(a) QUESTION THREE The differential equations for a competing model system is given as dx dt...
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(a) QUESTION THREE The differential equations for a competing model system is given as dx dt dt =r₁x - α₁xy = r₂y - α₂xy Where α₁ and a₂ are two constants. (1) Obtain the solution for x in the absence of the second species i.e. when y = 0 Obtain the non-trivial steady state point of the system (xx,y*) (4 marks) Show that the equilibrium density of one species depends upon the proportional growth and the coefficient of inter-specific coefficient of the other species. (4 marks) Examine the stability of the steady state (x,y4) using the perturbation technique. (5 marks) (ii) (iii) (iv) (a) QUESTION THREE The differential equations for a competing model system is given as dx dt dt =r₁x - α₁xy = r₂y - α₂xy Where α₁ and a₂ are two constants. (1) Obtain the solution for x in the absence of the second species i.e. when y = 0 Obtain the non-trivial steady state point of the system (xx,y*) (4 marks) Show that the equilibrium density of one species depends upon the proportional growth and the coefficient of inter-specific coefficient of the other species. (4 marks) Examine the stability of the steady state (x,y4) using the perturbation technique. (5 marks) (ii) (iii) (iv)
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