Study of two species prey–predator model in imprecise environment with harvesting scenario

Abstract

This study proposes and explores a prey–predator model that presents a functional response to group behavior of prey–predator harvesting. We study a non-linear model of prey–predator growths in two species. The proposed model is supported by theoretical and numerical results. Some numerical descriptions are provided to help our analytical and theoretical conclusions. For all possible parameter values occurring in a prey–predator system, we solved it by using both VIM (variational iteration method) and HPM (homotopy perturbation method). We also used MATLAB coding to compare our approximate analytical expressions with numerical simulations. We have found that there is no significant difference when comparing analytical and numerical results.

Complex dynamics and chaos control in a nonlinear discrete prey–predator model

“…Hereafter, we determine the center manifold W c (0, 0) of ( 19) about (0, 0) in a small neighborhood of s * . Thus, there exists a center manifold [35] W c (0, 0) that can be represented as follows: 2 is a function with order at least three in their variables (X t , s * ). Moreover, the center manifold must satisfy…”

“…Predator-prey interactions are the most well-studied processes in ecological systems, and they are crucial to understanding community dynamics and ecosystems. Interactions in populations with overlapping generations are typically described by differential equations due to the continuous nature of birth and death processes in such populations [1][2][3][4]. Births occur in regular breeding seasons for species with synchronized generations, such as insects and birds.…”

Dynamical behavior of predator–prey model with non-smooth prey harvesting

“…Several forms of harvesting in predator-prey models have been widely studied. Researchers have added the harvest to the prey component [4,10,18] or to the predator [5,8,11,19] or to both species simultaneously [20][21][22]. The most common one of these harvesting forms is a nonzero constant or a linear harvesting rate.…”

“…Many authors have studied the problem of predator-prey interactions under the constant or linear rate of harvesting of either species or both species simultaneously: Xiao and Jennings [10], Xiao et al [11] have studied the dynamics of ratio-dependent predator-prey models with constant harvesting rates. Vijayalakshmi and Senthamarai [22], Xiao and Cao [9], Y. Zhang and Q. Zhang [12], have investigated a predator-prey model with a linear harvesting rate. Models studied with linear or constant harvesting rates exhibit far richer and more complex dynamics compared to the models with no harvesting.…”

Chemical reaction and viscous dissipation effect on MHD oscillatory blood flow in tapered asymmetric channel

“…The analysis made and reviewed about various environments of blood flow analysis by numerous authors, it has been decided to consider the viscous dissipation effect in blood flow analysis, the flow of the fluid is oscillatory and the channel in which the fluid flows is tapered asymmetric. As the governing equations are non-linear, it has been used homotopy perturbation method which is proved to be faster convergence towards the accurate solution [16,17]. Hence its most reliable method for solving problems on nonlinear coupled equations which is widely encountered in fluid dynamics research area to solve it and results discussed.…”