Systems of Equations 13P A predator prey system where the prey is resource

# Systems of equations 13p a predator prey system where

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Question: 2(Systems of Equations)13P.A predator-prey system where the prey is resource limited can be represented as thefollowing system of ODEs:x0=-kx+bxyy0=my-bxy-cy2wherem, k, bandcare all greater than 0.a). Find the points where this system will be in equilibrium.(2P.)b). Linearise the system at the critical point(mb-ckb2,kb).(3P.)c). Determine the nature of the critical point at(mb-ckb2,kb)(you do not need to dis-tinguish between proper or degenerate nodes).(6P.)Hint: there are 3 possibilities.d). What is the influence of the resource limit term-cy2on the location of the equi-librium points?(1P.)Hint: compare the solution to that whencdecreases to zero, and increases to themaximum possible value(c=mbk).e). What is the influence of the resource limit term-cy2on the trajectory of the systemin thex, yplane?(1P.)Hint: again, consider the trajectory whencdecreases to zero, and increases to themaximum possible value(c=mbk). Begin Your Solution Here Page 5 of 19 - DIFFERENTIAL EQUATIONS AND APPLICATIONS - (MATH2305)
Extra space for previous question ) (c) Find Nature of the critical point at(mb-ckb2,kb Page 6 of 19 - DIFFERENTIAL EQUATIONS AND APPLICATIONS - (MATH2305)
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