In the competition model for two species with populations N1 and N2 N2 b12 K1 dN1 N1 dt K1 dN2 N1 = 12N2 (1 – b21 dt K2 where only one species, N1, has limited carrying capacity. 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 cir- cumstances the species N2 becomes extinct.

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.