Open AccessQualitative Analysis of a Leslie-Gower Predator-Prey System with Nonlinear Harvesting in Predator
Author(s) -
Manoj Kumar Singh,
B. S. Bhadauria,
Brajesh Kumar Singh
Publication year - 2016
Publication title -
international journal of engineering mathematics
Language(s) - English
Resource type - Journals
eISSN - 2356-7007
pISSN - 2314-6109
DOI - 10.1155/2016/2741891
Subject(s) - mathematics , bifurcation , biological applications of bifurcation theory , homoclinic orbit , hopf bifurcation , bogdanov–takens bifurcation , saddle node bifurcation , predator , transcritical bifurcation , nonlinear system , homoclinic bifurcation , stability (learning theory) , control theory (sociology) , predation , ecology , computer science , physics , biology , control (management) , quantum mechanics , machine learning , artificial intelligence
This paper deals with the study of the stability and the bifurcation analysis of a Leslie-Gower predator-prey model with Michaelis-Menten type predator harvesting. It is shown that the proposed model exhibits the bistability for certain parametric conditions. Dulac’s criterion has been adopted to obtain the sufficient conditions for the global stability of the model. Moreover, the model exhibits different kinds of bifurcations (e.g., the saddle-node bifurcation, the subcritical and supercritical Hopf bifurcations, Bogdanov-Takens bifurcation, and the homoclinic bifurcation) whenever the values of parameters of the model vary. The analytical findings and numerical simulations reveal far richer and complex dynamics in comparison to the models with no harvesting and with constant-yield predator harvesting
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