QUADRATIC HARVESTING IN A DISCRETE PREY-PREDATOR MODEL WITH SCAVENGER
A.George Maria Selvam
Department of Mathematics, Sacred Heart College, Tirupattur – 635 601, Vellore Dt., Tamil Nadu, S.India , IN
R. Dhineshbabu
Department of Mathematics, Sacred Heart College, Tirupattur – 635 601, Vellore Dt., Tamil Nadu, S.India , IN
Mary Jacintha
Department of Mathematics, Sacred Heart College, Tirupattur – 635 601, Vellore Dt., Tamil Nadu, S.India , IN
Keywords: Discrete Time, Equilibria, Scavenger, Harvesting, Stability, Limit Cycles, Bifurcation Diagrams.
Abstract
The work is related to dynamical nature of a discrete time three species prey-predator-scavenger model in the presence of quadratic harvesting on predator population. We investigate existence and parametric conditions for local stability of positive equilibrium point of this model. Moreover, it is also proved that the system under goes Neimark-Sacker (NS) and Period-Doubling bifurcation (PDB) at certain parametric values for positive equilibrium point with the help of an explicit criterion for NS and PDB. The trajectories and phase plane diagrams are plotted for biologically meaningful sets of parameter values. Also bifurcation diagram are shown for selected range of growth parameter. Finally, a numerical example is provided for justifying the validity of the theoretical analysis and visualizes the model with and without harvesting on predator.
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