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J. Bifurcation Chaos"],"published-print":{"date-parts":[[2024,5]]},"abstract":"<jats:p> In this paper, we introduce constant-yield prey harvesting into the Holling\u2013Tanner model with generalist predator. We prove that the unique positive equilibrium is a cusp of codimension 4. As the parameter values change, the system exhibits degenerate Bogdanov\u2013Takens bifurcation of codimension 4. Using the resultant elimination method, we show that the positive equilibrium is a weak focus of order 2, and the system undergoes degenerate Hopf bifurcation of codimension 2 and has two limit cycles. By numerical simulations, we demonstrate that the system exhibits homoclinic bifurcation and saddle\u2013node bifurcation of limit cycles as the parameters are varied. 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