The Numerical Bifurcation Analysis Of Leslie-Gower Predator-Prey Model With Different Types Of Predator Harvesting Strategies - Ahmad, Fazilah (2023)
The predator-prey model is the most common model dealing with the interaction between two species. The dynamics of a predator-prey model has attracted a lot of attention from many ecologists and mathematicians. This study shows theoretical and numerical results on the analysis of the Leslie-Gower predator-prey model with different types of predator harvesting strategies namely linear, constant-yield and nonlinear predator harvesting models. We illustrate the numerical bifurcations analysis of codimension-one and codimension-two to show the stability of the steady-states and the behaviour of the model when the harvesting rate change under different harvesting strategies. We analyse each model to determine the existence of local bifurcations such as saddle-node, transcritical, Hopf, and Bogdanov-Takens bifurcations and compare the different type of bifurcations that occurs for each predator harvesting strategy. This study investigates the dynamics of the Leslie-Gower predator-prey model with different harvesting strategies through numerical analysis that corroborate with the critical harvesting rate determined from the theoretical analysis. This study also discovers the significance of predator harvesting strategies in the optimal management of renewable resources using the Leslie-Gower predator-prey model. The choice of the parameter values is crucial with the small difference in the values may cause the predator species extinct if the harvesting rate is greater than the critical harvesting rate.