Open AccessDynamics of a Discrete-time Predator-Prey Model of Leslie type with Predator Harvesting
Author(s) -
S. Vinoth,
R. Sivasamy,
K. Sathiyanathan
Publication year - 2021
Publication title -
journal of physics. conference series
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.21
H-Index - 85
eISSN - 1742-6596
pISSN - 1742-6588
DOI - 10.1088/1742-6596/1850/1/012120
Subject(s) - phase portrait , mathematics , lyapunov exponent , bifurcation , center manifold , nonlinear system , chaotic , bifurcation diagram , discrete time and continuous time , statistical physics , mathematical analysis , control theory (sociology) , hopf bifurcation , physics , computer science , statistics , control (management) , quantum mechanics , artificial intelligence
In the present work, we attempt to analyze the discrete form of Leslie type predator-prey system with the extension of nonlinear type harvesting of predators. The proposed model is obtained with the help of theory of piecewise constant argument for differential equations. We give the local stability properties of all possible non-negative fixed points. Also, our study reveals that the discrete system admits two bifurcations which are flip and Neimark-Sacker by making the use of center manifold argument and bifurcation theory, where the harvesting parameter is varied in order to take place of such bifurcations. Some simulations are carried out to depicts the obtained analytical results such as bifurcation plots and phase portraits. Also, it can be confirmed from numerical simulations that the considered system exhibits chaotic behavior for smaller values of harvesting parameter and becomes stable for larger values of same parameter. The largest Lyapunov exponents are plotted to show the sensitivity of chaotic regime.