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Discontinuity, Nonlinearity, and Complexity 13(2) (2024) 269--278 | DOI:10.5890/DNC.2024.06.005

Md Golam Mortuja$^1$, Mithilesh Kumar Chaube$^2$, Santosh Kumar$^2$

$^1$ SR University, Warangal, Telangana, 506371, India

$^2$ Dr. Shyama Prasad Mukherjee International Institute of Information Technology Naya Raipur, Raipur, Chhattisgarh, 493661, India

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Abstract

A dynamical predator-prey model with constant prey harvesting, proportional harvesting in predator has been studied. The square root functional response has also been included in the system to characterise the behaviour of the prey herd when the average handling time is zero. The existence and local stability of the system's equilibria have been discussed. It is examined that the system has two sorts of bifurcations. The two forms of bifurcations were studied, and it was explored that the saddle-node bifurcation offers the highest sustainable yield. It has been observed that if the harvesting rate exceeds the maximum sustainable yield, the prey population is eliminated from the system, and the predator population is wiped out. However, if such harvesting rate is below than the sustainable yield, the prey population may be able to sustain. An unstable limit cycle around the interior equilibrium point has been found by investigating the Hopf bifurcation. To verify the results, further numerical simulations are run.

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