1. In the population model F=-OF+ 3(M)F M = -AM + (M)F, where a > 0,8 0,7 > 0, and F and M are the female and male populations. In both cases the death-rates are a. The birth-rate is governed by the coefficient (M)=1-e-M > 0, so that for large M the birth-rate of females is 8F and that for males is y, the rates being unequal in general. (a) In the case a = 1,8 = 2,7 = In 2, k = 1 show that there are only two equilibrium states at finite values of F and M, at {(0,0). (2. In 2)}. Show that the origin is stable and that the other equilibrium point is a saddle, according to their linear approximations (b) Verify that M = In (2) F is a particular solution, by determining dM/F in this CINE Identify the other two straight lines which are also particular solutions. (c) Sketch the phase diagram and discuss the stability of the populations. Le, identify in which regions of phase space populations undergo collapse, or never-ending growth etc. 1. In the population model F=-OF+ 3(M)F M = -AM + (M)F, where a > 0,8 0,7 > 0, and F and M are the female and male populations. In both cases the death-rates are a. The birth-rate is governed by the coefficient (M)=1-e-M > 0, so that for large M the birth-rate of females is 8F and that for males is y, the rates being unequal in general. (a) In the case a = 1,8 = 2,7 = In 2, k = 1 show that there are only two equilibrium states at finite values of F and M, at {(0,0). (2. In 2)}. Show that the origin is stable and that the other equilibrium point is a saddle, according to their linear approximations (b) Verify that M = In (2) F is a particular solution, by determining dM/F in this CINE Identify the other two straight lines which are also particular solutions. (c) Sketch the phase diagram and discuss the stability of the populations. Le, identify in which regions of phase space populations undergo collapse, or never-ending growth etc