PLEASE HELP:::::: A model for competition among two species is given by Pt+1 = (

Question

PLEASE HELP::::::

A model for competition among two species is given by

Pt+1 = (r1Pt)/ (1 + a1Pt + b1Qt)

Qt+1 = (r2Qt)/ (1 + a2Qt + b2Pt)

where Pt and Qt are the size of the population of two species at time t, respectively. ri is growth rate of each species, ai is a measure of the effects of intraspecific (occurring within a species) competition on growth rate, and bi is a measure of the effects of interspecific (occurring between species) competition on growth rate.

(a) Identify all the steady states of the population.

(b) There are four equilibrium points and three of the equilibria lack one or both species. Determine the conditions under which each of these three equilibria are stable.

(c) If the parameters are estimated as follows: r1 = 1.24,r2 = 1.06,a1 = 0.01,a2 = 0.01,b1 = 0.06,b2 = 0.006. Determine whether any of three equilibria in (b) is stable.

Explanation / Answer

where Pt and Qt are the size of the population of two species at time t, respectively. ri is growth rate of each species, ai is a measure of the effects of intraspecific (occurring within a species) competition on growth rate, and bi is a measure of the effects of interspecific (occurring between species) competition on growth rat

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