propose a tritrophic predator–prey model with harvesting where the top-predator population is partially supported with alternative food. We report the consequences of providing alternative food to the top-predator in a top-predator harvested model. The extinction criterion for top-predator population, local stability of equilibrium points and persistence conditions are discussed theoretically. Pontryagins maximum principle is used to characterize the optimal control of harvesting. We have derived the condition of Hopf bifurcation by varying harvesting effort. The bifurcation diagrams of the system with respect to harvesting effort in presence of alternative food are given. Our analysis show that alternative food can prevent top-predator extinction risk at higher harvesting effort and plays a vital role for biological conservation of species. [Copyright &y& Elsevier]

Published
2014
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