Question

A previous exercise modeled populations of aphids and ladybugs with a Lotka-Volterra system. Suppose we modify those equations as follows: · = 3A(1 – 0.00025 A) – 0.04AL dL = -0.9L + 0.0003 AL dt (a). Find the equilibrium solutions. Enter your answer as a list of ordered pairs (A, L), where A is the number of aphids and L the number of ladybugs. For example, if you found three equilibrium solutions, one with 100 aphids and 10 ladybugs, one with 200 aphids and 20 ladybugs, and one with 300 aphids and 30 ladybugs, you would enter (100, 10), (200, 20), (300, 30). Do not round fractional answers to the nearest integer. Answer = (b). Find an expression for dL/dA. dL dĀ =

Answer 1

Answer:- Given that MA = 3A (1-0.00095 A 1-0-04 AL dla -0.94 +0.0003AL dt co) An Equill: burm solution is a solution for which both A and are constant if Ais constant then dA-0 so the first equation become 3A-004AL=0 A (3-0.042)=0 A=0 so if AFO and L is constant then diso NO W the second Equation reduces to 0=-0.92 +0.04AL 0:-0.9L+ 0.04(0) L 0= -0.9L CS Scanned with soko CamScanner

Thus CA,L) = (0,0) is one equilibrium solution on other hand if (= 300 and Ais Constant 0:-0.9 (300) +0.004 A(300) = -270+ 12 A A- 270-22.5) Here CA,L) = (22.5,300) is equalibrium point (0,0) (22.5)(300) de da . dh x da - da ^ dt 1. dL da dalat 3A (1-0.00025 A) -0.04 AL -0.92 +0.0003 AL Scanned with CamScanner