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Discontinuity, Nonlinearity, and Complexity 10(1) (2021) 151--159 | DOI:10.5890/DNC.2021.03.011

Nurul Huda Gazi, Subrata Kumar Biswas

Department of Mathematics and Statistics, Aliah University, IIA/27, Newtown, Kolkata-700160, India

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Abstract

In this paper we modify Holling-Tanner predator-prey model by using type-IV functional response in prey species in lieu of type-II functional response. Harvesting is used in predator as well as prey species. This model is compared with a special type of Kolmogorov model. In the case of quadratic harvesting, the fixed points are computed after nondimensionalization. For the non-existence of periodic orbits in the first quadrant we apply a condition of the general Kolmogorov model to exist a Dulac function. We show that this system does not have periodic orbits with the help of numerical simulation and graphical representation.

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