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Differential EquationsMediumExistence, Uniqueness & Bifurcations

Existence, Uniqueness & Bifurcations · Medium problem

A logistic population with proportional harvesting obeys y′=2y(1−y50)−Eyy' = 2y\left(1 - \dfrac{y}{50}\right) - Ey, where E≥0E \ge 0 is the fishing effort. At what effort EE does the equilibrium y=0y = 0 change from unstable to stable (a transcritical bifurcation)?