A very simple two-compartment model for gap dynamics in a forest assumes that gaps are created...

 

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A very simple two-compartment model for gap dynamics in a forest assumes that gaps are created by disturbances (wind, fire, etc.) and that gaps revert to forest as trees grow in the gaps. We denote by g(t) the area occupied by gaps and by a(t) the area occupied by adult trees. We assume that the dynamics are given by: dg =-0.9g+1.4a dt da = 0.99 -1.4a dt On paper, draw the corresponding compartment diagram. Solve the given system, assuming that g(0) = 6 and a(0) = 24. g(t)=(420/23)-[(282/23)e^(-2.3t)] a(t)=(270/23)+|(282/23)e^(-2.31)] At time t, what fraction of the forest is occupied by adult trees? Fraction occupied by adult trees is (282/23)e^(-2.31)-(397/23) A very simple two-compartment model for gap dynamics in a forest assumes that gaps are created by disturbances (wind, fire, etc.) and that gaps revert to forest as trees grow in the gaps. We denote by g(t) the area occupied by gaps and by a(t) the area occupied by adult trees. We assume that the dynamics are given by: dg =-0.9g+1.4a dt da = 0.99 -1.4a dt On paper, draw the corresponding compartment diagram. Solve the given system, assuming that g(0) = 6 and a(0) = 24. g(t)=(420/23)-[(282/23)e^(-2.3t)] a(t)=(270/23)+|(282/23)e^(-2.31)] At time t, what fraction of the forest is occupied by adult trees? Fraction occupied by adult trees is (282/23)e^(-2.31)-(397/23)