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i need help understanding this please d_:1: (it p dt 0.15:: 0.0002332 0.000531; 0.023; 0.000083;2 0.000233; where :r 2 O and y 3 D, is
i need help understanding this please
d_:1: (it p dt 0.15:: 0.0002332 0.000531; 0.023; 0.000083;2 0.000233; where :r 2 O and y 3 D, is a model for two species (of size a: and y} that either compete for the same resources or cooperate for mutual benet (owering plants and insect pollinators, for instance). (a) In the absence of any interaction terms between the two species (terms depending on both a: and y}, what does the model predict? (b) Decide whether the system as written describes competition or cooperation, and explain why. (c) Algebraically determine the equilibria, and interpret each equilibrium in terms in terms of the population levels of both species. ((1) Complete a phase plane analysis. You should show the rst quadrant of the phase plane, with all the nullclines clearly indicated, all equilibria clearly indicated, direction arrows in each of the regions separated by the nullclines, and direction arrows on each of the nullclines (for example, as shown in Figure 9.2.6 in the pro-class materials). (e) Use the phase plane plotter found at http-s://aeb019.hosted.uark.edu/pplane.html to simulate possible solutions in the phase plane. For the best display, use the following inputs: minimum a: = 0, maximum 2: = 1000, minimum 1; = 0, max- imum y = 400, arrow length = 15, and number of arrows = 50. Then click on 'Graph Phase Plane', and then click your cursor on various initial conditions in the phase plane to see solutions in red. i. What is the outcome for any initial condition that does not have :r(0) = 0 or y(0) = 0? Interpret the outcome in terms of the population levels of both species. ii. Which of the equilibria are stable; which are unstable? iii. Submit a screenshot or picture of your resultStep by Step Solution
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