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6 Nov 2019
A proportion p of spatially separated patches is occupied by subpopulations at time t. Each subpopulation has mortality rate m. where m is a positive constant, and each vacant patch is recolonised at a rate 2p. At time t= 0. a proportion 0.2 of the patches (all of which are vacant at that moment) becomes permanently unavailable for colonisation due to human activity The differential equation governing p is dp/dt=2p(0.8-p)-mp. Explain carefully how each term in the differential equation arises Without quoting solutions studied m class, find the equilibria of this differential equation, distinguishing cases as necessary. Determine the stability of the equilibria both analytically (where possible) and graphically. Show transcribed image text
A proportion p of spatially separated patches is occupied by subpopulations at time t. Each subpopulation has mortality rate m. where m is a positive constant, and each vacant patch is recolonised at a rate 2p. At time t= 0. a proportion 0.2 of the patches (all of which are vacant at that moment) becomes permanently unavailable for colonisation due to human activity The differential equation governing p is dp/dt=2p(0.8-p)-mp. Explain carefully how each term in the differential equation arises Without quoting solutions studied m class, find the equilibria of this differential equation, distinguishing cases as necessary. Determine the stability of the equilibria both analytically (where possible) and graphically.
Show transcribed image text