Nondimensionalise the
system and determine the steady states. Investigate their stability and sketch the
phase plane trajectories. Show that irrespective of the size of the parameters the principle of competitive exclusion holds. Brieﬂy describe under what ecological circumstances the species N2 becomes extinct.

Question

Nondimensionalise the
system and determine the steady states. Investigate their stability and sketch the
phase plane trajectories. Show that irrespective of the size of the parameters the principle of competitive exclusion holds. Brieﬂy describe under what ecological circumstances the species N2 becomes extinct.

anonymous · Answer

$$\frac{ dN _{1} }{dt}=r_1 N_1 (1-\frac{ N_1 }{K_1 }- b_{12} \frac{ N_2 }{ K_1} $$

anonymous · Answer

$$\frac{ dN _{2} }{dt}=r_2 N_2 (1- b_{21} \frac{ N_1 }{ K_2}$$

anonymous · Answer

b and r are constants?

anonymous · Answer

yes.

anonymous · Answer

seen the solution of these equations for case but can't remember sorry

anonymous · Answer

oh. ok thanks anyway.

anonymous · Answer

http://en.wikipedia.org/wiki/Lotka%E2%80%93Volterra_inter-specific_competition_equations