Question

5. Two herds of vicious animals are fighting each other to the death. During the fight, the populations (t) and y(t) of these two species can be modeled by the following system of linear differential equations: dz - 4y dt -I dt a. Which species has the more vicious (or more efficient) fighters? b. Who wins the fight in the sense that some individuals of that species are left while the other is eradicated)? c. How does your answer depend on the initial popul...ions? o (hp pits delet &

Answer 1

Anwea: from have the given data lighting Two hade of miciau animals are Giren Equator. dx 1-uy dy at (0) which species that the mae microur (om de efficients fighter? Now da anuy at So, date of change of population (a rate of declaring) of axit) i utimes the population of 'y'. dt cat, so, date of decreasing of ly population i equal to the coment Population 'Y' speuer à more villay bight (in the same that some individuale of are left while the other ei eradicated ? (b) who wing that special the coefficient hatrin The eigenvalues given by 12 / 20 224=o p = 12

so the critical point (90) i unstable and no specan critical So, the point (0,o) is a saddle paint. as none of them to as 'o' al olin the fight will convage (C) How does your Anwer dopend your Anwer depend on the initial population? - As the critical point (0,0) i always saddle point, no matter what the initial condition i so, the behaviour of the population doan't daard on initial condition, € xx =)