• Journal for History of Mathematics
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• v.27 no.3
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• pp.197-210
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• 2014

Species like insects and fishes have, in many cases, non-overlapping time intervals of one generation and their descendant one. So the population dynamics of such species can be formulated as discrete models. In this paper various discrete population models are introduced in chronological order. The author's investigation starts with the Malthusian model suggested in 1798, and continues through Verhulst model(the discrete logistic model), Ricker model, the Beverton-Holt stock-recruitment model, Shep-herd model, Hassell model and Sigmoid type Beverton-Holt model. We discuss the mathematical and practical significance of each model and analyze its properties. Also the stability properties of stationary solutions of the models are studied analytically and illustratively using GSP, a computer software. The visual outputs generated by GSP are compared with the analytical stability results.

• Journal of applied mathematics & informatics
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• v.40 no.5_6
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• pp.1199-1215
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• 2022

This article aims to study the dynamical behaviours of a two species model in which non-selective harvesting of a prey-predator system by using a reasonable catch-rate function instead of usual catch-per-unit-effort hypothesis is used. A system of two ordinary differential equations(ODE's) has been proposed and analyzed with the predator functional response to prey density is considered as Hassell-Varley type functional responses to study the dynamics of the system. Positivity and boundedness of the system are studied. We have discussed the existence of different equilibrium points and stability of the system at these equilibrium points. We also analysed the system undergoes a Hopf-bifurcation around interior equilibrium point for a various parametric values which has very significant ecological impacts in this work. Computer simulation are carried out to validate our analytical findings. The biological implications of analytical and numerical findings are discussed critically.