Question

Math 2050 Group Assignment 1: Qualitative Analysis of Differential Equations #!Suppose a population grows according to the logistic equation but is subject to a constant per cap harvest rate of h. If N(t) is the population size at time t, the population can be given by the equation dN Different values of h result in different equilibrium population sizes ifh is large enough, we m extinction. a) Suppose r - 2 and K- 1000. Find all equilibria. What va Determine the values of h that make the nonzero equilibrium in part an locally stable. Assume h# 2 b) c) lues of h will guarantee the nonzero equilibrium stays positive?

Answer 1

Solutton Given, A consant pes Capta haavest ate of h The populatton Canhe gtven by the eqtuortto equiltbrtem ports ae at dN the dN dt I- 下.

The equotem pint are N tand) too。 (2-6) 500 (2 Tb The nonzeso equthostum th peot Co locally stnble Assurneれ+8 Petnt nt is tocaltly stble o cohese

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